WorldWideScience

Sample records for non-riemannian spacetime geometry

  1. Non-Riemannian geometry

    CERN Document Server

    Eisenhart, Luther Pfahler

    2005-01-01

    This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.

  2. Classification of non-Riemannian doubled-yet-gauged spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Morand, Kevin [Universidad Andres Bello, Departamento de Ciencias Fisicas, Santiago de Chile (Chile); Universidad Tecnica Federico Santa Maria, Centro Cientifico-Tecnologico de Valparaiso, Departamento de Fisica, Valparaiso (Chile); Park, Jeong-Hyuck [Sogang University, Department of Physics, Seoul (Korea, Republic of); Institute for Basic Science (IBS), Center for Theoretical Physics of the Universe, Seoul (Korea, Republic of)

    2017-10-15

    Assuming O(D,D) covariant fields as the 'fundamental' variables, double field theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally. Here we present a complete classification of such non-Riemannian spacetimes in terms of two non-negative integers, (n, anti n), 0 ≤ n + anti n ≤ D. Upon these backgrounds, strings become chiral and anti-chiral over n and anti n directions, respectively, while particles and strings are frozen over the n + anti n directions. In particular, we identify (0, 0) as Riemannian manifolds, (1, 0) as non-relativistic spacetime, (1, 1) as Gomis-Ooguri non-relativistic string, (D-1, 0) as ultra-relativistic Carroll geometry, and (D, 0) as Siegel's chiral string. Combined with a covariant Kaluza-Klein ansatz which we further spell, (0, 1) leads to Newton-Cartan gravity. Alternative to the conventional string compactifications on small manifolds, non-Riemannian spacetime such as D = 10, (3, 3) may open a new scheme for the dimensional reduction from ten to four. (orig.)

  3. Transformation optics, isotropic chiral media and non-Riemannian geometry

    International Nuclear Information System (INIS)

    Horsley, S A R

    2011-01-01

    The geometrical interpretation of electromagnetism in transparent media (transformation optics) is extended to include chiral media that are isotropic but inhomogeneous. It was found that such media may be described through introducing the non-Riemannian geometrical property of torsion into the Maxwell equations, and it is shown how such an interpretation may be applied to the design of optical devices.

  4. Local conformal symmetry in non-Riemannian geometry and the origin of physical scales

    Energy Technology Data Exchange (ETDEWEB)

    De Cesare, Marco [King' s College London, Theoretical Particle Physics and Cosmology Group, Department of Physics, London (United Kingdom); Moffat, John W. [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Sakellariadou, Mairi [King' s College London, Theoretical Particle Physics and Cosmology Group, Department of Physics, London (United Kingdom); Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)

    2017-09-15

    We introduce an extension of the Standard Model and General Relativity built upon the principle of local conformal invariance, which represents a generalization of a previous work by Bars, Steinhardt and Turok. This is naturally realized by adopting as a geometric framework a particular class of non-Riemannian geometries, first studied by Weyl. The gravitational sector is enriched by a scalar and a vector field. The latter has a geometric origin and represents the novel feature of our approach. We argue that physical scales could emerge from a theory with no dimensionful parameters, as a result of the spontaneous breakdown of conformal and electroweak symmetries. We study the dynamics of matter fields in this modified gravity theory and show that test particles follow geodesics of the Levi-Civita connection, thus resolving an old criticism raised by Einstein against Weyl's original proposal. (orig.)

  5. Spacetime and Euclidean geometry

    Science.gov (United States)

    Brill, Dieter; Jacobson, Ted

    2006-04-01

    Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.

  6. Spacetime edge geometry

    International Nuclear Information System (INIS)

    Dodson, C.T.J.

    1977-02-01

    This is the second part of a monograph intended to be a mathematically rigorous account of the current position of the bundle-completion of spacetime in general relativity; some new material is included

  7. Electrodynamics and Spacetime Geometry: Foundations

    Science.gov (United States)

    Cabral, Francisco; Lobo, Francisco S. N.

    2017-02-01

    We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.

  8. Probability of stochastic processes and spacetime geometry

    International Nuclear Information System (INIS)

    Canessa, E.

    2007-01-01

    We made a first attempt to associate a probabilistic description of stochastic processes like birth-death processes with spacetime geometry in the Schwarzschild metrics on distance scales from the macro- to the micro-domains. We idealize an ergodic system in which system states communicate through a curved path composed of transition arrows where each arrow corresponds to a positive, analogous birth or death rate. (author)

  9. The causal structure of spacetime is a parameterized Randers geometry

    Energy Technology Data Exchange (ETDEWEB)

    Skakala, Jozef; Visser, Matt, E-mail: jozef.skakala@msor.vuw.ac.nz, E-mail: matt.visser@msor.vuw.ac.nz [School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, PO Box 600, Wellington (New Zealand)

    2011-03-21

    There is a well-established isomorphism between stationary four-dimensional spacetimes and three-dimensional purely spatial Randers geometries-these Randers geometries being a particular case of the more general class of three-dimensional Finsler geometries. We point out that in stably causal spacetimes, by using the (time-dependent) ADM decomposition, this result can be extended to general non-stationary spacetimes-the causal structure (conformal structure) of the full spacetime is completely encoded in a parameterized (t-dependent) class of Randers spaces, which can then be used to define a Fermat principle, and also to reconstruct the null cones and causal structure.

  10. The causal structure of spacetime is a parameterized Randers geometry

    International Nuclear Information System (INIS)

    Skakala, Jozef; Visser, Matt

    2011-01-01

    There is a well-established isomorphism between stationary four-dimensional spacetimes and three-dimensional purely spatial Randers geometries-these Randers geometries being a particular case of the more general class of three-dimensional Finsler geometries. We point out that in stably causal spacetimes, by using the (time-dependent) ADM decomposition, this result can be extended to general non-stationary spacetimes-the causal structure (conformal structure) of the full spacetime is completely encoded in a parameterized (t-dependent) class of Randers spaces, which can then be used to define a Fermat principle, and also to reconstruct the null cones and causal structure.

  11. The Finsler spacetime framework. Backgrounds for physics beyond metric geometry

    Energy Technology Data Exchange (ETDEWEB)

    Pfeifer, Christian

    2013-11-15

    The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the

  12. The Finsler spacetime framework. Backgrounds for physics beyond metric geometry

    International Nuclear Information System (INIS)

    Pfeifer, Christian

    2013-11-01

    The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the

  13. Singularities and the geometry of spacetime

    Science.gov (United States)

    Hawking, Stephen

    2014-11-01

    The aim of this essay is to investigate certain aspects of the geometry of the spacetime manifold in the General Theory of Relativity with particular reference to the occurrence of singularities in cosmological solutions and their relation with other global properties. Section 2 gives a brief outline of Riemannian geometry. In Section 3, the General Theory of Relativity is presented in the form of two postulates and two requirements which are common to it and to the Special Theory of Relativity, and a third requirement, the Einstein field equations, which distinguish it from the Special Theory. There does not seem to be any alternative set of field equations which would not have some undeseriable features. Some exact solutions are described. In Section 4, the physical significance of curvature is investigated using the deviation equation for timelike and null curves. The Riemann tensor is decomposed into the Ricci tensor which represents the gravitational effect at a point of matter at that point and the Welyl tensor which represents the effect at a point of gravitational radiation and matter at other points. The two tensors are related by the Bianchi identities which are presented in a form analogous to the Maxwell equations. Some lemmas are given for the occurrence of conjugate points on timelike and null geodesics and their relation with the variation of timelike and null curves is established. Section 5 is concerned with properties of causal relations between points of spacetime. It is shown that these could be used to determine physically the manifold structure of spacetime if the strong causality assumption held. The concepts of a null horizon and a partial Cauchy surface are introduced and are used to prove a number of lemmas relating to the existence of a timelike curve of maximum length between two sets. In Section 6, the definition of a singularity of spacetime is given in terms of geodesic incompleteness. The various energy assumptions needed to prove

  14. Tensorial spacetime geometries and background-independent quantum field theory

    International Nuclear Information System (INIS)

    Raetzel, Dennis

    2012-01-01

    Famously, Einstein read off the geometry of spacetime from Maxwell's equations. Today, we take this geometry that serious that our fundamental theory of matter, the standard model of particle physics, is based on it. However, it seems that there is a gap in our understanding if it comes to the physics outside of the solar system. Independent surveys show that we need concepts like dark matter and dark energy to make our models fit with the observations. But these concepts do not fit in the standard model of particle physics. To overcome this problem, at least, we have to be open to matter fields with kinematics and dynamics beyond the standard model. But these matter fields might then very well correspond to different spacetime geometries. This is the basis of this thesis: it studies the underlying spacetime geometries and ventures into the quantization of those matter fields independently of any background geometry. In the first part of this thesis, conditions are identified that a general tensorial geometry must fulfill to serve as a viable spacetime structure. Kinematics of massless and massive point particles on such geometries are introduced and the physical implications are investigated. Additionally, field equations for massive matter fields are constructed like for example a modified Dirac equation. In the second part, a background independent formulation of quantum field theory, the general boundary formulation, is reviewed. The general boundary formulation is then applied to the Unruh effect as a testing ground and first attempts are made to quantize massive matter fields on tensorial spacetimes.

  15. On the architecture of spacetime geometry

    International Nuclear Information System (INIS)

    Bianchi, Eugenio; Myers, Robert C

    2014-01-01

    We propose entanglement entropy as a probe of the architecture of spacetime in quantum gravity. We argue that the leading contribution to this entropy satisfies an area law for any sufficiently large region in a smooth spacetime, which, in fact, is given by the Bekenstein–Hawking formula. This conjecture is supported by various lines of evidence from perturbative quantum gravity, simplified models of induced gravity, the AdS/CFT correspondence and loop quantum gravity, as well as Jacobson's ‘thermodynamic’ perspective of gravity. (paper)

  16. Special relativity and space-time geometry.

    Science.gov (United States)

    Molski, M.

    An attempt has been made to formulate the special theory of relativity in a space-time that is explicitly absolute and strictly determines the kinematical characteristics of a particle in uniform translational motion. The approach developed is consistent with Einstein's relativity and permits explanation of the inertia phenomenon.

  17. Space-Time Geometry of Quark and Strange Quark Matter

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    We study quark and strange quark matter in the context of general relativity. For this purpose, we solve Einstein's field equations for quark and strange quark matter in spherical symmetric space-times. We analyze strange quark matter for the different equations of state (EOS) in the spherical symmetric space-times, thus we are able to obtain the space-time geometries of quark and strange quark matter. Also, we discuss die features of the obtained solutions. The obtained solutions are consistent with the results of Brookhaven Laboratory, i.e. the quark-gluon plasma has a vanishing shear (i.e. quark-gluon plasma is perfect).

  18. Statistical geometry and space-time

    International Nuclear Information System (INIS)

    Grauert, H.

    1976-01-01

    In this paper I try to construct a mathematical tool by which the full structure of Lorentz geometry to space time can be given, but beyond that the background - to speak pictorially - the subsoil for electromagnetic and matter waves, too. The tool could be useful to describe the connections between various particles, electromagnetism and gravity and to compute observables which were not theoretically related, up to now. Moreover, the tool is simpler than the Riemann tensor: it consists just of a set S of line segments in space time, briefly speaking. (orig.) [de

  19. Tensorial spacetime geometries carrying predictive, interpretable and quantizable matter dynamics

    International Nuclear Information System (INIS)

    Rivera Hernandez, Sergio

    2012-01-01

    Which tensor fields G on a smooth manifold M can serve as a spacetime structure? In the first part of this thesis, it is found that only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry predictive, interpretable and quantizable matter dynamics. The obvious dependence of this characterization of admissible tensorial spacetime geometries on specific matter is not a weakness, but rather presents an insight: it was Maxwell theory that justified Einstein to promote Lorentzian manifolds to the status of a spacetime geometry. Any matter that does not mimick the structure of Maxwell theory, will force us to choose another geometry on which the matter dynamics of interest are predictive, interpretable and quantizable. These three physical conditions on matter impose three corresponding algebraic conditions on the totally symmetric contravariant coefficient tensor field P that determines the principal symbol of the matter field equations in terms of the geometric tensor G: the tensor field P must be hyperbolic, time-orientable and energy-distinguishing. Remarkably, these physically necessary conditions on the geometry are mathematically already sufficient to realize all kinematical constructions familiar from Lorentzian geometry, for precisely the same structural reasons. This we were able to show employing a subtle interplay of convex analysis, the theory of partial differential equations and real algebraic geometry. In the second part of this thesis, we then explore general properties of any hyperbolic, time-orientable and energy-distinguishing tensorial geometry. Physically most important are the construction of freely falling non-rotating laboratories, the appearance of admissible modified dispersion relations to particular observers, and the identification of a mechanism that explains why massive particles that are faster than some massless particles can radiate off energy until they are slower than all

  20. Tensorial spacetime geometries carrying predictive, interpretable and quantizable matter dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Rivera Hernandez, Sergio

    2012-02-15

    Which tensor fields G on a smooth manifold M can serve as a spacetime structure? In the first part of this thesis, it is found that only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry predictive, interpretable and quantizable matter dynamics. The obvious dependence of this characterization of admissible tensorial spacetime geometries on specific matter is not a weakness, but rather presents an insight: it was Maxwell theory that justified Einstein to promote Lorentzian manifolds to the status of a spacetime geometry. Any matter that does not mimick the structure of Maxwell theory, will force us to choose another geometry on which the matter dynamics of interest are predictive, interpretable and quantizable. These three physical conditions on matter impose three corresponding algebraic conditions on the totally symmetric contravariant coefficient tensor field P that determines the principal symbol of the matter field equations in terms of the geometric tensor G: the tensor field P must be hyperbolic, time-orientable and energy-distinguishing. Remarkably, these physically necessary conditions on the geometry are mathematically already sufficient to realize all kinematical constructions familiar from Lorentzian geometry, for precisely the same structural reasons. This we were able to show employing a subtle interplay of convex analysis, the theory of partial differential equations and real algebraic geometry. In the second part of this thesis, we then explore general properties of any hyperbolic, time-orientable and energy-distinguishing tensorial geometry. Physically most important are the construction of freely falling non-rotating laboratories, the appearance of admissible modified dispersion relations to particular observers, and the identification of a mechanism that explains why massive particles that are faster than some massless particles can radiate off energy until they are slower than all

  1. The algebraic approach to space-time geometry

    International Nuclear Information System (INIS)

    Heller, M.; Multarzynski, P.; Sasin, W.

    1989-01-01

    A differential manifold can be defined in terms of smooth real functions carried by it. By rejecting the postulate, in such a definition, demanding the local diffeomorphism of a manifold to the Euclidean space, one obtains the so-called differential space concept. Every subset of R n turns out to be a differential space. Extensive parts of differential geometry on differential spaces, developed by Sikorski, are reviewed and adapted to relativistic purposes. Differential space as a new model of space-time is proposed. The Lorentz structure and Einstein's field equations on differential spaces are discussed. 20 refs. (author)

  2. Founding Gravitation in 4D Euclidean Space-Time Geometry

    International Nuclear Information System (INIS)

    Winkler, Franz-Guenter

    2010-01-01

    The Euclidean interpretation of special relativity which has been suggested by the author is a formulation of special relativity in ordinary 4D Euclidean space-time geometry. The natural and geometrically intuitive generalization of this view involves variations of the speed of light (depending on location and direction) and a Euclidean principle of general covariance. In this article, a gravitation model by Jan Broekaert, which implements a view of relativity theory in the spirit of Lorentz and Poincare, is reconstructed and shown to fulfill the principles of the Euclidean approach after an appropriate reinterpretation.

  3. Spacetime and Geometry: An Introduction to General Relativity

    International Nuclear Information System (INIS)

    Poisson, E

    2005-01-01

    The ever growing relevance of general relativity to astrophysics and cosmology continues to motivate the publication of new textbooks which put the theory in a fresh perspective informed by recent developments. While the 1970s were the decade of Weinberg and Misner et al and the 80s the decade of Schutz and Wald, this is clearly the decade of Hartle and Carroll. Hartle has introduced a novel pedagogical approach to teaching general relativity, which he convincingly argues should be done in the standard undergraduate physics curriculum. His 'physics-first approach' emphasizes physical phenomena and minimizes mathematical formalism. Hartle achieves a lot by introducing only the spacetime metric and the geodesic equation, which are the main tools needed to explore curved spacetime and extract physical consequences. To be sure, to explain how the metric is obtained in the first place does require a background of differential geometry and the formulation of the Einstein field equations. But in Hartle's book this material is wisely presented at a later stage, after an ample sampling of the physics of curved spacetime has motivated the need for the advanced mathematics. Carroll follows instead the traditional route, what Hartle calls the 'math-first approach', in which one introduces first the required mathematical formalism and only then derives the physical consequences. He is, of course, in good company, as this is the method followed in all existing textbooks (with Hartle's being the sole exception). Carroll's approach may not be original, but it is tried and true, and the result of Carroll's efforts is an excellent introduction to general relativity. The book covers the standard topics that would be found in virtually all textbooks (differential geometry, the field equations, linearized theory, black holes, and cosmology), but in addition it contains topics (such as quantum field theory in curved spacetime) which can rarely be found in introductory texts. All these

  4. Quasilocal energy and surface geometry of Kerr spacetime

    Science.gov (United States)

    Yu, Chengjie; Liu, Jian-Liang

    2017-04-01

    We study the quasilocal energy (QLE) and the surface geometry for Kerr spacetime in the Boyer-Lindquist coordinates without taking the slow rotation approximation. We also consider in the region r ≤2 m , which is inside the ergosphere. For a certain region, r >rk(a ) , the Gaussian curvature of the surface with constant t , r is positive, and for r >√{3 }a the critical value of the QLE is positive. We found that the three curves: the outer horizon r =r+(a ), r =rk(a ) and r =√{3 }a intersect at the point a =√{3 }m /2 , which is the limit for the horizon to be isometrically embedded into R3. The numerical result indicates that the Kerr QLE is monotonically decreasing to the ADM m from the region inside the ergosphere to large r . Based on the second law of black hole dynamics, the QLE is increasing with respect to the irreducible mass Mir. From the results of Chen-Wang-Yau, we conclude that in a certain region, r >rh(a ), the critical value of the Kerr QLE is a global minimum.

  5. Dark energy and dark matter from hidden symmetry of gravity model with a non-Riemannian volume form

    Energy Technology Data Exchange (ETDEWEB)

    Guendelman, Eduardo [Ben-Gurion University of the Negev, Department of Physics, Beersheba (Israel); Nissimov, Emil; Pacheva, Svetlana [Bulgarian Academy of Sciences, Institute for Nuclear Research and Nuclear Energy, Sofia (Bulgaria)

    2015-10-15

    We show that dark energy and dark matter can be described simultaneously by ordinary Einstein gravity interacting with a single scalar field provided the scalar field Lagrangian couples in a symmetric fashion to two different spacetime volume forms (covariant integration measure densities) on the spacetime manifold - one standard Riemannian given by √(-g) (square root of the determinant of the pertinent Riemannian metric) and another non-Riemannian volume form independent of the Riemannian metric, defined in terms of an auxiliary antisymmetric tensor gauge field of maximal rank. Integration of the equations of motion of the latter auxiliary gauge field produce an a priori arbitrary integration constant that plays the role of a dynamically generated cosmological constant or dark energy. Moreover, the above modified scalar field action turns out to possess a hidden Noether symmetry whose associated conserved current describes a pressureless ''dust'' fluid which we can identify with the dark matter completely decoupled from the dark energy. The form of both the dark energy and dark matter that results from the above class of models is insensitive to the specific form of the scalar field Lagrangian. By adding an appropriate perturbation, which breaks the above hidden symmetry and along with this couples dark matter and dark energy, we also suggest a way to obtain growing dark energy in the present universe's epoch without evolution pathologies. (orig.)

  6. Radar orthogonality and radar length in Finsler and metric spacetime geometry

    Science.gov (United States)

    Pfeifer, Christian

    2014-09-01

    The radar experiment connects the geometry of spacetime with an observers measurement of spatial length. We investigate the radar experiment on Finsler spacetimes which leads to a general definition of radar orthogonality and radar length. The directions radar orthogonal to an observer form the spatial equal time surface an observer experiences and the radar length is the physical length the observer associates to spatial objects. We demonstrate these concepts on a forth order polynomial Finsler spacetime geometry which may emerge from area metric or premetric linear electrodynamics or in quantum gravity phenomenology. In an explicit generalization of Minkowski spacetime geometry we derive the deviation from the Euclidean spatial length measure in an observers rest frame explicitly.

  7. Spinor Field Nonlinearity and Space-Time Geometry

    Science.gov (United States)

    Saha, Bijan

    2018-03-01

    Within the scope of Bianchi type VI,VI0,V, III, I, LRSBI and FRW cosmological models we have studied the role of nonlinear spinor field on the evolution of the Universe and the spinor field itself. It was found that due to the presence of non-trivial non-diagonal components of the energy-momentum tensor of the spinor field in the anisotropic space-time, there occur some severe restrictions both on the metric functions and on the components of the spinor field. In this report we have considered a polynomial nonlinearity which is a function of invariants constructed from the bilinear spinor forms. It is found that in case of a Bianchi type-VI space-time, depending of the sign of self-coupling constants, the model allows either late time acceleration or oscillatory mode of evolution. In case of a Bianchi VI 0 type space-time due to the specific behavior of the spinor field we have two different scenarios. In one case the invariants constructed from bilinear spinor forms become trivial, thus giving rise to a massless and linear spinor field Lagrangian. This case is equivalent to the vacuum solution of the Bianchi VI 0 type space-time. The second case allows non-vanishing massive and nonlinear terms and depending on the sign of coupling constants gives rise to accelerating mode of expansion or the one that after obtaining some maximum value contracts and ends in big crunch, consequently generating space-time singularity. In case of a Bianchi type-V model there occur two possibilities. In one case we found that the metric functions are similar to each other. In this case the Universe expands with acceleration if the self-coupling constant is taken to be a positive one, whereas a negative coupling constant gives rise to a cyclic or periodic solution. In the second case the spinor mass and the spinor field nonlinearity vanish and the Universe expands linearly in time. In case of a Bianchi type-III model the space-time remains locally rotationally symmetric all the time

  8. Fiber bundle geometry and space-time structure

    International Nuclear Information System (INIS)

    Nascimento, J.C.

    1977-01-01

    Within the framework of the geometric formulation of Gauge theories in fiber bundles, the general relation between the bundle connection (Gauge field) and the geometry of the base space is obtained. A possible Gauge theory for gravitation is presented [pt

  9. The projective geometry of the spacetime yielded by relativistic positioning systems and relativistic location systems

    OpenAIRE

    Rubin , Jacques ,

    2014-01-01

    Version de travail de thèse d'habilitation à diriger des recherches; Preprint; Current positioning systems are not primary, relativistic systems. Nevertheless, genuine, relativistic and primary positioning systems have been proposed recently by Bahder, Coll et al. and Rovelli to remedy such prior defects. These new designs all have in common an equivariant conformal geometry featuring, as the most basic ingredient, the spacetime geometry. We show how this conformal aspect can be the four-dime...

  10. Hyper-fast interstellar travel via a modification of spacetime geometry

    Energy Technology Data Exchange (ETDEWEB)

    Kheyfets, A. [Department of Mathematics, North Carolina State University, Raleigh, NC (United States); Miller, W.A. [Los Alamos National Lab., NM (United States)

    1997-08-01

    We analyze difficulties with proposals for hyper-fast interstellar travel via modifying the spacetime geometry, using as illustrations the Alcubierre warp drive and the Krasnikov tube. As it is easy to see, no violations of local causality or any other known physical principles are involved as far as motion of spacecrafts is concerned. However, the generation and support of the appropriate spacetime geometry configurations does create problems, the most significant of which are a violation of the weak energy condition, a violation of local causality, and a violation of the global causality protection. The violation of the chronology protection is the most serious of them as it opens a possibility of time travel. We trace the origin of the difficulties to the classical nature of the gravity field. This strongly indicates that hyper-fast interstellar travel should be transferred to the realm of a fully quantized gravitational theory. We outline an approach to further the research in this direction.

  11. Physics in a general length space-time geometry: Call for experimental revision of the light speed anisotropy

    OpenAIRE

    Exirifard, Qasem

    2013-01-01

    We present a phenomenological model for the nature in the Finsler and Randers space-time geometries. We show that the parity-odd light speed anisotropy perpendicular to the gravitational equipotential surfaces encodes the deviation from the Riemann geometry toward the Randers geometry. We utilize an asymmetrical ring resonator and propose a setup in order to directly measure this deviation. We address the constraints that the current technology will impose on the deviation should the anisotro...

  12. Local differential geometry of null curves in conformally flat space-time

    International Nuclear Information System (INIS)

    Urbantke, H.

    1989-01-01

    The conformally invariant differential geometry of null curves in conformally flat space-times is given, using the six-vector formalism which has generalizations to higher dimensions. This is then paralleled by a twistor description, with a twofold merit: firstly, sometimes the description is easier in twistor terms, sometimes in six-vector terms, which leads to a mutual enlightenment of both; and secondly, the case of null curves in timelike pseudospheres or 2+1 Minkowski space we were only able to treat twistorially, making use of an invariant differential found by Fubini and Cech. The result is the expected one: apart from stated exceptional cases there is a conformally invariant parameter and two conformally invariant curvatures which, when specified in terms of this parameter, serve to characterize the curve up to conformal transformations. 12 refs. (Author)

  13. Digital atom interferometer with single particle control on a discretized space-time geometry.

    Science.gov (United States)

    Steffen, Andreas; Alberti, Andrea; Alt, Wolfgang; Belmechri, Noomen; Hild, Sebastian; Karski, Michał; Widera, Artur; Meschede, Dieter

    2012-06-19

    Engineering quantum particle systems, such as quantum simulators and quantum cellular automata, relies on full coherent control of quantum paths at the single particle level. Here we present an atom interferometer operating with single trapped atoms, where single particle wave packets are controlled through spin-dependent potentials. The interferometer is constructed from a sequence of discrete operations based on a set of elementary building blocks, which permit composing arbitrary interferometer geometries in a digital manner. We use this modularity to devise a space-time analogue of the well-known spin echo technique, yielding insight into decoherence mechanisms. We also demonstrate mesoscopic delocalization of single atoms with a separation-to-localization ratio exceeding 500; this result suggests their utilization beyond quantum logic applications as nano-resolution quantum probes in precision measurements, being able to measure potential gradients with precision 5 x 10(-4) in units of gravitational acceleration g.

  14. Riemann-Christoffel Tensor in Differential Geometry of Fractional Order Application to Fractal Space-Time

    Science.gov (United States)

    Jumarie, Guy

    2013-04-01

    By using fractional differences, one recently proposed an alternative to the formulation of fractional differential calculus, of which the main characteristics is a new fractional Taylor series and its companion Rolle's formula which apply to non-differentiable functions. The key is that now we have at hand a differential increment of fractional order which can be manipulated exactly like in the standard Leibniz differential calculus. Briefly the fractional derivative is the quotient of fractional increments. It has been proposed that this calculus can be used to construct a differential geometry on manifold of fractional order. The present paper, on the one hand, refines the framework, and on the other hand, contributes some new results related to arc length of fractional curves, area on fractional differentiable manifold, covariant fractal derivative, Riemann-Christoffel tensor of fractional order, fractional differential equations of fractional geodesic, strip modeling of fractal space time and its relation with Lorentz transformation. The relation with Nottale's fractal space-time theory then appears in quite a natural way.

  15. A quantum field theory of simplicial geometry and the emergence of spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Oriti, Daniele [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Minnaert Building, Leuvenlaan 4, Utrecht (Netherlands)

    2007-05-15

    We present the case for a fundamentally discrete quantum spacetime and for Group Field Theories as a candidate consistent description of it, briefly reviewing the key properties of the GFT formalism. We then argue that the outstanding problem of the emergence of a continuum spacetime and of General Relativity from fundamentally discrete quantum structures should be tackled from a condensed matter perspective and using purely QFT methods, adapted to the GFT context. We outline the picture of continuum spacetime as a condensed phase of a GFT and a research programme aimed at realizing this picture in concrete terms.

  16. Spherical spacelike geometries in static spherically symmetric spacetimes: Generalized Painlevè–Gullstrand coordinates, foliation, and embedding

    Energy Technology Data Exchange (ETDEWEB)

    Akbar, M.M., E-mail: akbar@utdallas.edu

    2017-06-10

    It is well known that static spherically symmetric spacetimes can admit foliations by flat spacelike hypersurfaces, which are best described in terms of the Painlevè–Gullstrand coordinates. The uniqueness and existence of such foliations were addressed earlier. In this paper, we prove, purely geometrically, that any possible foliation of a static spherically symmetric spacetime by an arbitrary codimension-one spherical spacelike geometry, up to time translation and rotation, is unique, and we find the algebraic condition under which it exists. This leads us to what can be considered as the most natural generalization of the Painlevè–Gullstrand coordinate system for static spherically symmetric metrics, which, in turn, makes it easy to derive generic conclusions on foliation and to study specific cases as well as to easily reproduce previously obtained generalizations as special cases. In particular, we note that the existence of foliation by flat hypersurfaces guarantees the existence of foliation by hypersurfaces whose Ricci curvature tensor is everywhere non-positive (constant negative curvature is a special case). The study of uniqueness and the existence concurrently solves the question of embeddability of a spherical spacelike geometry in one-dimensional higher static spherically symmetric spacetimes, and this produces known and new results geometrically, without having to go through the momentum and Hamiltonian constraints.

  17. The Expanding Universe and the Large-Scale Geometry of Spacetime.

    Science.gov (United States)

    Shu, Frank

    1983-01-01

    Presents a condensed version of textbook account of cosmological theory and principles. Topics discussed include quasars, general and special relativity, relativistic cosmology, and the curvature of spacetime. Some philosophical assumptions necessary to the theory are also discussed. (JM)

  18. Quantum field theory in curved graphene spacetimes, Lobachevsky geometry, Weyl symmetry, Hawking effect, and all that

    Science.gov (United States)

    Iorio, Alfredo; Lambiase, Gaetano

    2014-07-01

    The solutions of many issues, of the ongoing efforts to make deformed graphene a tabletop quantum field theory in curved spacetimes, are presented. A detailed explanation of the special features of curved spacetimes, originating from embedding portions of the Lobachevsky plane into R3, is given, and the special role of coordinates for the physical realizations in graphene is explicitly shown, in general, and for various examples. The Rindler spacetime is reobtained, with new important differences with respect to earlier results. The de Sitter spacetime naturally emerges, for the first time, paving the way to future applications in cosmology. The role of the Bañados, Teitelboim, and Zanelli (BTZ) black hole is also briefly addressed. The singular boundary of the pseudospheres, "Hilbert horizon," is seen to be closely related to the event horizon of the Rindler, de Sitter, and BTZ kind. This gives new, and stronger, arguments for the Hawking phenomenon to take place. An important geometric parameter, c, overlooked in earlier work, takes here its place for physical applications, and it is shown to be related to graphene's lattice spacing, ℓ. It is shown that all surfaces of constant negative curvature, K =-r-2, are unified, in the limit c/r→0, where they are locally applicable to the Beltrami pseudosphere. This, and c=ℓ, allow us (a) to have a phenomenological control on the reaching of the horizon; (b) to use spacetimes different from the Rindler spacetime for the Hawking phenomenon; and (c) to approach the generic surface of the family. An improved expression for the thermal LDOS is obtained. A nonthermal term for the total LDOS is found. It takes into account (i) the peculiarities of the graphene-based Rindler spacetime; (ii) the finiteness of a laboratory surface; and (iii) the optimal use of the Minkowski quantum vacuum, through the choice of this Minkowski-static boundary.

  19. Space-time philosophy reconstructed via massive Nordström scalar gravities? Laws vs. geometry, conventionality, and underdetermination

    Science.gov (United States)

    Pitts, J. Brian

    2016-02-01

    What if gravity satisfied the Klein-Gordon equation? Both particle physics from the 1920-30s and the 1890s Neumann-Seeliger modification of Newtonian gravity with exponential decay suggest considering a "graviton mass term" for gravity, which is algebraic in the potential. Unlike Nordström's "massless" theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman-Cunningham conformal group. It therefore exhibits the whole of Minkowski space-time structure, albeit only indirectly concerning volumes. Massive scalar gravity is plausible in terms of relativistic field theory, while violating most interesting versions of Einstein's principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide to understanding massive scalar gravity(s): matter sees a conformally flat metric due to universal coupling, but gravity also sees the rest of the flat metric (barely or on long distances) in the mass term. What is the 'true' geometry, one might wonder, in line with Poincaré's modal conventionality argument? Infinitely many theories exhibit this bimetric 'geometry,' all with the total stress-energy's trace as source; thus geometry does not explain the field equations. The irrelevance of the Ehlers-Pirani-Schild construction to a critique of conventionalism becomes evident when multi-geometry theories are contemplated. Much as Seeliger envisaged, the smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities-indeed an unconceived alternative. At least one version easily could have been developed before General Relativity; it then would have motivated thinking of Einstein's equations along the lines of Einstein's newly re-appreciated "physical strategy" and particle physics and would have suggested a rivalry from massive spin 2 variants of General Relativity (massless spin 2, Pauli and Fierz

  20. Fluctuating geometries, q-observables, and infrared growth in inflationary spacetimes

    DEFF Research Database (Denmark)

    B. Giddings, Steven; Sloth, Martin Snoager

    2012-01-01

    and in standard slow-roll inflation. These become large, signaling breakdown of a perturbative description of the geometry via such observables, and consistent with perturbative instability of de Sitter space. In particular, we show that the geodesic distance on constant time slices during inflation becomes non......-perturbative a few e-folds after a given scale has left the horizon, by distances \\sim 1/H^3 \\sim RS, obstructing use of such geodesics in constructing IR-safe observables based on the spatial geometry. We briefly discuss other possible measures of such geometrical fluctuations....

  1. More on the rainbow chain: entanglement, space-time geometry and thermal states

    International Nuclear Information System (INIS)

    Rodríguez-Laguna, Javier; Dubail, Jérôme; Ramírez, Giovanni; Calabrese, Pasquale; Sierra, Germán

    2017-01-01

    The rainbow chain is an inhomogenous exactly solvable local spin model that, in its ground state, displays a half-chain entanglement entropy growing linearly with the system size. Although many exact results about the rainbow chain are known, the structure of the underlying quantum field theory has not yet been unraveled. Here we show that the universal scaling features of this model are captured by a massless Dirac fermion in a curved space-time with constant negative curvature R   =  − h "2 ( h is the amplitude of the inhomogeneity). This identification allows us to use recently developed techniques to study inhomogeneous conformal systems and to analytically characterise the entanglement entropies of more general bipartitions. These results are carefully tested against exact numerical calculations. Finally, we study the entanglement entropies of the rainbow chain in thermal states, and find that there is a non-trivial interplay between the rainbow effective temperature T_R and the physical temperature T . (paper)

  2. Analysis of aeroplane boarding via spacetime geometry and random matrix theory

    International Nuclear Information System (INIS)

    Bachmat, E; Berend, D; Sapir, L; Skiena, S; Stolyarov, N

    2006-01-01

    We show that aeroplane boarding can be asymptotically modelled by two-dimensional Lorentzian geometry. Boarding time is given by the maximal proper time among curves in the model. Discrepancies between the model and simulation results are closely related to random matrix theory. The models can be used to explain why some commonly practiced airline boarding policies are ineffective and even detrimental. (letter to the editor)

  3. Spacetime information

    International Nuclear Information System (INIS)

    Hartle, J.B.

    1995-01-01

    In usual quantum theory, the information available about a quantum system is defined in terms of the density matrix describing it on a spacelike surface. This definition must be generalized for extensions of quantum theory which neither require, nor always permit, a notion of state on a spacelike surface. In particular, it must be generalized for the generalized quantum theories appropriate when spacetime geometry fluctuates quantum mechanically or when geometry is fixed but not foliable by spacelike surfaces. This paper introduces a four-dimensional notion of the information available about a quantum system's boundary conditions in the various sets of decohering, coarse-grained histories it may display. This spacetime notion of information coincides with the familiar one when quantum theory is formulable in terms of states on spacelike surfaces but generalizes this notion when it cannot be so formulated. The idea of spacetime information is applied in several contexts: When spacetime geometry is fixed the information available through alternatives restricted to a fixed spacetime region is defined. The information available through histories of alternatives of general operators is compared to that obtained from the more limited coarse grainings of sum-over-histories quantum mechanics that refer only to coordinates. The definition of information is considered in generalized quantum theories. We consider as specific examples time-neutral quantum mechanics with initial and final conditions, quantum theories with nonunitary evolution, and the generalized quantum frameworks appropriate for quantum spacetime. In such theories complete information about a quantum system is not necessarily available on any spacelike surface but must be searched for throughout spacetime. The information loss commonly associated with the ''evolution of pure states into mixed states'' in black hole evaporation is thus not in conflict with the principles of generalized quantum mechanics

  4. Spacetime equals entanglement

    Energy Technology Data Exchange (ETDEWEB)

    Nomura, Yasunori [Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, Kashiwa 277-8583 (Japan); Salzetta, Nico, E-mail: nsalzetta@berkeley.edu [Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Sanches, Fabio; Weinberg, Sean J. [Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States)

    2016-12-10

    We study the Hilbert space structure of classical spacetimes under the assumption that entanglement in holographic theories determines semiclassical geometry. We show that this simple assumption has profound implications; for example, a superposition of classical spacetimes may lead to another classical spacetime. Despite its unconventional nature, this picture admits the standard interpretation of superpositions of well-defined semiclassical spacetimes in the limit that the number of holographic degrees of freedom becomes large. We illustrate these ideas using a model for the holographic theory of cosmological spacetimes.

  5. Geometry of the Universe

    International Nuclear Information System (INIS)

    Gurevich, L.Eh.; Gliner, Eh.B.

    1978-01-01

    Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding

  6. Geometries

    CERN Document Server

    Sossinsky, A B

    2012-01-01

    The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...

  7. Geometry

    Indian Academy of Sciences (India)

    . In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...

  8. Geometry

    CERN Document Server

    Prasolov, V V

    2015-01-01

    This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.

  9. Clustering in Hilbert simplex geometry

    KAUST Repository

    Nielsen, Frank

    2017-04-03

    Clustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differential-geometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the information-geometric structure induced by a smooth dissimilarity measure, called a divergence. In this paper, we introduce a novel computationally-friendly non-Riemannian framework for modeling the probability simplex: Hilbert simplex geometry. We discuss the pros and cons of those three statistical modelings, and compare them experimentally for clustering tasks.

  10. Geometry

    CERN Document Server

    Pedoe, Dan

    1988-01-01

    ""A lucid and masterly survey."" - Mathematics Gazette Professor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to he

  11. Phase transition and thermodynamical geometry for Schwarzschild AdS black hole in AdS_5×S"5 spacetime

    International Nuclear Information System (INIS)

    Zhang, Jia-Lin; Cai, Rong-Gen; Yu, Hongwei

    2015-01-01

    We study the thermodynamics and thermodynamic geometry of a five-dimensional Schwarzschild AdS black hole in AdS_5×S"5 spacetime by treating the cosmological constant as the number of colors in the boundary gauge theory and its conjugate quantity as the associated chemical potential. It is found that the chemical potential is always negative in the stable branch of black hole thermodynamics and it has a chance to be positive, but appears in the unstable branch. We calculate the scalar curvatures of the thermodynamical Weinhold metric, Ruppeiner metric and Quevedo metric, respectively and we find that the scalar curvature in the Weinhold metric is always vanishing, while in the Ruppeiner metric the divergence of the scalar curvature is related to the divergence of the heat capacity with fixed chemical potential, and in the Quevedo metric the divergence of the scalar curvature is related to the divergence of the heat capacity with fixed number of colors and to the vanishing of the heat capacity with fixed chemical potential.

  12. Bosonization in a two-dimensional Riemann Cartan geometry

    International Nuclear Information System (INIS)

    Denardo, G.; Spallucci, E.

    1987-01-01

    We study the vacuum functional for a Dirac field in a two dimensional Riemann-Cartan geometry. Torsion is treated as a quantum variable while the metric is considered as a classical background field. Decoupling spinors from the non-Riemannian part of the geometry introduces a chiral Jacobian into the vacuum generating functional. We compute this functional Jacobian determinant by means of the Alvarez method. Finally, we show that the effective action for the background geometry is of the Liouville type and does not preserve any memory of the initial torsion field. (author)

  13. Spacetime from unentanglement

    Science.gov (United States)

    Nomura, Yasunori; Rath, Pratik; Salzetta, Nico

    2018-05-01

    The past decade has seen a tremendous effort toward unraveling the relationship between entanglement and emergent spacetime. These investigations have revealed that entanglement between holographic degrees of freedom is crucial for the existence of bulk spacetime. We examine this connection from the other end of the entanglement spectrum and clarify the assertion that maximally entangled states have no reconstructable spacetime. To do so, we first define the conditions for bulk reconstructability. Under these terms, we scrutinize two cases of maximally entangled holographic states. One is the familiar example of AdS black holes; these are dual to thermal states of the boundary conformal field theory. Sending the temperature to the cutoff scale makes the state maximally entangled and the respective black hole consumes the spacetime. We then examine the de Sitter limit of Friedmann-Robertson-Walker (FRW) spacetimes. This limit is maximally entangled if one formulates the boundary theory on the holographic screen. Paralleling the anti-de Sitter (AdS) black hole, we find the resulting reconstructable region of spacetime vanishes. Motivated by these results, we prove a theorem showing that maximally entangled states have no reconstructable spacetime. Evidently, the emergence of spacetime is endemic to intermediate entanglement. By studying the manner in which intermediate entanglement is achieved, we uncover important properties about the boundary theory of FRW spacetimes. With this clarified understanding, our final discussion elucidates the natural way in which holographic Hilbert spaces may house states dual to different geometries. This paper provides a coherent picture clarifying the link between spacetime and entanglement and develops many promising avenues of further work.

  14. Matter fields in curved space-time

    International Nuclear Information System (INIS)

    Viet, Nguyen Ai; Wali, Kameshwar C.

    2000-01-01

    We study the geometry of a two-sheeted space-time within the framework of non-commutative geometry. As a prelude to the Standard Model in curved space-time, we present a model of a left- and a right- chiral field living on the two sheeted-space time and construct the action functionals that describe their interactions

  15. Metric Relativity and the Dynamical Bridge: highlights of Riemannian geometry in physics

    Energy Technology Data Exchange (ETDEWEB)

    Novello, Mario [Centro Brasileiro de Pesquisas Fisicas (ICRA/CBPF), Rio de Janeiro, RJ (Brazil). Instituto de Cosmologia Relatividade e Astrofisica; Bittencourt, Eduardo, E-mail: eduardo.bittencourt@icranet.org [Physics Department, La Sapienza University of Rome (Italy)

    2015-12-15

    which states the dynamic equivalence of nonlinear theories (driven by arbitrary scalar, spinor or vector fields) that occur in Minkowski background to theories described in associated curved geometries generated by each one of these fields. We shall see that it is possible to map the dynamical properties of a theory, say Maxwell electrodynamics in Minkowski space-time, into Born-Infeld electrodynamics described in a curved space-time the metric of which is defined in terms of the electromagnetic field itself in such way that it yields the same dynamics. It is clear that when considered in whatever unique geometrical structure, these two theories are not the same; they do not describe the same phenomenon. However, we shall see that by a convenient modification of the metric of space-time, an equivalence appears that establishes a bridge between these two theories making they represent the same phenomenon. This method was recently used to achieve a successful geometric scalar theory of gravity. At the end, we briefly review the proposal of geometrization of quantum mechanics in the de Broglie-Bohm formulation using an enlarged non-Riemannian (Weyl) structure. (author)

  16. Quantum spacetime

    International Nuclear Information System (INIS)

    Doplicher, S.

    1996-01-01

    We review some recent result and work in progress on the quantum structure of spacetime at scales comparable with the Planck length; the models discussed here are operationally motivated by the limitations in the accuracy of localization of events in spacetime imposed by the interplay between quantum mechanics and classical general relativity. (orig.)

  17. Charged fluid distribution in higher dimensional spheroidal space-time

    Indian Academy of Sciences (India)

    A general solution of Einstein field equations corresponding to a charged fluid distribution on the background of higher dimensional spheroidal space-time is obtained. The solution generates several known solutions for superdense star having spheroidal space-time geometry.

  18. Spatial infinity in higher dimensional spacetimes

    International Nuclear Information System (INIS)

    Shiromizu, Tetsuya; Tomizawa, Shinya

    2004-01-01

    Motivated by recent studies on the uniqueness or nonuniqueness of higher dimensional black hole spacetime, we investigate the asymptotic structure of spatial infinity in n-dimensional spacetimes (n≥4). It turns out that the geometry of spatial infinity does not have maximal symmetry due to the nontrivial Weyl tensor (n-1) C abcd in general. We also address static spacetime and its multipole moments P a 1 a 2 ···a s . Contrasting with four dimensions, we stress that the local structure of spacetimes cannot be unique under fixed multipole moments in static vacuum spacetimes. For example, we consider the generalized Schwarzschild spacetimes which are deformed black hole spacetimes with the same multipole moments as spherical Schwarzschild black holes. To specify the local structure of the static vacuum solution we need some additional information, at least the Weyl tensor (n-2) C abcd at spatial infinity

  19. Gravitation and spacetime

    CERN Document Server

    Ohanian, Hans C

    2013-01-01

    The third edition of this classic textbook is a quantitative introduction for advanced undergraduates and graduate students. It gently guides students from Newton's gravitational theory to special relativity, and then to the relativistic theory of gravitation. General relativity is approached from several perspectives: as a theory constructed by analogy with Maxwell's electrodynamics, as a relativistic generalization of Newton's theory, and as a theory of curved spacetime. The authors provide a concise overview of the important concepts and formulas, coupled with the experimental results underpinning the latest research in the field. Numerous exercises in Newtonian gravitational theory and Maxwell's equations help students master essential concepts for advanced work in general relativity, while detailed spacetime diagrams encourage them to think in terms of four-dimensional geometry. Featuring comprehensive reviews of recent experimental and observational data, the text concludes with chapters on cosmology an...

  20. Semiclassical expanding discrete space-times

    International Nuclear Information System (INIS)

    Cobb, W.K.; Smalley, L.L.

    1981-01-01

    Given the close ties between general relativity and geometry one might reasonably expect that quantum effects associated with gravitation might also be tied to the geometry of space-time, namely, to some sort of discreteness in space-time itself. In particular it is supposed that space-time consists of a discrete lattice of points rather than the usual continuum. Since astronomical evidence seems to suggest that the universe is expanding, the lattice must also expand. Some of the implications of such a model are that the proton should presently be stable, and the universe should be closed although the mechanism for closure is quantum mechanical. (author)

  1. Geometry of multihadron production

    Energy Technology Data Exchange (ETDEWEB)

    Bjorken, J.D.

    1994-10-01

    This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.

  2. Geometry of multihadron production

    International Nuclear Information System (INIS)

    Bjorken, J.D.

    1994-10-01

    This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions

  3. Spacetimes foliated by Killing horizons

    International Nuclear Information System (INIS)

    Pawlowski, Tomasz; Lewandowski, Jerzy; Jezierski, Jacek

    2004-01-01

    It seems to be expected that a horizon of a quasi-local type, such as a Killing or an isolated horizon, by analogy with a globally defined event horizon, should be unique in some open neighbourhood in the spacetime, provided the vacuum Einstein or the Einstein-Maxwell equations are satisfied. The aim of our paper is to verify whether that intuition is correct. If one can extend a so-called Kundt metric, in such a way that its null, shear-free surfaces have spherical spacetime sections, the resulting spacetime is foliated by so-called non-expanding horizons. The obstacle is Kundt's constraint induced at the surfaces by the Einstein or the Einstein-Maxwell equations, and the requirement that a solution be globally defined on the sphere. We derived a transformation (reflection) that creates a solution to Kundt's constraint out of data defining an extremal isolated horizon. Using that transformation, we derived a class of exact solutions to the Einstein or Einstein-Maxwell equations of very special properties. Each spacetime we construct is foliated by a family of the Killing horizons. Moreover, it admits another, transversal Killing horizon. The intrinsic and extrinsic geometries of the transversal Killing horizon coincide with the one defined on the event horizon of the extremal Kerr-Newman solution. However, the Killing horizon in our example admits yet another Killing vector tangent to and null at it. The geometries of the leaves are given by the reflection

  4. Perturbations of higher-dimensional spacetimes

    Energy Technology Data Exchange (ETDEWEB)

    Durkee, Mark; Reall, Harvey S, E-mail: M.N.Durkee@damtp.cam.ac.uk, E-mail: H.S.Reall@damtp.cam.ac.uk [DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom)

    2011-02-07

    We discuss linearized gravitational perturbations of higher-dimensional spacetimes. For algebraically special spacetimes (e.g. Myers-Perry black holes), we show that there exist local gauge invariant quantities linear in the metric perturbation. These are the higher-dimensional generalizations of the 4D Newman-Penrose scalars that (in an algebraically special vacuum spacetime) satisfy decoupled equations of motion. We show that decoupling occurs in more than four dimensions if, and only if, the spacetime admits a null geodesic congruence with vanishing expansion, rotation and shear. Decoupling of electromagnetic perturbations occurs under the same conditions. Although these conditions are not satisfied in black hole spacetimes, they are satisfied in the near-horizon geometry of an extreme black hole.

  5. Realization of Robertson-Walker spacetimes as affine hypersurfaces

    International Nuclear Information System (INIS)

    Chen Bangyen

    2007-01-01

    Due to the growing interest in embeddings of spacetimes in higher dimensional spaces, we consider a special type of embedding. We prove that Robertson-Walker spacetimes can be embedded as centroaffine hypersurfaces and graph hypersurfaces in some affine spaces in such a way that the induced relative metrics are exactly the Lorentzian metrics on the Robertson-Walker spacetimes. Such realizations allow us to view Robertson-Walker spacetimes and their submanifolds as affine submanifolds in a natural way. Consequently, our realizations make it possible to apply the tools of affine differential geometry to study Robertson-Walker spacetimes and their submanifolds

  6. The Historical Origins of Spacetime

    Science.gov (United States)

    Walter, Scott

    The idea of spacetime investigated in this chapter, with a view toward understanding its immediate sources and development, is the one formulated and proposed by Hermann Minkowski in 1908. Until recently, the principle source used to form historical narratives of Minkowski's discovery of spacetime has been Minkowski's own discovery account, outlined in the lecture he delivered in Cologne, entitled Space and time [1]. Minkowski's lecture is usually considered as a bona fide first-person narrative of lived events. According to this received view, spacetime was a natural outgrowth of Felix Klein's successful project to promote the study of geometries via their characteristic groups of transformations. Or as Minkowski expressed the same basic thought himself, the theory of relativity discovered by physicists in 1905 could just as well have been proposed by some late-nineteenth-century mathematician, by simply reflecting upon the groups of transformations that left invariant the form of the equation of a propagating light wave. Minkowski's publications and research notes provide a contrasting picture of the discovery of spacetime, in which group theory plays no direct part. In order to relate the steps of Minkowski's discovery, we begin with an account of Poincaré's theory of gravitation, where Minkowski found some of the germs of spacetime. Poincaré's geometric interpretation of the Lorentz transformation is examined, along with his reasons for not pursuing a four-dimensional vector calculus. In the second section, Minkowski's discovery and presentation of the notion of a world line in spacetime is presented. In the third and final section, Poincaré's and Minkowski's diagrammatic interpretations of the Lorentz transformation are compared.

  7. Generalizing optical geometry

    International Nuclear Information System (INIS)

    Jonsson, Rickard; Westman, Hans

    2006-01-01

    We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity

  8. Quantum mechanics in fractional and other anomalous spacetimes

    NARCIS (Netherlands)

    Calcagni, Gianluca; Nardelli, Giuseppe; Scalisi, Marco

    2012-01-01

    We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the wave-functions minimizing the uncertainty are found. In spite of the

  9. Dark energy from discrete spacetime.

    Directory of Open Access Journals (Sweden)

    Aaron D Trout

    Full Text Available Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, [Formula: see text] in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies.

  10. Dark energy from discrete spacetime.

    Science.gov (United States)

    Trout, Aaron D

    2013-01-01

    Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, [Formula: see text] in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies.

  11. Physics and geometry

    International Nuclear Information System (INIS)

    Konopleva, N.P.

    2009-01-01

    The basic ideas of description methods of physical fields and elementary particle interactions are discussed. One of such ideas is the conception of space-time geometry. In this connection experimental measurement methods are analyzed. It is shown that measure procedures are the origin of geometrical axioms. The connection between space symmetry properties and the conservation laws is considered

  12. Lorentz violations in multifractal spacetimes

    Energy Technology Data Exchange (ETDEWEB)

    Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, Madrid (Spain)

    2017-05-15

    Using the recent observation of gravitational waves (GW) produced by a black-hole merger, we place a lower bound on the energy above which a multifractal spacetime would display an anomalous geometry and, in particular, violations of Lorentz invariance. In the so-called multifractional theory with q-derivatives, we show that the deformation of dispersion relations is much stronger than in generic quantum-gravity approaches (including loop quantum gravity) and, contrary to the latter, present observations on GWs can place very strong bounds on the characteristic scales at which spacetime deviates from standard Minkowski. The energy at which multifractal effects should become apparent is E{sub *} > 10{sup 14} GeV (thus improving previous bounds by 12 orders of magnitude) when the exponents in the measure are fixed to their central value 1 / 2. We also estimate, for the first time, the effect of logarithmic oscillations in the measure (corresponding to a discrete spacetime structure) and find that they do not change much the bounds obtained in their absence, unless the amplitude of the oscillations is fine tuned. This feature, unavailable in known quantum-gravity scenarios, may help the theory to avoid being ruled out by gamma-ray burst (GRB) observations, for which E{sub *} > 10{sup 17} GeV or greater. (orig.)

  13. Causal structure of analogue spacetimes

    International Nuclear Information System (INIS)

    Barcelo, Carlos; Liberati, Stefano; Sonego, Sebastiano; Visser, Matt

    2004-01-01

    The so-called 'analogue models of general relativity' provide a number of specific physical systems, well outside the traditional realm of general relativity, that nevertheless are well-described by the differential geometry of curved spacetime. Specifically, the propagation of perturbations in these condensed matter systems is described by 'effective metrics' that carry with them notions of 'causal structure' as determined by an exchange of quasi-particles. These quasi-particle-induced causal structures serve as specific examples of what can be done in the presence of a Lorentzian metric without having recourse to the Einstein equations of general relativity. (After all, the underlying analogue model is governed by its own specific physics, not necessarily by the Einstein equations.) In this paper we take a careful look at what can be said about the causal structure of analogue spacetimes, focusing on those containing quasi-particle horizons, both with a view to seeing what is different from standard general relativity, and what the similarities might be. For definiteness, and because the physics is particularly simple to understand, we will phrase much of the discussion in terms of acoustic disturbances in moving fluids, where the underlying physics is ordinary fluid mechanics, governed by the equations of traditional hydrodynamics, and the relevant quasi-particles are the phonons. It must however be emphasized that this choice of example is only for the sake of pedagogical simplicity and that our considerations apply generically to wide classes of analogue spacetimes

  14. Border of spacetime

    International Nuclear Information System (INIS)

    Harada, Tomohiro; Nakao, Ken-ichi

    2004-01-01

    It is still uncertain whether the cosmic censorship conjecture is true or not. To get a new insight into this issue, we propose the concept of the border of spacetime as a generalization of the spacetime singularity and discuss its visibility. The visible border, corresponding to the naked singularity, is not only relevant to mathematical completeness of general relativity but also a window into new physics in strongly curved spacetimes, which is in principle observable

  15. Entropy in Spacetime and Topological Hair

    Science.gov (United States)

    Hyun, Young-Hwan; Kim, Yoonbai

    2018-01-01

    Global topological soliton of the hedgehog ansatz is added to de Sitter spacetime in arbitrary dimensions larger than three, and then thermodynamic law is checked at the cosmological horizon. All geometric and thermodynamic quantities are varied in the presence of a long-range interacting matter distribution with negative pressure, however the entropy-area relation is satisfied in the exact form. Its geometry involves deficit solid angle but maintains a single horizon which allows unique temperature normalization, different from the case of Schwarzschild-de Sitter spacetime.

  16. Geodesic congruences in warped spacetimes

    International Nuclear Information System (INIS)

    Ghosh, Suman; Dasgupta, Anirvan; Kar, Sayan

    2011-01-01

    In this article, we explore the kinematics of timelike geodesic congruences in warped five-dimensional bulk spacetimes, with and without thick or thin branes. Beginning with geodesic flows in the Randall-Sundrum anti-de Sitter geometry without and with branes, we find analytical expressions for the expansion scalar and comment on the effects of including thin branes on its evolution. Later, we move on to congruences in more general warped bulk geometries with a cosmological thick brane and a time-dependent extra dimensional scale. Using analytical expressions for the velocity field, we interpret the expansion, shear and rotation (ESR) along the flows, as functions of the extra dimensional coordinate. The evolution of a cross-sectional area orthogonal to the congruence, as seen from a local observer's point of view, is also shown graphically. Finally, the Raychaudhuri and geodesic equations in backgrounds with a thick brane are solved numerically in order to figure out the role of initial conditions (prescribed on the ESR) and spacetime curvature on the evolution of the ESR.

  17. Twistor Cosmology and Quantum Space-Time

    International Nuclear Information System (INIS)

    Brody, D.C.; Hughston, L.P.

    2005-01-01

    The purpose of this paper is to present a model of a 'quantum space-time' in which the global symmetries of space-time are unified in a coherent manner with the internal symmetries associated with the state space of quantum-mechanics. If we take into account the fact that these distinct families of symmetries should in some sense merge and become essentially indistinguishable in the unified regime, our framework may provide an approximate description of or elementary model for the structure of the universe at early times. The quantum elements employed in our characterisation of the geometry of space-time imply that the pseudo-Riemannian structure commonly regarded as an essential feature in relativistic theories must be dispensed with. Nevertheless, the causal structure and the physical kinematics of quantum space-time are shown to persist in a manner that remains highly analogous to the corresponding features of the classical theory. In the case of the simplest conformally flat cosmological models arising in this framework, the twistorial description of quantum space-time is shown to be effective in characterising the various physical and geometrical properties of the theory. As an example, a sixteen-dimensional analogue of the Friedmann-Robertson-Walker cosmologies is constructed, and its chronological development is analysed in some detail. More generally, whenever the dimension of a quantum space-time is an even perfect square, there exists a canonical way of breaking the global quantum space-time symmetry so that a generic point of quantum space-time can be consistently interpreted as a quantum operator taking values in Minkowski space. In this scenario, the breakdown of the fundamental symmetry of the theory is due to a loss of quantum entanglement between space-time and internal quantum degrees of freedom. It is thus possible to show in a certain specific sense that the classical space-time description is an emergent feature arising as a consequence of a

  18. Antigravity from a spacetime defect

    OpenAIRE

    Klinkhamer, F. R.; Queiruga, J. M.

    2018-01-01

    We argue that there may exist spacetime defects embedded in Minkowski spacetime, which have negative active gravitational mass. One such spacetime defect then repels a test particle, corresponding to what may be called "antigravity."

  19. On relational nature of geometry of microphysics

    International Nuclear Information System (INIS)

    Chylinski, Z.

    1985-11-01

    A relativity principle and a curiosity of Galilei space-time is described. An internal space-time of R 4 relation is presented. Lorentz limit of R 4 geometry and a field theory is given. The sources of the effects of R 4 hypothesis are characterized. The completeness of quantum description is discussed. 32 refs. (A.S.)

  20. Presheaves of Superselection Structures in Curved Spacetimes

    Science.gov (United States)

    Vasselli, Ezio

    2015-04-01

    We show that superselection structures on curved spacetimes that are expected to describe quantum charges affected by the underlying geometry are categories of sections of presheaves of symmetric tensor categories. When an embedding functor is given, the superselection structure is a Tannaka-type dual of a locally constant group bundle, which hence becomes a natural candidate for the role of the gauge group. Indeed, we show that any locally constant group bundle (with suitable structure group) acts on a net of C* algebras fulfilling normal commutation relations on an arbitrary spacetime. We also give examples of gerbes of C* algebras, defined by Wightman fields and constructed using projective representations of the fundamental group of the spacetime, which we propose as solutions for the problem that existence and uniqueness of the embedding functor are not guaranteed.

  1. Singularities in FLRW Spacetimes

    NARCIS (Netherlands)

    Lam, Huibert het; Prokopec, Tom

    2017-01-01

    We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept

  2. Type II universal spacetimes

    Czech Academy of Sciences Publication Activity Database

    Hervik, S.; Málek, Tomáš; Pravda, Vojtěch; Pravdová, Alena

    2015-01-01

    Roč. 32, č. 24 (2015), s. 245012 ISSN 0264-9381 R&D Projects: GA ČR GA13-10042S Institutional support: RVO:67985840 Keywords : einstein spacetimes * generalized gravities * universal spacetimes Subject RIV: BA - General Mathematics Impact factor: 2.837, year: 2015 http://iopscience.iop.org/article/10.1088/0264-9381/32/24/245012

  3. Quantum gravity from noncommutative spacetime

    International Nuclear Information System (INIS)

    Lee, Jungjai; Yang, Hyunseok

    2014-01-01

    We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative *-algebra) of quantum gravity.

  4. Quantum gravity from noncommutative spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Jungjai [Daejin University, Pocheon (Korea, Republic of); Yang, Hyunseok [Korea Institute for Advanced Study, Seoul (Korea, Republic of)

    2014-12-15

    We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative *-algebra) of quantum gravity.

  5. A Lorentzian quantum geometry

    Energy Technology Data Exchange (ETDEWEB)

    Grotz, Andreas

    2011-10-07

    In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

  6. A Lorentzian quantum geometry

    International Nuclear Information System (INIS)

    Grotz, Andreas

    2011-01-01

    In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

  7. Spacetime coarse grainings in nonrelativistic quantum mechanics

    International Nuclear Information System (INIS)

    Hartle, J.B.

    1991-01-01

    Sum-over-histories generalizations of nonrelativistic quantum mechanics are explored in which probabilities are predicted, not just for alternatives defined on spacelike surfaces, but for alternatives defined by the behavior of spacetime histories with respect to spacetime regions. Closed, nonrelativistic systems are discussed whose histories are paths in a given configuration space. The action and the initial quantum state are assumed fixed and given. A formulation of quantum mechanics is used which assigns probabilities to members of sets of alternative coarse-grained histories of the system, that is, to the individual classes of a partition of its paths into exhaustive and exclusive classes. Probabilities are assigned to those sets which decohere, that is, whose probabilities are consistent with the sum rules of probability theory. Coarse graining by the behavior of paths with respect to regions of spacetime is described. For example, given a single region, the set of all paths may be partitioned into those which never pass through the region and those which pass through the region at least once. A sum-over-histories decoherence functional is defined for sets of alternative histories coarse-grained by spacetime regions. Techniques for the definition and effective computation of the relevant sums over histories by operator-product formulas are described and illustrated by examples. Methods based on Euclidean stochastic processes are also discussed and illustrated. Models of decoherence and measurement for spacetime coarse grainings are described. Issues of causality are investigated. Such spacetime generalizations of nonrelativistic quantum mechanics may be useful models for a generalized quantum mechanics of spacetime geometry

  8. Relativistic positioning in Schwarzschild space-time

    International Nuclear Information System (INIS)

    Puchades, Neus; Sáez, Diego

    2015-01-01

    In the Schwarzschild space-time created by an idealized static spherically symmetric Earth, two approaches -based on relativistic positioning- may be used to estimate the user position from the proper times broadcast by four satellites. In the first approach, satellites move in the Schwarzschild space-time and the photons emitted by the satellites follow null geodesics of the Minkowski space-time asymptotic to the Schwarzschild geometry. This assumption leads to positioning errors since the photon world lines are not geodesics of any Minkowski geometry. In the second approach -the most coherent one- satellites and photons move in the Schwarzschild space-time. This approach is a first order one in the dimensionless parameter GM/R (with the speed of light c=1). The two approaches give different inertial coordinates for a given user. The differences are estimated and appropriately represented for users located inside a great region surrounding Earth. The resulting values (errors) are small enough to justify the use of the first approach, which is the simplest and the most manageable one. The satellite evolution mimics that of the GALILEO global navigation satellite system. (paper)

  9. Geometry, topology, and string theory

    Energy Technology Data Exchange (ETDEWEB)

    Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)

    2003-01-01

    A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.

  10. Geometry, topology, and string theory

    International Nuclear Information System (INIS)

    Varadarajan, Uday

    2003-01-01

    A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated

  11. Geometry of higher-dimensional black hole thermodynamics

    International Nuclear Information System (INIS)

    Aaman, Jan E.; Pidokrajt, Narit

    2006-01-01

    We investigate thermodynamic curvatures of the Kerr and Reissner-Nordstroem (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in four-dimensional spacetime. The thermodynamic geometries are the Ruppeiner geometry and the conformally related Weinhold geometry. The Ruppeiner geometry for a d=5 Kerr black hole is curved and divergent in the extremal limit. For a d≥6 Kerr black hole there is no extremality but the Ruppeiner curvature diverges where one suspects that the black hole becomes unstable. The Weinhold geometry of the Kerr black hole in arbitrary dimension is a flat geometry. For the RN black hole the Ruppeiner geometry is flat in all spacetime dimensions, whereas its Weinhold geometry is curved. In d≥5 the Kerr black hole can possess more than one angular momentum. Finally we discuss the Ruppeiner geometry for the Kerr black hole in d=5 with double angular momenta

  12. On the minimum uncertainty of space-time geodesics

    International Nuclear Information System (INIS)

    Diosi, L.; Lukacs, B.

    1989-10-01

    Although various attempts for systematic quantization of the space-time geometry ('gravitation') have appeared, none of them is considered fully consistent or final. Inspired by a construction of Wigner, the quantum relativistic limitations of measuring the metric tensor of a certain space-time were calculated. The result is suggested to be estimate for fluctuations of g ab whose rigorous determination will be a subject of a future relativistic quantum gravity. (author) 11 refs

  13. Neutrino oscillations in curved spacetime: A heuristic treatment

    International Nuclear Information System (INIS)

    Cardall, C.Y.; Fuller, G.M.

    1997-01-01

    We discuss neutrino oscillations in curved spacetime. Our heuristic approach can accommodate matter effects and gravitational contributions to neutrino spin precession in the presence of a magnetic field. By way of illustration, we perform explicit calculations in the Schwarzschild geometry. In this case, gravitational effects on neutrino oscillations are intimately related to the redshift. We discuss how spacetime curvature could affect the resonance position and adiabaticity of matter-enhanced neutrino flavor conversion. copyright 1997 The American Physical Society

  14. Spinning geometry = Twisted geometry

    International Nuclear Information System (INIS)

    Freidel, Laurent; Ziprick, Jonathan

    2014-01-01

    It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)

  15. Warped product space-times

    Science.gov (United States)

    An, Xinliang; Wong, Willie Wai Yeung

    2018-01-01

    Many classical results in relativity theory concerning spherically symmetric space-times have easy generalizations to warped product space-times, with a two-dimensional Lorentzian base and arbitrary dimensional Riemannian fibers. We first give a systematic presentation of the main geometric constructions, with emphasis on the Kodama vector field and the Hawking energy; the construction is signature independent. This leads to proofs of general Birkhoff-type theorems for warped product manifolds; our theorems in particular apply to situations where the warped product manifold is not necessarily Einstein, and thus can be applied to solutions with matter content in general relativity. Next we specialize to the Lorentzian case and study the propagation of null expansions under the assumption of the dominant energy condition. We prove several non-existence results relating to the Yamabe class of the fibers, in the spirit of the black-hole topology theorem of Hawking–Galloway–Schoen. Finally we discuss the effect of the warped product ansatz on matter models. In particular we construct several cosmological solutions to the Einstein–Euler equations whose spatial geometry is generally not isotropic.

  16. Spacetime extensions Pt. 1

    International Nuclear Information System (INIS)

    Racz, I.

    1991-09-01

    The problem of the existence of local extensions of spacetime is considered. It is shown that for a spacetime including an incomplete inextendible non-coiling causal geodesic curve there exists a particular C k (resp. C k- ) local extension provided that the curvature and its covariant derivatives are well behaved up to order k + 1 (resp. k) along a family of causal geodetics (around the chosen one). (R.P.) 15 refs

  17. Null geodesics and embedding diagrams of the interior Schwarzschild--de Sitter spacetimes with uniform density

    International Nuclear Information System (INIS)

    Stuchlik, Zdenek; Hledik, Stanislav; Soltes, Jiri; Ostgaard, Erlend

    2001-01-01

    Null geodesics and embedding diagrams of central planes in the ordinary space geometry and the optical reference geometry of the interior Schwarzschild--de Sitter spacetimes with uniform density are studied. For completeness, both positive and negative values of the cosmological constant are considered. The null geodesics are restricted to the central planes of these spacetimes, and their properties can be reflected by an 'effective potential.' If the interior spacetime is extremely compact, the effective potential has a local maximum corresponding to a stable circular null geodesic around which bound null geodesics are concentrated. The upper limit on the size of the interior spacetimes containing bound null geodesics is R=3M, independently of the value of the cosmological constant. The embedding diagrams of the central planes of the ordinary geometry into three-dimensional Euclidean space are well defined for the complete interior of all spacetimes with a repulsive cosmological constant, but the planes cannot be embedded into the Euclidean space in the case of spacetimes with subcritical values of an attractive cosmological constant. On the other hand, the embedding diagrams of the optical geometry are well defined for all of the spacetimes, and the turning points of these diagrams correspond to the radii of the circular null geodesics. All the embedding diagrams, for both the ordinary and optical geometry, are smoothly matched to the corresponding embedding diagrams of the external vacuum Schwarzschild--de Sitter spacetimes

  18. General Relativity: Geometry Meets Physics

    Science.gov (United States)

    Thomsen, Dietrick E.

    1975-01-01

    Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…

  19. Singularities in FLRW spacetimes

    Science.gov (United States)

    het Lam, Huibert; Prokopec, Tomislav

    2017-12-01

    We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept following that geodesic. That indicates a breakdown of the particle's description, which is why we should not consider those trajectories for the definition of an initial singularity. When one only considers test particles that do not have this breakdown of their trajectory, it turns out that the only singular FLRW spacetimes are the ones that have a scale parameter that vanishes at some initial time.

  20. Symmetry, structure, and spacetime

    CERN Document Server

    Rickles, Dean

    2007-01-01

    In this book Rickles considers several interpretative difficulties raised by gauge-type symmetries (those that correspond to no change in physical state). The ubiquity of such symmetries in modern physics renders them an urgent topic in philosophy of physics. Rickles focuses on spacetime physics, and in particular classical and quantum general relativity. Here the problems posed are at their most pathological, involving the apparent disappearance of spacetime! Rickles argues that both traditional ontological positions should be replaced by a structuralist account according to which relational

  1. On the electromagnetic field and the Teukolsky relations in arbitrary space-times

    International Nuclear Information System (INIS)

    Coll, B.; Ferrando, J.J.

    1985-01-01

    The relations on the electromagnetic field obtained by Teukolsky for type D, vacuum space-times are studied. The role played by the maxwellian geometry of the basic tetrad is shown. It is proved that Teukolsky relations are, generically, incomplete. Once completed, their generalization to arbitrary space-times is given [fr

  2. Energy in the Kantowski–Sachs space-time using teleparallel ...

    Indian Academy of Sciences (India)

    Energy in the Kantowski–Sachs space-time using teleparallel geometry ... Kantowski–Sachs metric; teleparallelism; gravitational energy. Abstract. The purpose of this paper is to examine the energy content of the inflationary Universe described by Kantowski–Sachs space-time in quasilocal approach of teleparallel gravity ...

  3. On scattering of scalar waves in static space-times, particularly Schwarzschild

    International Nuclear Information System (INIS)

    Beig, R.

    1982-01-01

    This paper aims at laying foundations of a rigorous scattering theory for scalar waves in a static space-time. The treatment includes geometries which can be thought of as representing the exterior of a black hole. Schwarzschild space-time, as a particular example, is studied in more detail. (Auth.)

  4. Thermodynamics of quantum spacetime histories

    Science.gov (United States)

    Smolin, Lee

    2017-11-01

    We show that the simplicity constraints, which define the dynamics of spin foam models, imply, and are implied by, the first law of thermodynamics, when the latter is applied to causal diamonds in the quantum spacetime. This result reveals an intimate connection between the holographic nature of gravity, as reflected by the Bekenstein entropy, and the fact that general relativity and other gravitational theories can be understood as constrained topological field theories. To state and derive this correspondence we describe causal diamonds in the causal structure of spin foam histories and generalize arguments given for the near horizon region of black holes by Frodden, Gosh and Perez [Phys. Rev. D 87, 121503 (2013); , 10.1103/PhysRevD.87.121503Phys. Rev. D 89, 084069 (2014); , 10.1103/PhysRevD.89.084069Phys. Rev. Lett. 107, 241301 (2011); , 10.1103/PhysRevLett.107.241301Phys. Rev. Lett.108, 169901(E) (2012)., 10.1103/PhysRevLett.108.169901] and Bianchi [arXiv:1204.5122.]. This allows us to apply a recent argument of Jacobson [Phys. Rev. Lett. 116, 201101 (2016).10.1103/PhysRevLett.116.201101] to show that if a spin foam history has a semiclassical limit described in terms of a smooth metric geometry, that geometry satisfies the Einstein equations. These results suggest also a proposal for a quantum equivalence principle.

  5. Curvature tensor copies in affine geometry

    International Nuclear Information System (INIS)

    Srivastava, P.P.

    1981-01-01

    The sets of space-time and spin-connections which give rise to the same curvature tensor are constructed. The corresponding geometries are compared. Results are illustrated by an explicit calculation and comment on the copies in Einstein-Cartan and Weyl-Cartan geometries. (Author) [pt

  6. VIII International Meeting on Lorentzian Geometry

    CERN Document Server

    Flores, José; Palomo, Francisco; GeLoMa 2016; Lorentzian geometry and related topics

    2017-01-01

    This volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries and the oscillator spacetime. In the last decades Lorentzian geometry has experienced a significant impulse, which has transformed it from just a mathematical tool for general relativity to a consolidated branch of differential geometry, interesting in and of itself. Nowadays, this field provides a framework where many different mathematical techniques arise with applications to multiple parts of mathem...

  7. Cauchy horizons in Gowdy spacetimes

    International Nuclear Information System (INIS)

    Chrusciel, Piotr T; Lake, Kayll

    2004-01-01

    We analyse exhaustively the structure of non-degenerate Cauchy horizons in Gowdy spacetimes, and we establish existence of a large class of non-polarized Gowdy spacetimes with such horizons. Our results here, together with the deep new results of Ringstroem, establish strong cosmic censorship in (toroidal) Gowdy spacetimes

  8. Space-time structure

    CERN Document Server

    Schrödinger, Erwin

    1985-01-01

    In response to repeated requests this classic book on space-time structure by Professor Erwin Schrödinger is now available in the Cambridge Science Classics series. First published in 1950, and reprinted in 1954 and 1960, this lucid and profound exposition of Einstein's 1915 theory of gravitation still provides valuable reading for students and research workers in the field.

  9. W-geometry

    International Nuclear Information System (INIS)

    Hull, C.M.

    1993-01-01

    The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)

  10. The wave equation on a curved space-time

    International Nuclear Information System (INIS)

    Friedlander, F.G.

    1975-01-01

    It is stated that chapters on differential geometry, distribution theory, and characteristics and the propagation of discontinuities are preparatory. The main matter is in three chapters, entitled: fundamental solutions, representation theorems, and wave equations on n-dimensional space-times. These deal with general construction of fundamental solutions and their application to the Cauchy problem. (U.K.)

  11. Notes on a class of homogeneous space-times

    International Nuclear Information System (INIS)

    Calvao, M.O.; Reboucas, M.J.; Teixeira, A.F.F.; Silva Junior, W.M.

    1987-01-01

    The breakdown of causality in homogeneous Goedel-type space-time manifolds is examined. An extension of Reboucas-Tiomno (RT) study is made. The existence of noncausal curves is also investigated under two different conditions on the energy-momentum tensor. An integral representation of the infinitesimal generators of isometries is obtained extending previous works on the RT geometry. (Author) [pt

  12. Functional integration over geometries

    International Nuclear Information System (INIS)

    Mottola, E.

    1995-01-01

    The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted

  13. Arbitrariness of geometry and the aether

    International Nuclear Information System (INIS)

    Browne, P.F.

    1976-01-01

    As emphasized by Milne, an observer ultimately depends on the transmission and reception of light signals for the measurement of natural lengths and periods remote from his world point. The laws of geometry which are obeyed when these lengths and periods are plotted on a space--time depend, inevitably, on assumptions concerning the dependence of light velocity on the spatial and temporal coordinates. A convention regarding light velocity fixes the geometry, and conversely. However, the convention of flat space--time implies nonintegrable ''radar distances'' unless the concept of coordinate-dependent units of measure is employed. Einstein's space--time has the advantage of admitting a special reference system R with respect to which the aether fluid is at rest and the total gravitational field vanishes. A holonomic transformation from R to another reference system R belonging to the same space--time introduces a nonpermanent gravitational field and holonomic aether motion. A nonholonomic transformation from R to a reference system R* which belongs to a different space--time introduces a permanent gravitational field and nonholonomic aether motion. The arbitrariness of geometry is expressed by extending covariance to include the latter transformation. By means of a nonholonomic (or units) transformation it is possible, with the aid of the principle of equivalence, to obtain the Schwarzschild and de Sitter metrics from the Newtonian fields that would arise in a flat space--time description. Some light is thrown on the interpretation of cosmological models

  14. Space-time of class one

    International Nuclear Information System (INIS)

    Villasenor, R.F.; Bonilla, J.L.L.; Zuniga, G.O.; Matos, T.

    1989-01-01

    The authors study space-times embedded in E 5 (that means, pseudo-euclidean five-dimensional spaces) in the intrinsic rigidity case, i.e., when the second fundamental form b if can be determined by the internal geometry of the four-dimensional Riemannian space R 4 . They write down the Gauss and Codazzi equations determining the local isometric embedding of R 4 in E 5 and give some consequences of it. They prove that when there exists intrinsic rigidity, then b if is a linear combination of the metric and Ricci tensor; it is given some applications for the de Sitter and Einstein models

  15. Constraints on spacetime anisotropy and Lorentz violation from the GRAAL experiment

    Energy Technology Data Exchange (ETDEWEB)

    Chang, Zhe [Chinese Academy of Sciences, Institute of High Energy Physics, Beijing (China); Chinese Academy of Sciences, Theoretical Physics Center for Science Facilities, Beijing (China); Wang, Sai [Chinese Academy of Sciences, Institute of High Energy Physics, Beijing (China)

    2013-02-15

    The GRAAL experiment could constrain the variations of the speed of light. The anisotropy of the speed of light may imply that the spacetime is anisotropic. Finsler geometry is a reasonable candidate to deal with the spacetime anisotropy. In this paper, the Lorentz invariance violation (LIV) of the photon sector is investigated in the locally Minkowski spacetime. The locally Minkowski spacetime is a class of flat Finsler spacetime and refers a metric with the anisotropic departure from the Minkowski one. The LIV matrices used to fit the experimental data are represented in terms of these metric deviations. The GRAAL experiment constrains the spacetime anisotropy to be less than 10{sup -14}. In addition, we find that the simplest Finslerian photon sector could be viewed as a geometric representation of the photon sector in the minimal standard model extension (SME). (orig.)

  16. Spacetime extensions II

    Energy Technology Data Exchange (ETDEWEB)

    Racz, Istvan, E-mail: iracz@rmki.kfki.h [RMKI, H-1121 Budapest, Konkoly Thege Miklos ut 29-33 (Hungary)

    2010-08-07

    The global extendibility of smooth causal geodesically incomplete spacetimes is investigated. Denote by {gamma} one of the incomplete non-extendible causal geodesics of a causal geodesically incomplete spacetime (M, g{sub ab}). First, it is shown that it is always possible to select a synchronized family of causal geodesics {Gamma} and an open neighbourhood U of a final segment of {gamma} in M such that U comprises members of {Gamma}, and suitable local coordinates can be defined everywhere on U provided that {gamma} does not terminate either on a tidal force tensor singularity or on a topological singularity. It is also shown that if, in addition, the spacetime (M, g{sub ab}) is globally hyperbolic, and the components of the curvature tensor, and its covariant derivatives up to order k - 1 are bounded on U, and also the line integrals of the components of the kth-order covariant derivatives are finite along the members of {Gamma}-where all the components are meant to be registered with respect to a synchronized frame field on U-then there exists a C{sup k-} extension {Phi} : (M,g{sub ab}) {yields}(M,g{sub ab}) so that for each {gamma}-bar from {Gamma}, which is inextendible in (M, g{sub ab}), the image, {Phi}{gamma}-bar, is extendible in (M,g{sub ab}). Finally, it is also proved that whenever {gamma} does terminate on a topological singularity (M, g{sub ab}) cannot be generic.

  17. Translational spacetime symmetries in gravitational theories

    International Nuclear Information System (INIS)

    Petti, R J

    2006-01-01

    How to include spacetime translations in fibre bundle gauge theories has been a subject of controversy, because spacetime symmetries are not internal symmetries of the bundle structure group. The standard method for including affine symmetry in differential geometry is to define a Cartan connection on an affine bundle over spacetime. This is equivalent to (1) defining an affine connection on the affine bundle, (2) defining a zero section on the associated affine vector bundle and (3) using the affine connection and the zero section to define an 'associated solder form', whose lift to a tensorial form on the frame bundle becomes the solder form. The zero section reduces the affine bundle to a linear bundle and splits the affine connection into translational and homogeneous parts; however, it violates translational equivariance/gauge symmetry. This is the natural geometric framework for Einstein-Cartan theory as an affine theory of gravitation. The last section discusses some alternative approaches that claim to preserve translational gauge symmetry

  18. Translational spacetime symmetries in gravitational theories

    Energy Technology Data Exchange (ETDEWEB)

    Petti, R J [MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760 (United States)

    2006-02-07

    How to include spacetime translations in fibre bundle gauge theories has been a subject of controversy, because spacetime symmetries are not internal symmetries of the bundle structure group. The standard method for including affine symmetry in differential geometry is to define a Cartan connection on an affine bundle over spacetime. This is equivalent to (1) defining an affine connection on the affine bundle, (2) defining a zero section on the associated affine vector bundle and (3) using the affine connection and the zero section to define an 'associated solder form', whose lift to a tensorial form on the frame bundle becomes the solder form. The zero section reduces the affine bundle to a linear bundle and splits the affine connection into translational and homogeneous parts; however, it violates translational equivariance/gauge symmetry. This is the natural geometric framework for Einstein-Cartan theory as an affine theory of gravitation. The last section discusses some alternative approaches that claim to preserve translational gauge symmetry.

  19. Optical geometry across the horizon

    International Nuclear Information System (INIS)

    Jonsson, Rickard

    2006-01-01

    In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework

  20. Hierarchical Cantor set in the large scale structure with torus geometry

    Energy Technology Data Exchange (ETDEWEB)

    Murdzek, R. [Physics Department, ' Al. I. Cuza' University, Blvd. Carol I, Nr. 11, Iassy 700506 (Romania)], E-mail: rmurdzek@yahoo.com

    2008-12-15

    The formation of large scale structures is considered within a model with string on toroidal space-time. Firstly, the space-time geometry is presented. In this geometry, the Universe is represented by a string describing a torus surface. Thereafter, the large scale structure of the Universe is derived from the string oscillations. The results are in agreement with the cellular structure of the large scale distribution and with the theory of a Cantorian space-time.

  1. Born reciprocity in string theory and the nature of spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Freidel, Laurent, E-mail: lfreidel@perimeterinstitute.ca [Perimeter Institute for Theoretical Physics, 31 Caroline St., N, Ontario N2L 2Y5, Waterloo (Canada); Leigh, Robert G., E-mail: rgleigh@uiuc.edu [Department of Physics, University of Illinois, 1110 West Green St., Urbana, IL 61801 (United States); Minic, Djordje, E-mail: dminic@vt.edu [Department of Physics, Virginia Tech, Blacksburg, VA 24061 (United States)

    2014-03-07

    After many years, the deep nature of spacetime in string theory remains an enigma. In this Letter we incorporate the concept of Born reciprocity in order to provide a new point of view on string theory in which spacetime is a derived dynamical concept. This viewpoint may be thought of as a dynamical chiral phase space formulation of string theory, in which Born reciprocity is implemented as a choice of a Lagrangian submanifold of the phase space, and amounts to a generalization of T-duality. In this approach the fundamental symmetry of string theory contains phase space diffeomorphism invariance and the underlying string geometry should be understood in terms of dynamical bi-Lagrangian manifolds and an apparently new geometric structure, somewhat reminiscent of para-quaternionic geometry, which we call Born geometry.

  2. Born reciprocity in string theory and the nature of spacetime

    International Nuclear Information System (INIS)

    Freidel, Laurent; Leigh, Robert G.; Minic, Djordje

    2014-01-01

    After many years, the deep nature of spacetime in string theory remains an enigma. In this Letter we incorporate the concept of Born reciprocity in order to provide a new point of view on string theory in which spacetime is a derived dynamical concept. This viewpoint may be thought of as a dynamical chiral phase space formulation of string theory, in which Born reciprocity is implemented as a choice of a Lagrangian submanifold of the phase space, and amounts to a generalization of T-duality. In this approach the fundamental symmetry of string theory contains phase space diffeomorphism invariance and the underlying string geometry should be understood in terms of dynamical bi-Lagrangian manifolds and an apparently new geometric structure, somewhat reminiscent of para-quaternionic geometry, which we call Born geometry.

  3. Thin shells joining local cosmic string geometries

    Energy Technology Data Exchange (ETDEWEB)

    Eiroa, Ernesto F. [Universidad de Buenos Aires, Ciudad Universitaria Pabellon I, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Rubin de Celis, Emilio; Simeone, Claudio [Universidad de Buenos Aires, Ciudad Universitaria Pabellon I, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Ciudad Universitaria Pabellon I, IFIBA-CONICET, Buenos Aires (Argentina)

    2016-10-15

    In this article we present a theoretical construction of spacetimes with a thin shell that joins two different local cosmic string geometries. We study two types of global manifolds, one representing spacetimes with a thin shell surrounding a cosmic string or an empty region with Minkowski metric, and the other corresponding to wormholes which are not symmetric across the throat located at the shell. We analyze the stability of the static configurations under perturbations preserving the cylindrical symmetry. For both types of geometries we find that the static configurations can be stable for suitable values of the parameters. (orig.)

  4. Thin shells joining local cosmic string geometries

    International Nuclear Information System (INIS)

    Eiroa, Ernesto F.; Rubin de Celis, Emilio; Simeone, Claudio

    2016-01-01

    In this article we present a theoretical construction of spacetimes with a thin shell that joins two different local cosmic string geometries. We study two types of global manifolds, one representing spacetimes with a thin shell surrounding a cosmic string or an empty region with Minkowski metric, and the other corresponding to wormholes which are not symmetric across the throat located at the shell. We analyze the stability of the static configurations under perturbations preserving the cylindrical symmetry. For both types of geometries we find that the static configurations can be stable for suitable values of the parameters. (orig.)

  5. Some properties of spatially homogeneous spacetimes

    International Nuclear Information System (INIS)

    Coomer, G.C.

    1979-01-01

    This paper discusses two features of the universe which are influenced in a fundamental way by the spacetime geometry of the universe. The first is the growth of density fluctuations in the early stages of the evolution of the universe. The second is the propagation of electromagnetic radiation in the universe. A spatially homogeneous universe is assumed in both discussions. The gravitational instability theory of galaxy formation is investigated for a viscous fluid and for a charged, conducting fluid with a magnetic field added as a perturbation. It is found that the growth rate of density perturbations in both cases is lower than in the perfect fluid case. Spatially homogeneous but nonisotropic spacetimes are investigated next. Two perfect fluid solutions of Einstein's field equations are found which have spacelike hypersurfaces with Bianchi type II geometry. An expression for the spectrum of the cosmic microwave background radiation in a spatially homogeneous but nonisotropic universe is found. The expression is then used to determine the angular distribution of the intensity of the radiation in the simpler of the two solutions. When accepted values of the matter density and decoupling temperature are inserted into this solution, values for the age of the universe and the time of decoupling are obtained which agree reasonably well with the values of the standard model of the universe

  6. Systematics of IIB spinorial geometry

    OpenAIRE

    Gran, U.; Gutowski, J.; Papadopoulos, G.; Roest, D.

    2005-01-01

    We reduce the classification of all supersymmetric backgrounds of IIB supergravity to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This extends the work of [hep-th/0503046] to IIB supergravity. We give the expressions of the Killing spinor equations on all five types of spinors. In this way, the Killing spinor equations become a linear system for the fluxes, geometry and spacetime derivatives of...

  7. Global structure of spacetimes

    International Nuclear Information System (INIS)

    Geroch, R.; Horowitz, G.T.

    1979-01-01

    An extended introduction is followed by a section entitled: 'what is the topology of our universe', in which such topics are considered as the underlying manifold, the qualitative behaviour of the light-cones, causal structure, and determinism. In the next section - 'is our universe singular', the famous singularity theorems are discussed. Finally, under 'how noticeably singular is our universe', the issue of cosmic censorship is discussed, i.e. that of whether or not one expects in certain circumstances that surviving observers will be able to detect singular behaviour in spacetime. (U.K.)

  8. Space-Time Crystal and Space-Time Group.

    Science.gov (United States)

    Xu, Shenglong; Wu, Congjun

    2018-03-02

    Crystal structures and the Bloch theorem play a fundamental role in condensed matter physics. We extend the static crystal to the dynamic "space-time" crystal characterized by the general intertwined space-time periodicities in D+1 dimensions, which include both the static crystal and the Floquet crystal as special cases. A new group structure dubbed a "space-time" group is constructed to describe the discrete symmetries of a space-time crystal. Compared to space and magnetic groups, the space-time group is augmented by "time-screw" rotations and "time-glide" reflections involving fractional translations along the time direction. A complete classification of the 13 space-time groups in one-plus-one dimensions (1+1D) is performed. The Kramers-type degeneracy can arise from the glide time-reversal symmetry without the half-integer spinor structure, which constrains the winding number patterns of spectral dispersions. In 2+1D, nonsymmorphic space-time symmetries enforce spectral degeneracies, leading to protected Floquet semimetal states. We provide a general framework for further studying topological properties of the (D+1)-dimensional space-time crystal.

  9. Why we observe an almost classical spacetime

    OpenAIRE

    Rosales, Jose-Luis; Sanchez-Gomez, Jose-Luis

    1997-01-01

    We argue that, in order to obtain decoherence of spacetime, we should consider quantum conformal metric fluctuations of spacetime. This could be the required environment in the problem of selfmeasurement of spacetime in quantum gravity.

  10. On ``minimally curved spacetimes'' in general relativity

    OpenAIRE

    Dadhich, Naresh

    1997-01-01

    We consider a spacetime corresponding to uniform relativistic potential analogus to Newtonian potential as an example of ``minimally curved spacetime''. We also consider a radially symmetric analogue of the Rindler spacetime of uniform proper acceleration relative to infinity.

  11. Stationary metrics and optical Zermelo-Randers-Finsler geometry

    International Nuclear Information System (INIS)

    Gibbons, G. W.; Warnick, C. M.; Herdeiro, C. A. R.; Werner, M. C.

    2009-01-01

    We consider a triality between the Zermelo navigation problem, the geodesic flow on a Finslerian geometry of Randers type, and spacetimes in one dimension higher admitting a timelike conformal Killing vector field. From the latter viewpoint, the data of the Zermelo problem are encoded in a (conformally) Painleve-Gullstrand form of the spacetime metric, whereas the data of the Randers problem are encoded in a stationary generalization of the usual optical metric. We discuss how the spacetime viewpoint gives a simple and physical perspective on various issues, including how Finsler geometries with constant flag curvature always map to conformally flat spacetimes and that the Finsler condition maps to either a causality condition or it breaks down at an ergo surface in the spacetime picture. The gauge equivalence in this network of relations is considered as well as the connection to analogue models and the viewpoint of magnetic flows. We provide a variety of examples.

  12. Quantum field in η-ξ spacetime

    International Nuclear Information System (INIS)

    Gui, Y.

    1990-01-01

    A new spacetime, η-ξ spacetime, is constructed. The quantum field in η-ξ spacetime is discussed. It is shown that the vacuum state of quantum field in η-ξ spacetime is a thermal state for an inertial observer in Minkowski spacetime, and the vacuum Green's functions in η-ξ spacetime are just the thermal Green's functions in usual statistical mechanics

  13. Discrete causal theory emergent spacetime and the causal metric hypothesis

    CERN Document Server

    Dribus, Benjamin F

    2017-01-01

    This book evaluates and suggests potentially critical improvements to causal set theory, one of the best-motivated approaches to the outstanding problems of fundamental physics. Spacetime structure is of central importance to physics beyond general relativity and the standard model. The causal metric hypothesis treats causal relations as the basis of this structure. The book develops the consequences of this hypothesis under the assumption of a fundamental scale, with smooth spacetime geometry viewed as emergent. This approach resembles causal set theory, but differs in important ways; for example, the relative viewpoint, emphasizing relations between pairs of events, and relationships between pairs of histories, is central. The book culminates in a dynamical law for quantum spacetime, derived via generalized path summation.

  14. A geometric renormalization group in discrete quantum space-time

    International Nuclear Information System (INIS)

    Requardt, Manfred

    2003-01-01

    We model quantum space-time on the Planck scale as dynamical networks of elementary relations or time dependent random graphs, the time dependence being an effect of the underlying dynamical network laws. We formulate a kind of geometric renormalization group on these (random) networks leading to a hierarchy of increasingly coarse-grained networks of overlapping lumps. We provide arguments that this process may generate a fixed limit phase, representing our continuous space-time on a mesoscopic or macroscopic scale, provided that the underlying discrete geometry is critical in a specific sense (geometric long range order). Our point of view is corroborated by a series of analytic and numerical results, which allow us to keep track of the geometric changes, taking place on the various scales of the resolution of space-time. Of particular conceptual importance are the notions of dimension of such random systems on the various scales and the notion of geometric criticality

  15. On the quantization of spacetime

    International Nuclear Information System (INIS)

    Banai, M.

    1981-01-01

    A program of quantization of relativistic local field theories in terms of Hilbert modules over non-commutative Csup*-algebras is outlined. The spacetime of the considered systems should become a ''quantum'' represented by a Hilbert space. Two suggestions are given for the possible determination this quantum spacetime. (author)

  16. Quantum spacetime operationally based on propagators for extended test particles

    International Nuclear Information System (INIS)

    Prugovecki, E.

    1981-01-01

    By taking into account the quantum aspects intrinsic to any operational definition of spatio-temporal relationships, a stochastic concept of spacetime emerges. In relation to its classical counterpart is realized as a stochastic mean around which quantum fluctuations become negligible only in the limit of macroscopic spacetime intervals. The test-particle propagators used in the proposed quantum concept of spacetime are derived by solving in a consistent manner the localizability problem for relativistic particles. This is achieved in the framework of the stochastic phase space formulation of quantum mechanics, which in the nonrelativistic context is shown to result from systems of imprimitivity related to phase space conserved probability currents derivable from bona fide convariant probability densities in stochastic phase spaces of one particle systems, which can be interpreted as due to measurements performed with extended rather than pointlike test particles. The associated particle propagators can be therefore consistently related to coordinate probability densities measurable by the exchange of photons in between test particles from a chosen standard. Quantum spacetime is defined as the family of propagators corresponding to all conceivable coherent flows of test particles. This family of free-fall propagators has to satisfy certain self-consistency conditions as well as consistent laws of motion which inplicitly determine the stochastic geometro-dynamics of quantum space-time. Field theory on quantum spacetime retains many of the formal features of conventional quantum field theory. On a fundamental epistemological level stochastic geometries emerge as essential prerequisites in the construction of spacetime models that would be operationally based and yet consistent with the relativity principle as well as with the uncertinty principle

  17. Spacetime algebra as a powerful tool for electromagnetism

    Energy Technology Data Exchange (ETDEWEB)

    Dressel, Justin, E-mail: prof.justin.dressel@gmail.com [Department of Electrical and Computer Engineering, University of California, Riverside, CA 92521 (United States); Center for Emergent Matter Science (CEMS), RIKEN, Wako-shi, Saitama, 351-0198 (Japan); Bliokh, Konstantin Y. [Center for Emergent Matter Science (CEMS), RIKEN, Wako-shi, Saitama, 351-0198 (Japan); Interdisciplinary Theoretical Science Research Group (iTHES), RIKEN, Wako-shi, Saitama, 351-0198 (Japan); Nori, Franco [Center for Emergent Matter Science (CEMS), RIKEN, Wako-shi, Saitama, 351-0198 (Japan); Physics Department, University of Michigan, Ann Arbor, MI 48109-1040 (United States)

    2015-08-08

    We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry, with a particular focus on its intrinsic (and often overlooked) complex structure. Notably, the scalar imaginary that appears throughout the electromagnetic theory properly corresponds to the unit 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a single complex and frame-independent bivector field, which generalizes the Riemann–Silberstein complex vector that has recently resurfaced in studies of the single photon wavefunction. The complex structure of spacetime also underpins the emergence of electromagnetic waves, circular polarizations, the normal variables for canonical quantization, the distinction between electric and magnetic charge, complex spinor representations of Lorentz transformations, and the dual (electric–magnetic field exchange) symmetry that produces helicity conservation in vacuum fields. This latter symmetry manifests as an arbitrary global phase of the complex field, motivating the use of a complex vector potential, along with an associated transverse and gauge-invariant bivector potential, as well as complex (bivector and scalar) Hertz potentials. Our detailed treatment aims to encourage the use of spacetime algebra as a readily available and mature extension to existing vector calculus and tensor methods that can greatly simplify the analysis of fundamentally relativistic objects like the electromagnetic field.

  18. Spacetime algebra as a powerful tool for electromagnetism

    Science.gov (United States)

    Dressel, Justin; Bliokh, Konstantin Y.; Nori, Franco

    2015-08-01

    We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry, with a particular focus on its intrinsic (and often overlooked) complex structure. Notably, the scalar imaginary that appears throughout the electromagnetic theory properly corresponds to the unit 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a single complex and frame-independent bivector field, which generalizes the Riemann-Silberstein complex vector that has recently resurfaced in studies of the single photon wavefunction. The complex structure of spacetime also underpins the emergence of electromagnetic waves, circular polarizations, the normal variables for canonical quantization, the distinction between electric and magnetic charge, complex spinor representations of Lorentz transformations, and the dual (electric-magnetic field exchange) symmetry that produces helicity conservation in vacuum fields. This latter symmetry manifests as an arbitrary global phase of the complex field, motivating the use of a complex vector potential, along with an associated transverse and gauge-invariant bivector potential, as well as complex (bivector and scalar) Hertz potentials. Our detailed treatment aims to encourage the use of spacetime algebra as a readily available and mature extension to existing vector calculus and tensor methods that can greatly simplify the analysis of fundamentally relativistic objects like the electromagnetic field.

  19. Hyperbolic geometry

    CERN Document Server

    Iversen, Birger

    1992-01-01

    Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics

  20. ABC of multi-fractal spacetimes and fractional sea turtles

    Energy Technology Data Exchange (ETDEWEB)

    Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, Madrid (Spain)

    2016-04-15

    We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes. (orig.)

  1. ABC of multi-fractal spacetimes and fractional sea turtles

    International Nuclear Information System (INIS)

    Calcagni, Gianluca

    2016-01-01

    We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes. (orig.)

  2. ABC of multi-fractal spacetimes and fractional sea turtles

    Science.gov (United States)

    Calcagni, Gianluca

    2016-04-01

    We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes.

  3. Springer handbook of spacetime

    CERN Document Server

    Petkov, Vesselin

    2014-01-01

    The Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courses on these subjects. The Han...

  4. Relativity without spacetime

    CERN Document Server

    Cosgrove, Joseph K

    2018-01-01

    In 1908, three years after Einstein first published his special theory of relativity, the mathematician Hermann Minkowski introduced his four-dimensional “spacetime” interpretation of the theory. Einstein initially dismissed Minkowski’s theory, remarking that “since the mathematicians have invaded the theory of relativity I do not understand it myself anymore.” Yet Minkowski’s theory soon found wide acceptance among physicists, including eventually Einstein himself, whose conversion to Minkowski’s way of thinking was engendered by the realization that he could profitably employ it for the formulation of his new theory of gravity. The validity of Minkowski’s mathematical “merging” of space and time has rarely been questioned by either physicists or philosophers since Einstein incorporated it into his theory of gravity. Physicists often employ Minkowski spacetime with little regard to the whether it provides a true account of the physical world as opposed to a useful mathematical tool in th...

  5. The edge of spacetime

    International Nuclear Information System (INIS)

    Hawking, S.

    1989-01-01

    This chapter answers some fundamental questions about the limits, spatial and temporal of the universe. The Big Bang and Big Crunch, the temporal end pieces of the universe are explained in terms of curved spacetime using Einstein's theory of general relativity and quantum mechanics. Evidence for the Big Bang including large scale uniformity and discovery of the microwave background radiation are explained. In defining the boundary conditions of the universe, it is suggested that there are no boundary conditions, i.e. that time ceases to be well defined in the very early universe. Thus discussion about events prior to the Big Bang cease to have any meaning. The model offers, as yet unexplained, predictive potential. (U.K.)

  6. Polarized electrogowdy spacetimes censored

    International Nuclear Information System (INIS)

    Nungesser, Ernesto

    2010-01-01

    A sketch of the proof of strong cosmic censorship is presented for a class of solutions of the Einstein-Maxwell equations, those with polarized Gowdy symmetry. A key element of the argument is the observation that by means of a suitable choice of variables the central equations in this problem can be written in a form where they are identical to the central equations for general (i.e. non-polarized) vacuum Gowdy spacetimes. Using this it is seen that the results of Ringstroem on strong cosmic censorship in the vacuum case have implications for the Einstein-Maxwell case. Working out the geometrical meaning of these analytical results leads to the main conclusion.

  7. Polarized electrogowdy spacetimes censored

    Energy Technology Data Exchange (ETDEWEB)

    Nungesser, Ernesto, E-mail: ernesto.nungesser@aei.mpg.d [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, 14476 Potsdam (Germany)

    2010-05-01

    A sketch of the proof of strong cosmic censorship is presented for a class of solutions of the Einstein-Maxwell equations, those with polarized Gowdy symmetry. A key element of the argument is the observation that by means of a suitable choice of variables the central equations in this problem can be written in a form where they are identical to the central equations for general (i.e. non-polarized) vacuum Gowdy spacetimes. Using this it is seen that the results of Ringstroem on strong cosmic censorship in the vacuum case have implications for the Einstein-Maxwell case. Working out the geometrical meaning of these analytical results leads to the main conclusion.

  8. Twistor geometry

    NARCIS (Netherlands)

    van den Broek, P.M.

    1984-01-01

    The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.

  9. Non-commutative geometry and supersymmetry 2

    International Nuclear Information System (INIS)

    Hussain, F.; Thompson, G.

    1991-05-01

    Following the general construction of supersymmetric models, the model based on the idea of non-commutative geometry is formulated as a Yang-Mills theory of the graded Lie algebra U(2/1) over a graded space-time manifold. 4 refs

  10. Ambient cosmology and spacetime singularities

    International Nuclear Information System (INIS)

    Antoniadis, Ignatios; Cotsakis, Spiros

    2015-01-01

    We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary. (orig.)

  11. Ambient cosmology and spacetime singularities

    CERN Document Server

    Antoniadis, Ignatios

    2015-01-01

    We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary.

  12. Quantum physics, relativity and complex spacetime towards a new synthesis

    CERN Document Server

    Kaiser, Gerald

    1990-01-01

    A new synthesis of the principles of quantum mechanics and Relativity is proposed in the context of complex differential geometry. The positivity of the energy implies that wave functions and fields can be extended to complex spacetime, and it is shown that this complexification has a solid physical interpretation as an extended phase space. The extended fields can be said to be realistic wavelet transforms of the original fields. A new, algebraic theory of wavelets is developed.

  13. Extended Rindler spacetime and a new multiverse structure

    Science.gov (United States)

    Araya, Ignacio J.; Bars, Itzhak

    2018-04-01

    This is the first of a series of papers in which we use analyticity properties of quantum fields propagating on a spacetime to uncover a new multiverse geometry when the classical geometry has horizons and/or singularities. The nature and origin of the "multiverse" idea presented in this paper, that is shared by the fields in the standard model coupled to gravity, are different from other notions of a multiverse. Via analyticity we are able to establish definite relations among the universes. In this paper we illustrate these properties for the extended Rindler space, while black hole spacetime and the cosmological geometry of mini-superspace (see Appendix B) will appear in later papers. In classical general relativity, extended Rindler space is equivalent to flat Minkowski space; it consists of the union of the four wedges in (u ,v ) light-cone coordinates as in Fig. 1. In quantum mechanics, the wavefunction is an analytic function of (u ,v ) that is sensitive to branch points at the horizons u =0 or v =0 , with branch cuts attached to them. The wave function is uniquely defined by analyticity on an infinite number of sheets in the cut analytic (u ,v ) spacetime. This structure is naturally interpreted as an infinite stack of identical Minkowski geometries, or "universes", connected to each other by analyticity across branch cuts, such that each sheet represents a different Minkowski universe when (u ,v ) are analytically continued to the real axis on any sheet. We show in this paper that, in the absence of interactions, information does not flow from one Rindler sheet to another. By contrast, for an eternal black hole spacetime, which may be viewed as a modification of Rindler that includes gravitational interactions, analyticity shows how information is "lost" due to a flow to other universes, enabled by an additional branch point and cut due to the black hole singularity.

  14. Tracing light propagation to the intrinsic accuracy of spacetime geometry

    International Nuclear Information System (INIS)

    Crosta, Mariateresa

    2011-01-01

    Advancement in astronomical observations requires codification of light propagation and of the processes of its physical measurement at a high level of accuracy. This could unveil a new window of several subtle relativistic effects suffered by light while propagating. Indeed, light modeling and its subsequent detection should be conceived in a fully relativistic context, in order to interpret the outcome of the observing process in accordance with the geometrical environment affecting light propagation itself and the precepts of measurement. This paper deals with the complexity of such a topic by showing how the geometrical framework of RAMOD, a relativistic model initially developed for astrometric observations in the visible, constitutes an appropriate environment for back-tracing photons. Through gauging the energy content of a given gravitationally bound system, the geometrical aspects that match the required accuracy of present and future observational capabilities are evidenced. Then, by comparing different formulations of the null geodesic, their domain of validity within the given geometrical scheme is refined. Finally, by proving its ability in retrieving recent literature cases, RAMOD is promoted as a measurement-based general relativistic method for any present and future advancement in the light-tracing problem. (paper)

  15. Spacetime thermodynamics in the presence of torsion

    Science.gov (United States)

    Dey, Ramit; Liberati, Stefano; Pranzetti, Daniele

    2017-12-01

    It was shown by Jacobson in 1995 that the Einstein equation can be derived as a local constitutive equation for an equilibrium spacetime thermodynamics. With the aim to understand if such thermodynamical description is an intrinsic property of gravitation, many attempts have been made so far to generalize this treatment to a broader class of gravitational theories. Here we consider the case of the Einstein-Cartan theory as a prototype of theories with nonpropagating torsion. In doing so, we study the properties of Killing horizons in the presence of torsion, establish the notion of local causal horizon in Riemann-Cartan spacetimes, and derive the generalized Raychaudhuri equation for these kinds of geometries. Then, starting with the entropy that can be associated to these local causal horizons, we derive the Einstein-Cartan equation by implementing the Clausius equation. We outline two ways of proceeding with the derivation depending on whether we take torsion as a geometric field or as a matter field. In both cases we need to add internal entropy production terms to the Clausius equation as the shear and twist cannot be taken to be 0 a priori for our setup. This fact implies the necessity of a nonequilibrium thermodynamics treatment for the local causal horizon. Furthermore, it implies that a nonzero twist at the horizon in general contributes to the Hartle-Hawking tidal heating for black holes with possible implications for future observations.

  16. A Geometry in which all Triangles are Isosceles

    Indian Academy of Sciences (India)

    The real number line has a geometry which is Euclidean. Imagine a small pygmy tortoise trying to travel along a very long path; assume that its destination is at a very ..... are: geometry of space-time at small distances; classi- cal and quantum ...

  17. Relative-locality effects in Snyder spacetime

    International Nuclear Information System (INIS)

    Mignemi, S.; Samsarov, A.

    2017-01-01

    Most models of noncommutative geometry and doubly special relativity suggest that the principle of absolute locality should be replaced by the milder notion of relative locality. In particular, they predict the occurrence of a delay in the time of arrival of massless particle of different energies emitted by a distant observer. In this letter, we show that this is not the case with Snyder spacetime, essentially because the Lorentz invariance is not deformed in this case. Distant observers may however measure different times of flight for massive particles. - Highlights: • We discuss the dynamics of the Snyder model from the point of view of relative locality. • We show that no time delay is present for particles emitted by distant observers. • We ascribe this fact to the Lorentz invariance of the model. • Distant observers may however measure different times of flight for massive particle.

  18. Relative-locality effects in Snyder spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Mignemi, S., E-mail: smignemi@unica.it [Dipartimento di Matematica e Informatica, Università di Cagliari, viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy); Samsarov, A., E-mail: andjelo.samsarov@irb.hr [Rudjer Bošković Institute, Bijenička cesta 54, 10002 Zagreb (Croatia)

    2017-05-18

    Most models of noncommutative geometry and doubly special relativity suggest that the principle of absolute locality should be replaced by the milder notion of relative locality. In particular, they predict the occurrence of a delay in the time of arrival of massless particle of different energies emitted by a distant observer. In this letter, we show that this is not the case with Snyder spacetime, essentially because the Lorentz invariance is not deformed in this case. Distant observers may however measure different times of flight for massive particles. - Highlights: • We discuss the dynamics of the Snyder model from the point of view of relative locality. • We show that no time delay is present for particles emitted by distant observers. • We ascribe this fact to the Lorentz invariance of the model. • Distant observers may however measure different times of flight for massive particle.

  19. Fermions in curved spacetimes

    Energy Technology Data Exchange (ETDEWEB)

    Lippoldt, Stefan

    2016-01-21

    In this thesis we study a formulation of Dirac fermions in curved spacetime that respects general coordinate invariance as well as invariance under local spin base transformations. We emphasize the advantages of the spin base invariant formalism both from a conceptual as well as from a practical viewpoint. This suggests that local spin base invariance should be added to the list of (effective) properties of (quantum) gravity theories. We find support for this viewpoint by the explicit construction of a global realization of the Clifford algebra on a 2-sphere which is impossible in the spin-base non-invariant vielbein formalism. The natural variables for this formulation are spacetime-dependent Dirac matrices subject to the Clifford-algebra constraint. In particular, a coframe, i.e. vielbein field is not required. We disclose the hidden spin base invariance of the vielbein formalism. Explicit formulas for the spin connection as a function of the Dirac matrices are found. This connection consists of a canonical part that is completely fixed in terms of the Dirac matrices and a free part that can be interpreted as spin torsion. The common Lorentz symmetric gauge for the vielbein is constructed for the Dirac matrices, even for metrics which are not linearly connected. Under certain criteria, it constitutes the simplest possible gauge, demonstrating why this gauge is so useful. Using the spin base formulation for building a field theory of quantized gravity and matter fields, we show that it suffices to quantize the metric and the matter fields. This observation is of particular relevance for field theory approaches to quantum gravity, as it can serve for a purely metric-based quantization scheme for gravity even in the presence of fermions. Hence, in the second part of this thesis we critically examine the gauge, and the field-parametrization dependence of renormalization group flows in the vicinity of non-Gaussian fixed points in quantum gravity. While physical

  20. Molecular geometry

    CERN Document Server

    Rodger, Alison

    1995-01-01

    Molecular Geometry discusses topics relevant to the arrangement of atoms. The book is comprised of seven chapters that tackle several areas of molecular geometry. Chapter 1 reviews the definition and determination of molecular geometry, while Chapter 2 discusses the unified view of stereochemistry and stereochemical changes. Chapter 3 covers the geometry of molecules of second row atoms, and Chapter 4 deals with the main group elements beyond the second row. The book also talks about the complexes of transition metals and f-block elements, and then covers the organometallic compounds and trans

  1. Optical geometry

    International Nuclear Information System (INIS)

    Robinson, I.; Trautman, A.

    1988-01-01

    The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem

  2. Fermion fields in η-ξ spacetime

    International Nuclear Information System (INIS)

    Gui, Y.

    1992-01-01

    Fermion fields in η-ζ spacetime are discussed. By the path-integral formulation of quantum field theory, we show that the (zero-temperature) Green's functions for Dirac fields on the Euclidean section in η-ζ spacetime are equal to the imaginary-time thermal Green's functions in Minkowski spacetime, and that the (zero-temperature) Green's functions on the Lorentzian section in η-ζ spacetime correspond to the real-time thermal Green's functions in Minkowski spacetime. The antiperiodicity of fermion fields in η-ζ spacetime originates from Lorentz transformation properties of the fields

  3. Vacuum polarization in curved spacetime

    International Nuclear Information System (INIS)

    Guy, R.W.

    1979-01-01

    A necessary step in the process of understanding the quantum theory of gravity is the calculation of the stress-energy tensor of quantized fields in curved space-times. The determination of the stress tensor, a formally divergent object, is made possible in this dissertation by utilizing the zeta-function method of regularization and renormalization. By employing this scheme's representation of the renormalized effective action functional, an expression of the stress tensor for a massless, conformally invariant scalar field, first given by DeWitt, is derived. The form of the renormalized stress tensor is first tested in various examples of flat space-times. It is shown to vanish in Minkowski space and to yield the accepted value of the energy density in the Casimir effect. Next, the stress tensor is calculated in two space-times of constant curvature, the Einstein universe and the deSitter universe, and the results are shown to agree with those given by an expression of the stress tensor that is valid in conformally flat space-times. This work culminates in the determination of the stress tensor on the horizon of a Schwarzschild black hole. This is accomplished by approximating the radial part of the eigen-functions and the metric in the vicinity of the horizon. The stress tensor at this level approximation is found to be pure trace. The approximated forms of the Schwarzschild metric describes a conformally flat space-time that possesses horizons

  4. The BTZ black hole as a Lorentz-flat geometry

    Energy Technology Data Exchange (ETDEWEB)

    Alvarez, Pedro D., E-mail: alvarez@physics.ox.ac.uk [Rudolf Peierls Centre for Theoretical Physics, University of Oxford (United Kingdom); Pais, Pablo, E-mail: pais@cecs.cl [Centro de Estudios Científicos (CECs), Av. Arturo Prat 514, Valdivia (Chile); Universidad Andrés Bello, Av. República 440, Santiago (Chile); Rodríguez, Eduardo, E-mail: eduarodriguezsal@unal.edu.co [Departamento de Matemática y Física Aplicadas, Universidad Católica de la Santísima Concepción, Concepción (Chile); Salgado-Rebolledo, Patricio, E-mail: pasalgado@udec.cl [Centro de Estudios Científicos (CECs), Av. Arturo Prat 514, Valdivia (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050 Bruxelles (Belgium); Zanelli, Jorge, E-mail: z@cecs.cl [Centro de Estudios Científicos (CECs), Av. Arturo Prat 514, Valdivia (Chile); Universidad Andrés Bello, Av. República 440, Santiago (Chile)

    2014-11-10

    It is shown that 2+1 dimensional anti-de Sitter spacetimes are Lorentz-flat. This means, in particular, that any simply-connected patch of the BTZ black hole solution can be endowed with a Lorentz connection that is locally pure gauge. The result can be naturally extended to a wider class of black hole geometries and point particles in three-dimensional spacetime.

  5. IDEAL characterization of isometry classes of FLRW and inflationary spacetimes

    Science.gov (United States)

    Canepa, Giovanni; Dappiaggi, Claudio; Khavkine, Igor

    2018-02-01

    In general relativity, an IDEAL (Intrinsic, Deductive, Explicit, ALgorithmic) characterization of a reference spacetime metric g 0 consists of a set of tensorial equations T[g]  =  0, constructed covariantly out of the metric g, its Riemann curvature and their derivatives, that are satisfied if and only if g is locally isometric to the reference spacetime metric g 0. The same notion can be extended to also include scalar or tensor fields, where the equations T[g, φ]=0 are allowed to also depend on the extra fields ϕ. We give the first IDEAL characterization of cosmological FLRW spacetimes, with and without a dynamical scalar (inflaton) field. We restrict our attention to what we call regular geometries, which uniformly satisfy certain identities or inequalities. They roughly split into the following natural special cases: constant curvature spacetime, Einstein static universe, and flat or curved spatial slices. We also briefly comment on how the solution of this problem has implications, in general relativity and inflation theory, for the construction of local gauge invariant observables for linear cosmological perturbations and for stability analysis.

  6. Space-time structure and the origin of physical law

    International Nuclear Information System (INIS)

    Green, M.A.

    1980-01-01

    In the first part of this theses the author adopts a traditional world view, with space-time a topologically simple geometrical manifold, matter being represented by smooth classical fields, and space a Riemannian submanifold of space-time. It is shown how to characterize the space-time geometry in terms of fields defined on three-dimensional space. Accepting a finite number of the fields induced on space as independent initial data, a procedure is given for constructing dynamical and constraint equations which will propagate these fields forward in time. When the initial data are restricted to include only the hypersurface metric and the extrinsic curvature, the resulting equations combine to form the Einstein gravitational field equations with the cosmological term. The synthesis of gravitational and quantum physics is approached by proposing that the objective world underlying the perceived world is a four-dimensional topological manifold w, with no physically significant field structure and an unconstrianed and complex global topology. Conventional space-time is then a topologically simple replacement manifold for w. A preliminary outline of the correspondence is presented, based on a similarity between a natural graphical representation of 2 and the Feynman graphs of quantum field theory

  7. Architectural geometry

    KAUST Repository

    Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes

    2014-01-01

    Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

  8. Architectural geometry

    KAUST Repository

    Pottmann, Helmut

    2014-11-26

    Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

  9. Spectral dimension of quantum geometries

    International Nuclear Information System (INIS)

    Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes

    2014-01-01

    The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them. (paper)

  10. Beautiful geometry

    CERN Document Server

    Maor, Eli

    2014-01-01

    If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur

  11. Quantum mechanics on noncommutative spacetime

    International Nuclear Information System (INIS)

    Calmet, Xavier; Selvaggi, Michele

    2006-01-01

    We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a nonrelativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical noncommutative spacetime. An interesting new feature of quantum mechanics formulated on a noncommutative spacetime is an intrinsic electric dipole moment. We note, however, that noncommutative intrinsic dipole moments are not observable in present experiments searching for an electric dipole moment of leptons or nuclei such as the neutron since they are spin independent. These experiments are sensitive to the energy difference between two states and the noncommutative effect thus cancels out. Bounds on the noncommutative scale found in the literature relying on such intrinsic electric dipole moments are thus incorrect

  12. The geometry of special relativity

    International Nuclear Information System (INIS)

    Parizet, Jean

    2008-01-01

    This book for students in mathematics or physics shows the interest of geometry to understand special relativity as a consequence of invariance of Maxwell equations and of constancy of the speed of light. Space-time is actually provided with a geometrical structure and a physical interpretation: at each observer are associated his own time and his own physical space in which occur events he is concerned with. This leads to a natural approach to special relativity. The Lorentz group and its algebra are then studied by using matrices and the Pauli algebra. Quaternions are also addressed

  13. Hyperunified field theory and gravitational gauge-geometry duality

    International Nuclear Information System (INIS)

    Wu, Yue-Liang

    2018-01-01

    A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D h - 1). The dimension D h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)

  14. Hyperunified field theory and gravitational gauge-geometry duality

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Yue-Liang [International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), Beijing (China); Chinese Academy of Sciences, Institute of Theoretical Physics, Beijing (China); University of Chinese Academy of Sciences (UCAS), Beijing (China)

    2018-01-15

    A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D{sub h} - 1). The dimension D{sub h} of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)

  15. Hyperunified field theory and gravitational gauge-geometry duality

    Science.gov (United States)

    Wu, Yue-Liang

    2018-01-01

    A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D_h-1). The dimension D_h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond.

  16. Cosmic microwave background and inflation in multi-fractional spacetimes

    Energy Technology Data Exchange (ETDEWEB)

    Calcagni, Gianluca [Instituto de Estructura de la Materia,CSIC, Serrano 121, 28006 Madrid (Spain); Kuroyanagi, Sachiko [Department of Physics, Nagoya University,Chikusa, Nagoya 464-8602 (Japan); Institute for Advanced Research, Nagoya University,Chikusa, Nagoya 464-8602 (Japan); Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science,1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan)

    2016-08-18

    We use FIRAS and Planck 2015 data to place observational bounds on inflationary scenarios in multi-fractional spacetimes with q-derivatives. While a power-law expansion in the geometric time coordinate is subject to the usual constraints from the tensor-to-scalar ratio, model-independent best fits of the black-body and scalar spectra yield upper limits on the free parameters of the multi-fractal measure of the theory. When the measure describing the fractal spacetime geometry is non-oscillating, information on the CMB black-body spectrum places constraints on the theory independent from but weaker than those obtained from the Standard Model, astrophysical gravitational waves and gamma-ray bursts (GRBs). When log oscillations are included and the measure describes a discrete fractal spacetime at microscopic scales, we obtain the first observational constraints on the amplitudes of such oscillations and find, in general, strong constraints on the multi-scale geometry and on the dimension of space. These results complete the scan and reduction of the parameter space of the theory. Black-body bounds are obtained also for the theory with weighted derivatives.

  17. Cosmic microwave background and inflation in multi-fractional spacetimes

    International Nuclear Information System (INIS)

    Calcagni, Gianluca; Kuroyanagi, Sachiko; Tsujikawa, Shinji

    2016-01-01

    We use FIRAS and Planck 2015 data to place observational bounds on inflationary scenarios in multi-fractional spacetimes with q-derivatives. While a power-law expansion in the geometric time coordinate is subject to the usual constraints from the tensor-to-scalar ratio, model-independent best fits of the black-body and scalar spectra yield upper limits on the free parameters of the multi-fractal measure of the theory. When the measure describing the fractal spacetime geometry is non-oscillating, information on the CMB black-body spectrum places constraints on the theory independent from but weaker than those obtained from the Standard Model, astrophysical gravitational waves and gamma-ray bursts (GRBs). When log oscillations are included and the measure describes a discrete fractal spacetime at microscopic scales, we obtain the first observational constraints on the amplitudes of such oscillations and find, in general, strong constraints on the multi-scale geometry and on the dimension of space. These results complete the scan and reduction of the parameter space of the theory. Black-body bounds are obtained also for the theory with weighted derivatives.

  18. Geometry as an aspect of dynamics

    International Nuclear Information System (INIS)

    Videira, A.L.L.; Barros, A.L.R.; Fernandes, N.C.

    1982-07-01

    Contrary to the predominant way of doing physics, it is shown that the geometric structure of a general differentiable space-time manifold can be determined by means of the introduction in that manifold of a minimal set of fundamental dynamical quantities associated to a free particle endowed with the fundamental property of momentum. Thus, general relativistic physics implies a general pseudo-Riemannian geometry, whereas the physics of the special theory of relativity is tied up with Minkowski space-time, and Newtonian dynamics is bound to Newtonian space-time. While in the relativistic instance, the Riemannian character of the manifold is basically fixed by means only of the Hamiltonian state function of the free particle (its kynetic energy), in the latter case, it has to resort, perhaps not unexpectedly, to the two dynamical entities mass and energy, separately. (Author) [pt

  19. Geometry as an aspect of dynamics

    International Nuclear Information System (INIS)

    Videira, A.L.L.; Barros, A.L.R.; Fernandes, N.C.

    1983-12-01

    Contrary to the predominant way of doing physics, it is shown that the geometric structure of a general differentiable space-time manifold can be determined by means of the introduction in that manifold of a minimal set of fundamental dynamical quantities associated to a particle endowed with the fundamental property of covariant momentum. Thus, general relativistic physics implies a general pseudo-Riemannian geometry, whereas the physics of the special theory of relativity is tied up with Minkowski space-time, and Newtonian dynamics is bound to Newtonian space-time. While in the relativistic instance, the Riemannian character of the manifold is basically fixed by means only of the Hamiltonian state function of the particle (its energy), in the latter case, one have to resort, perhaps not unexpectedly, to the two dynamical entities mass energy, separately. (Author) [pt

  20. Analytische Geometrie

    Science.gov (United States)

    Kemnitz, Arnfried

    Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.

  1. Algebraic geometry

    CERN Document Server

    Lefschetz, Solomon

    2005-01-01

    An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.

  2. Information geometry

    CERN Document Server

    Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz

    2017-01-01

    The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...

  3. Observable Zitterbewegung in curved spacetimes

    Science.gov (United States)

    Kobakhidze, Archil; Manning, Adrian; Tureanu, Anca

    2016-06-01

    Zitterbewegung, as it was originally described by Schrödinger, is an unphysical, non-observable effect. We verify whether the effect can be observed in non-inertial reference frames/curved spacetimes, where the ambiguity in defining particle states results in a mixing of positive and negative frequency modes. We explicitly demonstrate that such a mixing is in fact necessary to obtain the correct classical value for a particle's velocity in a uniformly accelerated reference frame, whereas in cosmological spacetime a particle does indeed exhibit Zitterbewegung.

  4. Observable Zitterbewegung in curved spacetimes

    Energy Technology Data Exchange (ETDEWEB)

    Kobakhidze, Archil, E-mail: archilk@physics.usyd.edu.au [ARC Centre of Excellence for Particle Physics at the Terascale, School of Physics, The University of Sydney, NSW 2006 (Australia); Manning, Adrian, E-mail: a.manning@physics.usyd.edu.au [ARC Centre of Excellence for Particle Physics at the Terascale, School of Physics, The University of Sydney, NSW 2006 (Australia); Tureanu, Anca, E-mail: anca.tureanu@helsinki.fi [Department of Physics, University of Helsinki, P.O. Box 64, 00014 Helsinki (Finland)

    2016-06-10

    Zitterbewegung, as it was originally described by Schrödinger, is an unphysical, non-observable effect. We verify whether the effect can be observed in non-inertial reference frames/curved spacetimes, where the ambiguity in defining particle states results in a mixing of positive and negative frequency modes. We explicitly demonstrate that such a mixing is in fact necessary to obtain the correct classical value for a particle's velocity in a uniformly accelerated reference frame, whereas in cosmological spacetime a particle does indeed exhibit Zitterbewegung.

  5. Spacetime and gravitation.

    Science.gov (United States)

    Kopczyński, W.; Trautman, A.

    This book is a revised translation of the Polish original "Czasoprzestrzeń i grawitacja", Warszawa (Poland), Państwowe Wydawnictwo Naukowe, 1984. Ideas about space and time are at the root of one's understanding of nature, both at the intuitive level of everyday experience and in the framework of sophisticated physical theories. These ideas have led to the development of geometry and its applications to physics. The contemporary physical theory of space and time, including its extention to the phenomena of gravitation, is Einstein's theory of relativity. The book is a short introduction to this theory. A great deal of emphasis is given to the geometrical aspects of relativity theory and its comparison with the Newtonian view of the world. There are short chapters on the origins of Einstein's theory, gravitational waves, cosmology, spinors and the Einstein-Cartan theory.

  6. Quantum universe on extremely small space-time scales

    International Nuclear Information System (INIS)

    Kuzmichev, V.E.; Kuzmichev, V.V.

    2010-01-01

    The semiclassical approach to the quantum geometrodynamical model is used for the description of the properties of the Universe on extremely small space-time scales. Under this approach, the matter in the Universe has two components of the quantum nature which behave as antigravitating fluids. The first component does not vanish in the limit h → 0 and can be associated with dark energy. The second component is described by an extremely rigid equation of state and goes to zero after the transition to large spacetime scales. On small space-time scales, this quantum correction turns out to be significant. It determines the geometry of the Universe near the initial cosmological singularity point. This geometry is conformal to a unit four-sphere embedded in a five-dimensional Euclidean flat space. During the consequent expansion of the Universe, when reaching the post-Planck era, the geometry of the Universe changes into that conformal to a unit four-hyperboloid in a five-dimensional Lorentzsignatured flat space. This agrees with the hypothesis about the possible change of geometry after the origin of the expanding Universe from the region near the initial singularity point. The origin of the Universe can be interpreted as a quantum transition of the system from a region in the phase space forbidden for the classical motion, but where a trajectory in imaginary time exists, into a region, where the equations of motion have the solution which describes the evolution of the Universe in real time. Near the boundary between two regions, from the side of real time, the Universe undergoes almost an exponential expansion which passes smoothly into the expansion under the action of radiation dominating over matter which is described by the standard cosmological model.

  7. Conformal Killing vectors in Robertson-Walker spacetimes

    International Nuclear Information System (INIS)

    Maartens, R.; Maharaj, S.d.

    1986-01-01

    It is well known that Robertson-Walker spacetimes admit a conformal Killingl vector normal to the spacelike homogeneous hypersurfaces. Because these spacetimes are conformally flat, there are a further eight conformal Killing vectors, which are neither normal nor tangent to the homogeneous hypersurfaces. The authors find these further conformal Killing vectors and the Lie algebra of the full G 15 of conformal motions. Conditions on the metric scale factor are determined which reduce some of the conformal Killing vectors to homothetic Killing vectors or Killing vectors, allowing one to regain in a unified way the known special geometries. The non-normal conformal Killing vectors provide a counter-example to show that conformal motions do not, in general, map a fluid flow conformally. These non-normal vectors are also used to find the general solution of the null geodesic equation and photon Liouville equation. (author)

  8. Observables and dispersion relations in κ-Minkowski spacetime

    Science.gov (United States)

    Aschieri, Paolo; Borowiec, Andrzej; Pachoł, Anna

    2017-10-01

    We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on noncommutative spaces are derived from a quantum Hodge star operator. This general noncommutative geometry construction is then exemplified in the case of κ-Minkowski spacetime. The corresponding quantum Poincaré-Weyl Lie algebra of in-finitesimal translations, rotations and dilatations is obtained. The d'Alembert wave operator coincides with the quadratic Casimir of quantum translations and it is deformed as in Deformed Special Relativity theories. Also momenta (infinitesimal quantum translations) are deformed, and correspondingly the Einstein-Planck relation and the de Broglie one. The energy-momentum relations (dispersion relations) are consequently deduced. These results complement those of the phenomenological literature on the subject.

  9. On the differentiability of space-time

    International Nuclear Information System (INIS)

    Clarke, C.J.S.

    1977-01-01

    It is shown that the differentiability of a space-time is implied by that of its Riemann tensor, assuming a priori only boundedness of the first derivations of the metric. Consequently all the results on space-time singularities proved in earlier papers by the author hold true in C 2- space-times. (author)

  10. Divergence, spacetime dimension and fractal structure

    International Nuclear Information System (INIS)

    Nakamura, Hiroshi

    2000-01-01

    With a Cantor spacetime in mind, we assume the dimension of spacetime to be slightly smaller than four. Within the framework of QED, this dimension can be determined by calculating Feynman diagrams. We infer that the dimension of spacetime may be influenced by holes in space. (author)

  11. Physical meaning of the optical reference geometry

    International Nuclear Information System (INIS)

    Abramowicz, M.A.

    1990-09-01

    I show that contrary to a popular misconception the optical reference geometry, introduced a few years ago as a formally possible metric of a 3-space corresponding to a static spacetime, is quite satisfactory also from the physical point of view. The optical reference geometry has a clear physical meaning, as it may be constructed experimentally by measuring light round travel time between static observers. Distances and directions in the optical reference geometry are more strongly connected to experiment than distances and directions in the widely used directly projected metric (discussed e.g. in Landau and Lifshitz textbook. In addition, the optical reference geometry is more natural and convenient than the directly projected one in application to dynamics. In the optical geometry dynamical behaviour of matter is described by concepts and formulae identical to those well known in Newtonian dynamics on a given two dimensional (curved) surface. (author). 22 refs

  12. Distributed space-time coding

    CERN Document Server

    Jing, Yindi

    2014-01-01

    Distributed Space-Time Coding (DSTC) is a cooperative relaying scheme that enables high reliability in wireless networks. This brief presents the basic concept of DSTC, its achievable performance, generalizations, code design, and differential use. Recent results on training design and channel estimation for DSTC and the performance of training-based DSTC are also discussed.

  13. Space-Time Foam in 2D and the Sum Over Topologies

    International Nuclear Information System (INIS)

    Loll, R.; Westra, W.

    2003-01-01

    It is well-known that the sum over topologies in quantum gravity is ill-defined, due to a super-exponential growth of the number of geometries as a function of the space-time volume, leading to a badly divergent gravitational path integral. Not even in dimension 2, where a non-perturbative quantum gravity theory can be constructed explicitly from a (regularized) path integral, has this problem found a satisfactory solution. In the present work, we extend a previous 2d Lorentzian path integral, regulated in terms of Lorentzian random triangulations, to include space-times with an arbitrary number of handles. We show that after the imposition of physically motivated causality constraints, the combined sum over geometries and topologies is well-defined and possesses a continuum limit which yields a concrete model of space-time foam in two dimensions. (author)

  14. Can Topology and Geometry be Measured by an Operator Measurement in Quantum Gravity?

    Science.gov (United States)

    Berenstein, David; Miller, Alexandra

    2017-06-30

    In the context of Lin-Lunin-Maldacena geometries, we show that superpositions of classical coherent states of trivial topology can give rise to new classical limits where the topology of spacetime has changed. We argue that this phenomenon implies that neither the topology nor the geometry of spacetime can be the result of an operator measurement. We address how to reconcile these statements with the usual semiclassical analysis of low energy effective field theory for gravity.

  15. Analytic geometry

    CERN Document Server

    Burdette, A C

    1971-01-01

    Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st

  16. Geometry Revealed

    CERN Document Server

    Berger, Marcel

    2010-01-01

    Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,

  17. Vector geometry

    CERN Document Server

    Robinson, Gilbert de B

    2011-01-01

    This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom

  18. Noncommutative geometry

    CERN Document Server

    Connes, Alain

    1994-01-01

    This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat

  19. Non-Euclidean spacetime structure and the two-slit experiment

    International Nuclear Information System (INIS)

    El Naschie, M.S.

    2005-01-01

    A simple mathematical model for the two-slit experiment is given to account for the wave-particle duality. Subsequently, the various solutions are interpreted via the experimental evidence as a property of the underlying non-Euclidean spacetime topology and geometry at the quantum level

  20. The science of space-time

    International Nuclear Information System (INIS)

    Raine, D.J.; Heller, M.

    1981-01-01

    Analyzing the development of the structure of space-time from the theory of Aristotle to the present day, the present work attempts to sketch a science of relativistic mechanics. The concept of relativity is discussed in relation to the way in which space-time splits up into space and time, and in relation to Mach's principle concerning the relativity of inertia. Particular attention is given to the following topics: Aristotelian dynamics Copernican kinematics Newtonian dynamics the space-time of classical dynamics classical space-time in the presence of gravity the space-time of special relativity the space-time of general relativity solutions and problems in general relativity Mach's principle and the dynamics of space-time theories of inertial mass the integral formation of general relativity and the frontiers of relativity

  1. Pre-Big Bang, space-time structure, asymptotic Universe

    Directory of Open Access Journals (Sweden)

    Gonzalez-Mestres Luis

    2014-04-01

    Full Text Available Planck and other recent data in Cosmology and Particle Physics can open the way to controversial analyses concerning the early Universe and its possible ultimate origin. Alternatives to standard cosmology include pre-Big Bang approaches, new space-time geometries and new ultimate constituents of matter. Basic issues related to a possible new cosmology along these lines clearly deserve further exploration. The Planck collaboration reports an age of the Universe t close to 13.8 Gyr and a present ratio H between relative speeds and distances at cosmic scale around 67.3 km/s/Mpc. The product of these two measured quantities is then slightly below 1 (about 0.95, while it can be exactly 1 in the absence of matter and cosmological constant in patterns based on the spinorial space-time we have considered in previous papers. In this description of space-time we first suggested in 1996-97, the cosmic time t is given by the modulus of a SU(2 spinor and the Lundmark-Lemaître-Hubble (LLH expansion law turns out to be of purely geometric origin previous to any introduction of standard matter and relativity. Such a fundamental geometry, inspired by the role of half-integer spin in Particle Physics, may reflect an equilibrium between the dynamics of the ultimate constituents of matter and the deep structure of space and time. Taking into account the observed cosmic acceleration, the present situation suggests that the value of 1 can be a natural asymptotic limit for the product H t in the long-term evolution of our Universe up to possible small corrections. In the presence of a spinorial space-time geometry, no ad hoc combination of dark matter and dark energy would in any case be needed to get an acceptable value of H and an evolution of the Universe compatible with observation. The use of a spinorial space-time naturally leads to unconventional properties for the space curvature term in Friedmann-like equations. It therefore suggests a major modification of

  2. Projective Geometry

    Indian Academy of Sciences (India)

    mathematicians are trained to use very precise language, and so find it hard to simplify and state .... thing. If you take a plane on which there are two such triangles which enjoy the above ... within this geometry to simplify things if needed.

  3. Geometry -----------~--------------RESONANCE

    Indian Academy of Sciences (India)

    Parallel: A pair of lines in a plane is said to be parallel if they do not meet. Mathematicians were at war ... Subsequently, Poincare, Klein, Beltrami and others refined non-. Euclidean geometry. ... plane divides the plane into two half planes and.

  4. Spherically symmetric static spacetimes in vacuum f(T) gravity

    International Nuclear Information System (INIS)

    Ferraro, Rafael; Fiorini, Franco

    2011-01-01

    We show that Schwarzschild geometry remains as a vacuum solution for those four-dimensional f(T) gravitational theories behaving as ultraviolet deformations of general relativity. In the gentler context of three-dimensional gravity, we also find that the infrared-deformed f(T) gravities, like the ones used to describe the late cosmic speed up of the Universe, have as the circularly symmetric vacuum solution a Deser-de Sitter or a Banados, Teitelboim and Zanelli-like spacetime with an effective cosmological constant depending on the infrared scale present in the function f(T).

  5. Gravastars with higher dimensional spacetimes

    Science.gov (United States)

    Ghosh, Shounak; Ray, Saibal; Rahaman, Farook; Guha, B. K.

    2018-07-01

    We present a new model of gravastar in the higher dimensional Einsteinian spacetime including Einstein's cosmological constant Λ. Following Mazur and Mottola (2001, 2004) we design the star with three specific regions, as follows: (I) Interior region, (II) Intermediate thin spherical shell and (III) Exterior region. The pressure within the interior region is equal to the negative matter density which provides a repulsive force over the shell. This thin shell is formed by ultra relativistic plasma, where the pressure is directly proportional to the matter-energy density which does counter balance the repulsive force from the interior whereas the exterior region is completely vacuum assumed to be de Sitter spacetime which can be described by the generalized Schwarzschild solution. With this specification we find out a set of exact non-singular and stable solutions of the gravastar which seems physically very interesting and reasonable.

  6. Energy conditions and spacetime singularities

    International Nuclear Information System (INIS)

    Tipler, F.J.

    1978-01-01

    In this paper, a number of theorems are proven which collectively show that singularities will occur in spacetime under weaker energy conditions than the strong energy condition. In particular, the Penrose theorem, which uses only the weak energy condition but which applies only to open universes, is extended to all closed universes which have a Cauchy surface whose universal covering manifold is not a three-sphere. Furthermore, it is shown that the strong energy condition in the Hawking-Penrose theorem can be replaced by the weak energy condition and the assumption that the strong energy condition holds only on the average. In addition, it is demonstrated that if the Universe is closed, then the existence of singularities follows from the averaged strong energy condition alone. It is argued that any globally hyperbolic spacetime which satisfies the weak energy condition and which contains a black hole must be null geodesically incomplete

  7. Noncommutative Geometry, Quantum Fields and Motives

    CERN Document Server

    Connes, Alain

    2007-01-01

    The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book dea

  8. Thermal geometry from CFT at finite temperature

    Directory of Open Access Journals (Sweden)

    Wen-Cong Gan

    2016-09-01

    Full Text Available We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking–Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.

  9. Thermal geometry from CFT at finite temperature

    Energy Technology Data Exchange (ETDEWEB)

    Gan, Wen-Cong, E-mail: ganwencong@gmail.com [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China); Shu, Fu-Wen, E-mail: shufuwen@ncu.edu.cn [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China); Wu, Meng-He, E-mail: menghewu.physik@gmail.com [Department of Physics, Nanchang University, Nanchang 330031 (China); Center for Relativistic Astrophysics and High Energy Physics, Nanchang University, Nanchang 330031 (China)

    2016-09-10

    We present how the thermal geometry emerges from CFT at finite temperature by using the truncated entanglement renormalization network, the cMERA. For the case of 2d CFT, the reduced geometry is the BTZ black hole or the thermal AdS as expectation. In order to determine which spacetimes prefer to form, we propose a cMERA description of the Hawking–Page phase transition. Our proposal is in agreement with the picture of the recent proposed surface/state correspondence.

  10. Freudenthal duality and generalized special geometry

    Energy Technology Data Exchange (ETDEWEB)

    Ferrara, Sergio, E-mail: sergio.ferrara@cern.ch [Physics Department, Theory Unit, CERN, CH-1211, Geneva 23 (Switzerland); INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati (Italy); Marrani, Alessio, E-mail: Alessio.Marrani@cern.ch [Physics Department, Theory Unit, CERN, CH-1211, Geneva 23 (Switzerland); Yeranyan, Armen, E-mail: ayeran@lnf.infn.it [INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati (Italy); Department of Physics, Yerevan State University, Alex Manoogian St. 1, Yerevan, 0025 (Armenia)

    2011-07-27

    Freudenthal duality, introduced in Borsten et al. (2009) and defined as an anti-involution on the dyonic charge vector in d=4 space-time dimensions for those dualities admitting a quartic invariant, is proved to be a symmetry not only of the classical Bekenstein-Hawking entropy but also of the critical points of the black hole potential. Furthermore, Freudenthal duality is extended to any generalized special geometry, thus encompassing all N>2 supergravities, as well as N=2 generic special geometry, not necessarily having a coset space structure.

  11. Ringing in de Sitter spacetime

    Directory of Open Access Journals (Sweden)

    Alex Buchel

    2018-03-01

    Full Text Available Hydrodynamics is a universal effective theory describing relaxation of quantum field theories towards equilibrium. Massive QFTs in de Sitter spacetime are never at equilibrium. We use holographic gauge theory/gravity correspondence to describe relaxation of a QFT to its Bunch–Davies vacuum — an attractor of its late-time dynamics. Specifically, we compute the analogue of the quasinormal modes describing the relaxation of a holographic toy model QFT in de Sitter.

  12. Spacetimes containing slowly evolving horizons

    International Nuclear Information System (INIS)

    Kavanagh, William; Booth, Ivan

    2006-01-01

    Slowly evolving horizons are trapping horizons that are ''almost'' isolated horizons. This paper reviews their definition and discusses several spacetimes containing such structures. These include certain Vaidya and Tolman-Bondi solutions as well as (perturbatively) tidally distorted black holes. Taking into account the mass scales and orders of magnitude that arise in these calculations, we conjecture that slowly evolving horizons are the norm rather than the exception in astrophysical processes that involve stellar-scale black holes

  13. Space-Time Quantum Imaging

    Directory of Open Access Journals (Sweden)

    Ronald E. Meyers

    2015-03-01

    Full Text Available We report on an experimental and theoretical investigation of quantum imaging where the images are stored in both space and time. Ghost images of remote objects are produced with either one or two beams of chaotic laser light generated by a rotating ground glass and two sensors measuring the reference field and bucket field at different space-time points. We further observe that the ghost images translate depending on the time delay between the sensor measurements. The ghost imaging experiments are performed both with and without turbulence. A discussion of the physics of the space-time imaging is presented in terms of quantum nonlocal two-photon analysis to support the experimental results. The theoretical model includes certain phase factors of the rotating ground glass. These experiments demonstrated a means to investigate the time and space aspects of ghost imaging and showed that ghost imaging contains more information per measured photon than was previously recognized where multiple ghost images are stored within the same ghost imaging data sets. This suggests new pathways to explore quantum information stored not only in multi-photon coincidence information but also in time delayed multi-photon interference. The research is applicable to making enhanced space-time quantum images and videos of moving objects where the images are stored in both space and time.

  14. Thermal dimension of quantum spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Amelino-Camelia, Giovanni, E-mail: amelino@roma1.infn.it [Dipartimento di Fisica, Università “La Sapienza” and Sez. Roma1 INFN, P.le A. Moro 2, 00185 Roma (Italy); Brighenti, Francesco [Theoretical Physics, Blackett Laboratory, Imperial College, London, SW7 2BZ (United Kingdom); Dipartimento di Fisica e Astronomia dell' Università di Bologna and Sez. Bologna INFN, Via Irnerio 46, 40126 Bologna (Italy); Gubitosi, Giulia [Theoretical Physics, Blackett Laboratory, Imperial College, London, SW7 2BZ (United Kingdom); Santos, Grasiele [Dipartimento di Fisica, Università “La Sapienza” and Sez. Roma1 INFN, P.le A. Moro 2, 00185 Roma (Italy)

    2017-04-10

    Recent results suggest that a crucial crossroad for quantum gravity is the characterization of the effective dimension of spacetime at short distances, where quantum properties of spacetime become significant. This is relevant in particular for various scenarios of “dynamical dimensional reduction” which have been discussed in the literature. We are here concerned with the fact that the related research effort has been based mostly on analyses of the “spectral dimension”, which involves an unphysical Euclideanization of spacetime and is highly sensitive to the off-shell properties of a theory. As here shown, different formulations of the same physical theory can have wildly different spectral dimension. We propose that dynamical dimensional reduction should be described in terms of the “thermal dimension” which we here introduce, a notion that only depends on the physical content of the theory. We analyze a few models with dynamical reduction both of the spectral dimension and of our thermal dimension, finding in particular some cases where thermal and spectral dimension agree, but also some cases where the spectral dimension has puzzling properties while the thermal dimension gives a different and meaningful picture.

  15. Riemannian geometry

    CERN Document Server

    Petersen, Peter

    2016-01-01

    Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...

  16. Special geometry

    International Nuclear Information System (INIS)

    Strominger, A.

    1990-01-01

    A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)

  17. Emergent Geometry from Entropy and Causality

    Science.gov (United States)

    Engelhardt, Netta

    In this thesis, we investigate the connections between the geometry of spacetime and aspects of quantum field theory such as entanglement entropy and causality. This work is motivated by the idea that spacetime geometry is an emergent phenomenon in quantum gravity, and that the physics responsible for this emergence is fundamental to quantum field theory. Part I of this thesis is focused on the interplay between spacetime and entropy, with a special emphasis on entropy due to entanglement. In general spacetimes, there exist locally-defined surfaces sensitive to the geometry that may act as local black hole boundaries or cosmological horizons; these surfaces, known as holographic screens, are argued to have a connection with the second law of thermodynamics. Holographic screens obey an area law, suggestive of an association with entropy; they are also distinguished surfaces from the perspective of the covariant entropy bound, a bound on the total entropy of a slice of the spacetime. This construction is shown to be quite general, and is formulated in both classical and perturbatively quantum theories of gravity. The remainder of Part I uses the Anti-de Sitter/ Conformal Field Theory (AdS/CFT) correspondence to both expand and constrain the connection between entanglement entropy and geometry. The AdS/CFT correspondence posits an equivalence between string theory in the "bulk" with AdS boundary conditions and certain quantum field theories. In the limit where the string theory is simply classical General Relativity, the Ryu-Takayanagi and more generally, the Hubeny-Rangamani-Takayanagi (HRT) formulae provide a way of relating the geometry of surfaces to entanglement entropy. A first-order bulk quantum correction to HRT was derived by Faulkner, Lewkowycz and Maldacena. This formula is generalized to include perturbative quantum corrections in the bulk at any (finite) order. Hurdles to spacetime emergence from entanglement entropy as described by HRT and its quantum

  18. General Geometry and Geometry of Electromagnetism

    OpenAIRE

    Shahverdiyev, Shervgi S.

    2002-01-01

    It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...

  19. Gravitational Lensing from a Spacetime Perspective

    Directory of Open Access Journals (Sweden)

    Perlick Volker

    2004-09-01

    Full Text Available The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature. It includes the basic equations and the relevant techniques for calculating the position, the shape, and the brightness of images in an arbitrary general-relativistic spacetime. It also includes general theorems on the classification of caustics, on criteria for multiple imaging, and on the possible number of images. The general results are illustrated with examples of spacetimes where the lensing features can be explicitly calculated, including the Schwarzschild spacetime, the Kerr spacetime, the spacetime of a straight string, plane gravitational waves, and others.

  20. Statistics from dynamics in curved spacetime

    International Nuclear Information System (INIS)

    Parker, L.; Wang, Y.

    1989-01-01

    We consider quantum fields of spin 0, 1/2, 1, 3/2, and 2 with a nonzero mass in curved spacetime. We show that the dynamical Bogolubov transformations associated with gravitationally induced particle creation imply the connection between spin and statistics: By embedding two flat regions in a curved spacetime, we find that only when one imposes Bose-Einstein statistics for an integer-spin field and Fermi-Dirac statistics for a half-integer-spin field in the first flat region is the same type of statistics propagated from the first to the second flat region. This derivation of the flat-spacetime spin-statistics theorem makes use of curved-spacetime dynamics and does not reduce to any proof given in flat spacetime. We also show in the same manner that parastatistics, up to the fourth order, are consistent with the dynamical evolution of curved spacetime

  1. Possibility of extending space-time coordinates

    International Nuclear Information System (INIS)

    Wang Yongcheng.

    1993-11-01

    It has been shown that one coordinate system can describe a whole space-time region except some supersurfaces on which there are coordinate singularities. The conditions of extending a coordinate from real field to complex field are studied. It has been shown that many-valued coordinate transformations may help us to extend space-time regions and many-valued metric functions may make one coordinate region to describe more than one space-time regions. (author). 11 refs

  2. Fermion systems in discrete space-time

    International Nuclear Information System (INIS)

    Finster, Felix

    2007-01-01

    Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure

  3. Fermion systems in discrete space-time

    Energy Technology Data Exchange (ETDEWEB)

    Finster, Felix [NWF I - Mathematik, Universitaet Regensburg, 93040 Regensburg (Germany)

    2007-05-15

    Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.

  4. Fermion Systems in Discrete Space-Time

    OpenAIRE

    Finster, Felix

    2006-01-01

    Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.

  5. Fermion systems in discrete space-time

    Science.gov (United States)

    Finster, Felix

    2007-05-01

    Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.

  6. Circular geodesic of Bardeen and Ayon-Beato-Garcia regular black-hole and no-horizon spacetimes

    Science.gov (United States)

    Stuchlík, Zdeněk; Schee, Jan

    2015-12-01

    In this paper, we study circular geodesic motion of test particles and photons in the Bardeen and Ayon-Beato-Garcia (ABG) geometry describing spherically symmetric regular black-hole or no-horizon spacetimes. While the Bardeen geometry is not exact solution of Einstein's equations, the ABG spacetime is related to self-gravitating charged sources governed by Einstein's gravity and nonlinear electrodynamics. They both are characterized by the mass parameter m and the charge parameter g. We demonstrate that in similarity to the Reissner-Nordstrom (RN) naked singularity spacetimes an antigravity static sphere should exist in all the no-horizon Bardeen and ABG solutions that can be surrounded by a Keplerian accretion disc. However, contrary to the RN naked singularity spacetimes, the ABG no-horizon spacetimes with parameter g/m > 2 can contain also an additional inner Keplerian disc hidden under the static antigravity sphere. Properties of the geodesic structure are reflected by simple observationally relevant optical phenomena. We give silhouette of the regular black-hole and no-horizon spacetimes, and profiled spectral lines generated by Keplerian rings radiating at a fixed frequency and located in strong gravity region at or nearby the marginally stable circular geodesics. We demonstrate that the profiled spectral lines related to the regular black-holes are qualitatively similar to those of the Schwarzschild black-holes, giving only small quantitative differences. On the other hand, the regular no-horizon spacetimes give clear qualitative signatures of their presence while compared to the Schwarschild spacetimes. Moreover, it is possible to distinguish the Bardeen and ABG no-horizon spacetimes, if the inclination angle to the observer is known.

  7. Differential geometry

    CERN Document Server

    Ciarlet, Philippe G

    2007-01-01

    This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a selfcontained and accessible manner. Although the field is often considered a classical one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role. The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and

  8. Simulations of black holes in compactified spacetimes

    Energy Technology Data Exchange (ETDEWEB)

    Zilhao, Miguel; Herdeiro, Carlos [Centro de Fisica do Porto, Departamento de Fisica e Astronomia, Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto (Portugal); Cardoso, Vitor; Nerozzi, Andrea; Sperhake, Ulrich; Witek, Helvi [Centro Multidisciplinar de Astrofisica, Deptartamento de Fisica, Instituto Superior Tecnico, Universidade Tecnica de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa (Portugal); Gualtieri, Leonardo, E-mail: mzilhao@fc.up.pt [Dipartimento di Fisica, Universita di Roma ' Sapienza' and Sezione INFN Roma1, P.A. Moro 5, 00185, Roma (Italy)

    2011-09-22

    From the gauge/gravity duality to braneworld scenarios, black holes in compactified spacetimes play an important role in fundamental physics. Our current understanding of black hole solutions and their dynamics in such spacetimes is rather poor because analytical tools are capable of handling a limited class of idealized scenarios, only. Breakthroughs in numerical relativity in recent years, however, have opened up the study of such spacetimes to a computational treatment which facilitates accurate studies of a wider class of configurations. We here report on recent efforts of our group to perform numerical simulations of black holes in cylindrical spacetimes.

  9. The free Maxwell field in curved spacetime

    International Nuclear Information System (INIS)

    Kueskue, M.

    2001-09-01

    The aim of this thesis is to discuss quantizations of the free Maxwell field in flat and curved spacetimes. First we introduce briefly some notions from tensor analysis and the causal structure of spacetime. As an introduction to the main topic, we review some aspects of the two axiomatic quantum field theories, Wightman theory and algebraic quantum field theory. We also give an introduction into concepts of the quantization of fields on curved spacetime backgrounds. Then the wave equation and quantization of the Maxwell field in flat spacetimes is discussed. It follows a review of J. Dimock's quantization of the Maxwell field on curved spacetimes and then we come to our main result: We show explicitly that the Maxwell field, defined by dF=0 and δF=0, has a well posed initial value formulation on arbitrary globally hyperbolic spacetime manifolds. We prove the existence and uniqueness of fundamental solutions without employing a vector potential. Thus our solution is also applicable to spacetimes not satisfying the Poincare lemma and should lead to a quantization of the Maxwell field on non-trivial spacetime backgrounds. This in turn provides the opportunity to investigate physical states on non-trivial spacetime-topologies and could lead to the discovery of new quantum phenomena. (orig.)

  10. Conformal symmetry inheritance in null fluid spacetimes

    International Nuclear Information System (INIS)

    Tupper, B O J; Keane, A J; Hall, G S; Coley, A A; Carot, J

    2003-01-01

    We define inheriting conformal Killing vectors for null fluid spacetimes and find the maximum dimension of the associated inheriting Lie algebra. We show that for non-conformally flat null fluid spacetimes, the maximum dimension of the inheriting algebra is seven and for conformally flat null fluid spacetimes the maximum dimension is eight. In addition, it is shown that there are two distinct classes of non-conformally flat generalized plane wave spacetimes which possess the maximum dimension, and one class in the conformally flat case

  11. Gauge Gravity and Space-Time

    OpenAIRE

    Wu, Ning

    2012-01-01

    When we discuss problems on gravity, we can not avoid some fundamental physical problems, such as space-time, inertia, and inertial reference frame. The goal of this paper is to discuss the logic system of gravity theory and the problems of space-time, inertia, and inertial reference frame. The goal of this paper is to set up the theory on space-time in gauge theory of gravity. Based on this theory, it is possible for human kind to manipulate physical space-time on earth, and produce a machin...

  12. Exotic smoothness and physics differential topology and spacetime models

    CERN Document Server

    Asselmeyer-Maluga, T

    2007-01-01

    The recent revolution in differential topology related to the discovery of non-standard ("exotic") smoothness structures on topologically trivial manifolds such as R4 suggests many exciting opportunities for applications of potentially deep importance for the spacetime models of theoretical physics, especially general relativity. This rich panoply of new differentiable structures lies in the previously unexplored region between topology and geometry. Just as physical geometry was thought to be trivial before Einstein, physicists have continued to work under the tacit - but now shown to be incorrect - assumption that differentiability is uniquely determined by topology for simple four-manifolds. Since diffeomorphisms are the mathematical models for physical coordinate transformations, Einstein's relativity principle requires that these models be physically inequivalent. This book provides an introductory survey of some of the relevant mathematics and presents preliminary results and suggestions for further app...

  13. Particle creation in inhomogeneous spacetimes

    International Nuclear Information System (INIS)

    Frieman, J.A.

    1989-01-01

    We study the creation of particles by inhomogeneous perturbations of spatially flat Friedmann-Robertson-Walker cosmologies. For massless scalar fields, the pair-creation probability can be expressed in terms of geometric quantities (curvature invariants). The results suggest that inhomogeneities on scales up to the particle horizon will be damped out near the Planck time. Perturbations on scales larger than the horizon are explicitly shown to yield no created pairs. The results generalize to inhomogeneous spacetimes several earlier studies of pair creation in homogeneous anisotropic cosmologies

  14. Ray trajectories for Alcubierre spacetime

    International Nuclear Information System (INIS)

    Anderson, Tom H; Mackay, Tom G; Lakhtakia, Akhlesh

    2011-01-01

    The Alcubierre spacetime was simulated by means of a Tamm medium which is asymptotically identical to vacuum and has constitutive parameters which are continuous functions of the spatial coordinates. Accordingly, the Tamm medium is amenable to physical realization as a micro- or nanostructured metamaterial. A comprehensive characterization of ray trajectories in the Tamm medium was undertaken, within the geometric-optics regime. Propagation directions corresponding to evanescent waves were identified: these occur in the region of the Tamm medium which corresponds to the warp bubble of the Alcubierre spacetime, especially for directions perpendicular to the velocity of the warp bubble at high speeds of that bubble. Ray trajectories are acutely sensitive to the magnitude and direction of the warp bubble's velocity, but rather less sensitive to the thickness of the transition zone between the warp bubble and its background. In particular, for rays which travel in the same direction as the warp bubble, the latter acts as a focusing lens, most notably at high speeds

  15. Spacetime representation of topological phononics

    Science.gov (United States)

    Deymier, Pierre A.; Runge, Keith; Lucas, Pierre; Vasseur, Jérôme O.

    2018-05-01

    Non-conventional topology of elastic waves arises from breaking symmetry of phononic structures either intrinsically through internal resonances or extrinsically via application of external stimuli. We develop a spacetime representation based on twistor theory of an intrinsic topological elastic structure composed of a harmonic chain attached to a rigid substrate. Elastic waves in this structure obey the Klein–Gordon and Dirac equations and possesses spinorial character. We demonstrate the mapping between straight line trajectories of these elastic waves in spacetime and the twistor complex space. The twistor representation of these Dirac phonons is related to their topological and fermion-like properties. The second topological phononic structure is an extrinsic structure composed of a one-dimensional elastic medium subjected to a moving superlattice. We report an analogy between the elastic behavior of this time-dependent superlattice, the scalar quantum field theory and general relativity of two types of exotic particle excitations, namely temporal Dirac phonons and temporal ghost (tachyonic) phonons. These phonons live on separate sides of a two-dimensional frequency space and are delimited by ghost lines reminiscent of the conventional light cone. Both phonon types exhibit spinorial amplitudes that can be measured by mapping the particle behavior to the band structure of elastic waves.

  16. Dark Energy and Spacetime Symmetry

    Directory of Open Access Journals (Sweden)

    Irina Dymnikova

    2017-03-01

    Full Text Available The Petrov classification of stress-energy tensors provides a model-independent definition of a vacuum by the algebraic structure of its stress-energy tensor and implies the existence of vacua whose symmetry is reduced as compared with the maximally symmetric de Sitter vacuum associated with the Einstein cosmological term. This allows to describe a vacuum in general setting by dynamical vacuum dark fluid, presented by a variable cosmological term with the reduced symmetry which makes vacuum fluid essentially anisotropic and allows it to be evolving and clustering. The relevant solutions to the Einstein equations describe regular cosmological models with time-evolving and spatially inhomogeneous vacuum dark energy, and compact vacuum objects generically related to a dark energy: regular black holes, their remnants and self-gravitating vacuum solitons with de Sitter vacuum interiors—which can be responsible for observational effects typically related to a dark matter. The mass of objects with de Sitter interior is generically related to vacuum dark energy and to breaking of space-time symmetry. In the cosmological context spacetime symmetry provides a mechanism for relaxing cosmological constant to a needed non-zero value.

  17. Space-Time and Architecture

    Science.gov (United States)

    Field, F.; Goodbun, J.; Watson, V.

    Architects have a role to play in interplanetary space that has barely yet been explored. The architectural community is largely unaware of this new territory, for which there is still no agreed method of practice. There is moreover a general confusion, in scientific and related fields, over what architects might actually do there today. Current extra-planetary designs generally fail to explore the dynamic and relational nature of space-time, and often reduce human habitation to a purely functional problem. This is compounded by a crisis over the representation (drawing) of space-time. The present work returns to first principles of architecture in order to realign them with current socio-economic and technological trends surrounding the space industry. What emerges is simultaneously the basis for an ecological space architecture, and the representational strategies necessary to draw it. We explore this approach through a work of design-based research that describes the construction of Ocean; a huge body of water formed by the collision of two asteroids at the Translunar Lagrange Point (L2), that would serve as a site for colonisation, and as a resource to fuel future missions. Ocean is an experimental model for extra-planetary space design and its representation, within the autonomous discipline of architecture.

  18. Space-Time Data Fusion

    Science.gov (United States)

    Braverman, Amy; Nguyen, Hai; Olsen, Edward; Cressie, Noel

    2011-01-01

    Space-time Data Fusion (STDF) is a methodology for combing heterogeneous remote sensing data to optimally estimate the true values of a geophysical field of interest, and obtain uncertainties for those estimates. The input data sets may have different observing characteristics including different footprints, spatial resolutions and fields of view, orbit cycles, biases, and noise characteristics. Despite these differences all observed data can be linked to the underlying field, and therefore the each other, by a statistical model. Differences in footprints and other geometric characteristics are accounted for by parameterizing pixel-level remote sensing observations as spatial integrals of true field values lying within pixel boundaries, plus measurement error. Both spatial and temporal correlations in the true field and in the observations are estimated and incorporated through the use of a space-time random effects (STRE) model. Once the models parameters are estimated, we use it to derive expressions for optimal (minimum mean squared error and unbiased) estimates of the true field at any arbitrary location of interest, computed from the observations. Standard errors of these estimates are also produced, allowing confidence intervals to be constructed. The procedure is carried out on a fine spatial grid to approximate a continuous field. We demonstrate STDF by applying it to the problem of estimating CO2 concentration in the lower-atmosphere using data from the Atmospheric Infrared Sounder (AIRS) and the Japanese Greenhouse Gasses Observing Satellite (GOSAT) over one year for the continental US.

  19. Cosmic Censorship for Gowdy Spacetimes.

    Science.gov (United States)

    Ringström, Hans

    2010-01-01

    Due to the complexity of Einstein's equations, it is often natural to study a question of interest in the framework of a restricted class of solutions. One way to impose a restriction is to consider solutions satisfying a given symmetry condition. There are many possible choices, but the present article is concerned with one particular choice, which we shall refer to as Gowdy symmetry. We begin by explaining the origin and meaning of this symmetry type, which has been used as a simplifying assumption in various contexts, some of which we shall mention. Nevertheless, the subject of interest here is strong cosmic censorship. Consequently, after having described what the Gowdy class of spacetimes is, we describe, as seen from the perspective of a mathematician, what is meant by strong cosmic censorship. The existing results on cosmic censorship are based on a detailed analysis of the asymptotic behavior of solutions. This analysis is in part motivated by conjectures, such as the BKL conjecture, which we shall therefore briefly describe. However, the emphasis of the article is on the mathematical analysis of the asymptotics, due to its central importance in the proof and in the hope that it might be of relevance more generally. The article ends with a description of the results that have been obtained concerning strong cosmic censorship in the class of Gowdy spacetimes.

  20. Classical field theory in the space of reference frames. [Space-time manifold, action principle

    Energy Technology Data Exchange (ETDEWEB)

    Toller, M [Dipartimento di Matematica e Fisica, Libera Universita, Trento (Italy)

    1978-03-11

    The formalism of classical field theory is generalized by replacing the space-time manifold M by the ten-dimensional manifold S of all the local reference frames. The geometry of the manifold S is determined by ten vector fields corresponding to ten operationally defined infinitesimal transformations of the reference frames. The action principle is written in terms of a differential 4-form in the space S (the Lagrangian form). Densities and currents are represented by differential 3-forms in S. The field equations and the connection between symmetries and conservation laws (Noether's theorem) are derived from the action principle. Einstein's theory of gravitation and Maxwell's theory of electromagnetism are reformulated in this language. The general formalism can also be used to formulate theories in which charge, energy and momentum cannot be localized in space-time and even theories in which a space-time manifold cannot be defined exactly in any useful way.

  1. Born-Infeld determinantal gravity and the taming of the conical singularity in 3-dimensional spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Ferraro, Rafael, E-mail: ferraro@iafe.uba.a [Instituto de Astronomia y Fisica del Espacio, Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina); Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentina); Fiorini, Franco, E-mail: franco@iafe.uba.a [Instituto de Astronomia y Fisica del Espacio, Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina)

    2010-08-30

    In the context of Born-Infeld determinantal gravity formulated in an n-dimensional spacetime with absolute parallelism, we found an exact 3-dimensional vacuum circular symmetric solution without cosmological constant consisting in a rotating spacetime with non-singular behavior. The space behaves at infinity as the conical geometry typical of 3-dimensional General Relativity without cosmological constant. However, the solution has no conical singularity because the space ends at a minimal circle that no freely falling particle can ever reach in a finite proper time. The space is curved, but no divergences happen since the curvature invariants vanish at both asymptotic limits. Remarkably, this very mechanism also forbids the existence of closed timelike curves in such a spacetime.

  2. Born-Infeld determinantal gravity and the taming of the conical singularity in 3-dimensional spacetime

    International Nuclear Information System (INIS)

    Ferraro, Rafael; Fiorini, Franco

    2010-01-01

    In the context of Born-Infeld determinantal gravity formulated in an n-dimensional spacetime with absolute parallelism, we found an exact 3-dimensional vacuum circular symmetric solution without cosmological constant consisting in a rotating spacetime with non-singular behavior. The space behaves at infinity as the conical geometry typical of 3-dimensional General Relativity without cosmological constant. However, the solution has no conical singularity because the space ends at a minimal circle that no freely falling particle can ever reach in a finite proper time. The space is curved, but no divergences happen since the curvature invariants vanish at both asymptotic limits. Remarkably, this very mechanism also forbids the existence of closed timelike curves in such a spacetime.

  3. Brownian motion in Robertson-Walker spacetimes from electromagnetic vacuum fluctuations

    International Nuclear Information System (INIS)

    Bessa, Carlos H. G.; Bezerra, V. B.; Ford, L. H.

    2009-01-01

    We consider the effects of the vacuum fluctuations of a quantized electromagnetic field on particles in an expanding universe. We find that these particles typically undergo Brownian motion and acquire a nonzero mean squared velocity that depends on the scale factor of the universe. This Brownian motion can be interpreted as due to noncancellation of anticorrelated vacuum fluctuations in the time-dependent background spacetime. Alternatively, one can interpret this effect as the particles acquiring energy from the background spacetime geometry, a phenomenon that cannot occur in a static spacetime. We treat several types of coupling between the electromagnetic field and the particles and several model universes. We also consider both free particles, which, on the average, move on geodesics, and particles in bound systems. There are significant differences between these two cases, which illustrates that nongeodesic motion alters the effects of the vacuum fluctuations. We discuss the possible applications of this Brownian motion effect to cosmological scenarios.

  4. On Mass, Spacetime Curvature, and Gravity

    Science.gov (United States)

    Janis, Allen I.

    2018-01-01

    The frequently used analogy of a massive ball distorting an elastic sheet, which is used to illustrate why mass causes spacetime curvature and gravitational attraction, is criticized in this article. A different analogy that draws on the students' previous knowledge of spacetime diagrams in special relativity is suggested.

  5. Space-time and matter in 'prephysics'

    International Nuclear Information System (INIS)

    Terazawa, Hidezumi.

    1985-05-01

    Many fundamental questions concerning the space-time and matter are asked and answered in ''prephysics'', a new line of physics (or philosophy but not metaphysics). They include the following: 1) ''Why is our space-time of 4 dimensions.'', 2) ''What is the ultimate form of matter.'' and 3) ''How was our universe created.''. (author)

  6. Minkowski Spacetime A Hundred Years Later

    CERN Document Server

    Petkov, Vesselin

    2009-01-01

    This volume is dedicated to the one hundredth anniversary of the publication of Hermann Minkowski's paper "Space and Time" in 1909. His work on the spacetime representation of special relativity had a huge impact on the twentieth century physics to the extent that modern physics would be impossible without the notion of spacetime. While there is consensus on the mathematical significance of spacetime in theoretical physics, for a hundred years there has been no consensus on the nature of spacetime itself. We owe Minkowski a clear answer to the question of the nature of spacetime -- whether it is only a mathematical space or represents a real four-dimensional world. A century after its publication the original Minkowski paper still represents an enrichment to the physicists, especially the relativists, who read it with the intent to fully investigate the depth of Minkowski's ideas on space and time and the physical meaning of special relativity. The volume begins with an excellent retranslation of Minkowski's ...

  7. Partially massless graviton on beyond Einstein spacetimes

    Science.gov (United States)

    Bernard, Laura; Deffayet, Cédric; Hinterbichler, Kurt; von Strauss, Mikael

    2017-06-01

    We show that a partially massless graviton can propagate on a large set of spacetimes which are not Einstein spacetimes. Starting from a recently constructed theory for a massive graviton that propagates the correct number of degrees of freedom on an arbitrary spacetime, we first give the full explicit form of the scalar constraint responsible for the absence of a sixth degree of freedom. We then spell out generic conditions for the constraint to be identically satisfied, so that there is a scalar gauge symmetry which makes the graviton partially massless. These simplify if one assumes that spacetime is Ricci symmetric. Under this assumption, we find explicit non-Einstein spacetimes (some, but not all, with vanishing Bach tensors) allowing for the propagation of a partially massless graviton. These include in particular the Einstein static Universe.

  8. Exact geodesic distances in FLRW spacetimes

    Science.gov (United States)

    Cunningham, William J.; Rideout, David; Halverson, James; Krioukov, Dmitri

    2017-11-01

    Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3 +1 )-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.

  9. Spacetime symmetries and topology in bimetric relativity

    Science.gov (United States)

    Torsello, Francesco; Kocic, Mikica; Högâs, Marcus; Mörtsell, Edvard

    2018-04-01

    We explore spacetime symmetries and topologies of the two metric sectors in Hassan-Rosen bimetric theory. We show that, in vacuum, the two sectors can either share or have separate spacetime symmetries. If stress-energy tensors are present, a third case can arise, with different spacetime symmetries within the same sector. This raises the question of the best definition of spacetime symmetry in Hassan-Rosen bimetric theory. We emphasize the possibility of imposing ansatzes and looking for solutions having different Killing vector fields or different isometries in the two sectors, which has gained little attention so far. We also point out that the topology of spacetime imposes a constraint on possible metric combinations.

  10. Constraints on string vacua with spacetime supersymmetry

    International Nuclear Information System (INIS)

    Banks, T.; California Univ., Santa Cruz; Dixon, L.J.

    1988-01-01

    We examine the consequences of extended spacetime supersymmetry for classical superstring vacua with four dimensions uncompactified. N=2 spacetime supersymmetry implies that the 'internal' N=1 superconformal algebra with central charge c=6 splits into a piece with c=4 which has N=4 superconformal invariance, and a piece with c=2 which is constructed from two free dimension 1/2 superfields. N=4 spacetime supersymmetry requires that the entire c=6 algebra be represented by six free superfields. Using the world-sheet properties of N=1 spacetime supersymmetric classical vacua, we show that spacetime supersymmetry cannot be continuously broken within a family of classical vacua. Finally, we argue that the effective field theories for classical vacua of superstring theories (whether space time supersymmetric or not) have no continuous global symmetries - all continuous symmetries are gauged. (orig.)

  11. The G2 spinorial geometry of supersymmetric IIB backgrounds

    International Nuclear Information System (INIS)

    Gran, U; Gutowski, J; Papadopoulos, G

    2006-01-01

    We solve the Killing spinor equations of supersymmetric IIB backgrounds which admit one supersymmetry and the Killing spinor has stability subgroup G 2 in Spin(9, 1) x U(1). We find that such backgrounds admit a timelike Killing vector field and the geometric structure of the spacetime reduces from Spin(9, 1) x U(1) to G 2 . We determine the type of G 2 structure that the spacetime admits by computing the covariant derivatives of the spacetime forms associated with the Killing spinor bilinears. We also solve the Killing spinor equations of backgrounds with two supersymmetries and Spin(7) x R 8 -invariant spinors, and four supersymmetries with SU(4) x R 8 - and with G 2 -invariant spinors. We show that the Killing spinor equations factorize in two sets, one involving the geometry and the 5-form flux, and the other the 3-form flux and the scalars. In the Spin(7) x R 8 and SU(4) x R 8 cases, the spacetime admits a parallel null vector field and so the spacetime metric can be locally described in terms of Penrose coordinates adapted to the associated rotation free, null, geodesic congruence. The transverse space of the congruence is a Spin(7) and a SU(4) holonomy manifold, respectively. In the G 2 case, all the fluxes vanish and the spacetime is the product of a three-dimensional Minkowski space with a holonomy G 2 manifold

  12. Simulating triangulations. Graphs, manifolds and (quantum) spacetime

    International Nuclear Information System (INIS)

    Krueger, Benedikt

    2016-01-01

    Triangulations, which can intuitively be described as a tessellation of space into simplicial building blocks, are structures that arise in various different branches of physics: They can be used for describing complicated and curved objects in a discretized way, e.g., in foams, gels or porous media, or for discretizing curved boundaries for fluid simulations or dissipative systems. Interpreting triangulations as (maximal planar) graphs makes it possible to use them in graph theory or statistical physics, e.g., as small-world networks, as networks of spins or in biological physics as actin networks. Since one can find an analogue of the Einstein-Hilbert action on triangulations, they can even be used for formulating theories of quantum gravity. Triangulations have also important applications in mathematics, especially in discrete topology. Despite their wide occurrence in different branches of physics and mathematics, there are still some fundamental open questions about triangulations in general. It is a prior unknown how many triangulations there are for a given set of points or a given manifold, or even whether there are exponentially many triangulations or more, a question that relates to a well-defined behavior of certain quantum geometry models. Another major unknown question is whether elementary steps transforming triangulations into each other, which are used in computer simulations, are ergodic. Using triangulations as model for spacetime, it is not clear whether there is a meaningful continuum limit that can be identified with the usual and well-tested theory of general relativity. Within this thesis some of these fundamental questions about triangulations are answered by the use of Markov chain Monte Carlo simulations, which are a probabilistic method for calculating statistical expectation values, or more generally a tool for calculating high-dimensional integrals. Additionally, some details about the Wang-Landau algorithm, which is the primary used

  13. Simulating triangulations. Graphs, manifolds and (quantum) spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Krueger, Benedikt

    2016-07-01

    Triangulations, which can intuitively be described as a tessellation of space into simplicial building blocks, are structures that arise in various different branches of physics: They can be used for describing complicated and curved objects in a discretized way, e.g., in foams, gels or porous media, or for discretizing curved boundaries for fluid simulations or dissipative systems. Interpreting triangulations as (maximal planar) graphs makes it possible to use them in graph theory or statistical physics, e.g., as small-world networks, as networks of spins or in biological physics as actin networks. Since one can find an analogue of the Einstein-Hilbert action on triangulations, they can even be used for formulating theories of quantum gravity. Triangulations have also important applications in mathematics, especially in discrete topology. Despite their wide occurrence in different branches of physics and mathematics, there are still some fundamental open questions about triangulations in general. It is a prior unknown how many triangulations there are for a given set of points or a given manifold, or even whether there are exponentially many triangulations or more, a question that relates to a well-defined behavior of certain quantum geometry models. Another major unknown question is whether elementary steps transforming triangulations into each other, which are used in computer simulations, are ergodic. Using triangulations as model for spacetime, it is not clear whether there is a meaningful continuum limit that can be identified with the usual and well-tested theory of general relativity. Within this thesis some of these fundamental questions about triangulations are answered by the use of Markov chain Monte Carlo simulations, which are a probabilistic method for calculating statistical expectation values, or more generally a tool for calculating high-dimensional integrals. Additionally, some details about the Wang-Landau algorithm, which is the primary used

  14. Causal fermion systems: A quantum space-time emerging from an action principle

    Energy Technology Data Exchange (ETDEWEB)

    Finster, Felix [Mathematics Department, University of Regensburg (Germany)

    2013-07-01

    Causal fermion systems provide a general framework for the formulation of relativistic quantum theory. A particular feature is that space-time is a secondary object which emerges by minimizing an action. The aim of the talk is to give a simple introduction, with an emphasis on conceptual issues. We begin with Dirac spinors in Minkowski space and explain how to formulate the system as a causal fermion system. As an example in curved space-time, we then consider spinors on a globally hyperbolic space-time. An example on a space-time lattice illustrates that causal fermion systems also allow for the description of discrete space-times. These examples lead us to the general definition of causal fermion systems. The causal action principle is introduced. We outline how for a given minimizer, one has notions of causality, connection and curvature, which generalize the classical notions and give rise to a proposal for a ''quantum geometry''. In the last part of the talk, we outline how quantum field theory can be described in this framework and discuss the relation to other approaches.

  15. Quantum singularities in (2+1) dimensional matter coupled black hole spacetimes

    International Nuclear Information System (INIS)

    Unver, O.; Gurtug, O.

    2010-01-01

    Quantum singularities considered in the 3D Banados-Teitelboim-Zanelli (BTZ) spacetime by Pitelli and Letelier [Phys. Rev. D 77, 124030 (2008)] is extended to charged BTZ and 3D Einstein-Maxwell-dilaton gravity spacetimes. The occurrence of naked singularities in the Einstein-Maxwell extension of the BTZ spacetime both in linear and nonlinear electrodynamics as well as in the Einstein-Maxwell-dilaton gravity spacetimes are analyzed with the quantum test fields obeying the Klein-Gordon and Dirac equations. We show that with the inclusion of the matter fields, the conical geometry near r=0 is removed and restricted classes of solutions are admitted for the Klein-Gordon and Dirac equations. Hence, the classical central singularity at r=0 turns out to be quantum mechanically singular for quantum particles obeying the Klein-Gordon equation but nonsingular for fermions obeying the Dirac equation. Explicit calculations reveal that the occurrence of the timelike naked singularities in the considered spacetimes does not violate the cosmic censorship hypothesis as far as the Dirac fields are concerned. The role of horizons that clothes the singularity in the black hole cases is replaced by repulsive potential barrier against the propagation of Dirac fields.

  16. Interpolating from Bianchi attractors to Lifshitz and AdS spacetimes

    International Nuclear Information System (INIS)

    Kachru, Shamit; Kundu, Nilay; Saha, Arpan; Samanta, Rickmoy; Trivedi, Sandip P.

    2014-01-01

    We construct classes of smooth metrics which interpolate from Bianchi attractor geometries of Types II, III, VI and IX in the IR to Lifshitz or AdS 2 ×S 3 geometries in the UV. While we do not obtain these metrics as solutions of Einstein gravity coupled to a simple matter field theory, we show that the matter sector stress-energy required to support these geometries (via the Einstein equations) does satisfy the weak, and therefore also the null, energy condition. Since Lifshitz or AdS 2 ×S 3 geometries can in turn be connected to AdS 5 spacetime, our results show that there is no barrier, at least at the level of the energy conditions, for solutions to arise connecting these Bianchi attractor geometries to AdS 5 spacetime. The asymptotic AdS 5 spacetime has no non-normalizable metric deformation turned on, which suggests that furthermore, the Bianchi attractor geometries can be the IR geometries dual to field theories living in flat space, with the breaking of symmetries being either spontaneous or due to sources for other fields. Finally, we show that for a large class of flows which connect two Bianchi attractors, a C-function can be defined which is monotonically decreasing from the UV to the IR as long as the null energy condition is satisfied. However, except for special examples of Bianchi attractors (including AdS space), this function does not attain a finite and non-vanishing constant value at the end points

  17. Acoustic geometry for general relativistic barotropic irrotational fluid flow

    International Nuclear Information System (INIS)

    Visser, Matt; Molina-ParIs, Carmen

    2010-01-01

    'Acoustic spacetimes', in which techniques of differential geometry are used to investigate sound propagation in moving fluids, have attracted considerable attention over the last few decades. Most of the models currently considered in the literature are based on non-relativistic barotropic irrotational fluids, defined in a flat Newtonian background. The extension, first to special relativistic barotropic fluid flow and then to general relativistic barotropic fluid flow in an arbitrary background, is less straightforward than it might at first appear. In this paper, we provide a pedagogical and simple derivation of the general relativistic 'acoustic spacetime' in an arbitrary (d+1)-dimensional curved-space background.

  18. Transverse force on a moving vortex with the acoustic geometry

    International Nuclear Information System (INIS)

    Zhang Pengming; Cao Liming; Duan Yishi; Zhong Chengkui

    2004-01-01

    We consider the transverse force on a moving vortex with the acoustic metric using the phi-mapping topological current theory. In the frame of effective space-time geometry the vortex appear naturally by virtue of the vortex tensor in the Lorentz space-time and we show that it is just the vortex derived with the order parameter in the condensed matter. With the usual Lagrangian we obtain the equation of motion for the vortex. At last, we show that the transverse force on the moving vortex in our equation is just the usual Magnus force in a simple model

  19. Newtonian gravity on quantum spacetime

    Directory of Open Access Journals (Sweden)

    Majid Shahn

    2014-04-01

    Full Text Available The bicrossproduct model λ-Minkowski (or ‘κ-Minkowski’ quantum space-time has an anomaly for the action of the Poincaré quantum group which was resolved by an extra cotangent direction θ’ not visible classically. We show that gauging a coefficient of θ′ introduces gravity into the model. We solve and analyse the model nonrelativisticaly in a 1/r potential, finding an induced constant term in the effective potential energy and a weakening and separation of the effective gravitational and inertial masses as the test particle Klein-Gordon mass increases. The present work is intended as a proof of concept but the approach could be relevant to an understanding of dark energy and possibly to macroscopic quantum systems.

  20. Generating asymptotically plane wave spacetimes

    International Nuclear Information System (INIS)

    Hubeny, Veronika E.; Rangamani, Mukund

    2003-01-01

    In an attempt to study asymptotically plane wave spacetimes which admit an event horizon, we find solutions to vacuum Einstein's equations in arbitrary dimension which have a globally null Killing field and rotational symmetry. We show that while such solutions can be deformed to include ones which are asymptotically plane wave, they do not posses a regular event horizon. If we allow for additional matter, such as in supergravity theories, we show that it is possible to have extremal solutions with globally null Killing field, a regular horizon, and which, in addition, are asymptotically plane wave. In particular, we deform the extremal M2-brane solution in 11-dimensional supergravity so that it behaves asymptotically as a 10-dimensional vacuum plane wave times a real line. (author)

  1. Bubble Collision in Curved Spacetime

    International Nuclear Information System (INIS)

    Hwang, Dong-il; Lee, Bum-Hoon; Lee, Wonwoo; Yeom, Dong-han

    2014-01-01

    We study vacuum bubble collisions in curved spacetime, in which vacuum bubbles were nucleated in the initial metastable vacuum state by quantum tunneling. The bubbles materialize randomly at different times and then start to grow. It is known that the percolation by true vacuum bubbles is not possible due to the exponential expansion of the space among the bubbles. In this paper, we consider two bubbles of the same size with a preferred axis and assume that two bubbles form very near each other to collide. The two bubbles have the same field value. When the bubbles collide, the collided region oscillates back-and-forth and then the collided region eventually decays and disappears. We discuss radiation and gravitational wave resulting from the collision of two bubbles

  2. Toward a holographic theory for general spacetimes

    Science.gov (United States)

    Nomura, Yasunori; Salzetta, Nico; Sanches, Fabio; Weinberg, Sean J.

    2017-04-01

    We study a holographic theory of general spacetimes that does not rely on the existence of asymptotic regions. This theory is to be formulated in a holographic space. When a semiclassical description is applicable, the holographic space is assumed to be a holographic screen: a codimension-1 surface that is capable of encoding states of the gravitational spacetime. Our analysis is guided by conjectured relationships between gravitational spacetime and quantum entanglement in the holographic description. To understand basic features of this picture, we catalog predictions for the holographic entanglement structure of cosmological spacetimes. We find that qualitative features of holographic entanglement entropies for such spacetimes differ from those in AdS/CFT but that the former reduce to the latter in the appropriate limit. The Hilbert space of the theory is analyzed, and two plausible structures are found: a direct-sum and "spacetime-equals-entanglement" structure. The former preserves a naive relationship between linear operators and observable quantities, while the latter respects a more direct connection between holographic entanglement and spacetime. We also discuss the issue of selecting a state in quantum gravity, in particular how the state of the multiverse may be selected in the landscape.

  3. Non-commutative geometry inspired charged black holes

    International Nuclear Information System (INIS)

    Ansoldi, Stefano; Nicolini, Piero; Smailagic, Anais; Spallucci, Euro

    2007-01-01

    We find a new, non-commutative geometry inspired, solution of the coupled Einstein-Maxwell field equations describing a variety of charged, self-gravitating objects, including extremal and non-extremal black holes. The metric smoothly interpolates between de Sitter geometry, at short distance, and Reissner-Nordstrom geometry far away from the origin. Contrary to the ordinary Reissner-Nordstrom spacetime there is no curvature singularity in the origin neither 'naked' nor shielded by horizons. We investigate both Hawking process and pair creation in this new scenario

  4. Classification of Near-Horizon Geometries of Extremal Black Holes.

    Science.gov (United States)

    Kunduri, Hari K; Lucietti, James

    2013-01-01

    Any spacetime containing a degenerate Killing horizon, such as an extremal black hole, possesses a well-defined notion of a near-horizon geometry. We review such near-horizon geometry solutions in a variety of dimensions and theories in a unified manner. We discuss various general results including horizon topology and near-horizon symmetry enhancement. We also discuss the status of the classification of near-horizon geometries in theories ranging from vacuum gravity to Einstein-Maxwell theory and supergravity theories. Finally, we discuss applications to the classification of extremal black holes and various related topics. Several new results are presented and open problems are highlighted throughout.

  5. Spacetime averaging of exotic singularity universes

    International Nuclear Information System (INIS)

    Dabrowski, Mariusz P.

    2011-01-01

    Taking a spacetime average as a measure of the strength of singularities we show that big-rips (type I) are stronger than big-bangs. The former have infinite spacetime averages while the latter have them equal to zero. The sudden future singularities (type II) and w-singularities (type V) have finite spacetime averages. The finite scale factor (type III) singularities for some values of the parameters may have an infinite average and in that sense they may be considered stronger than big-bangs.

  6. Hyperbolic statics in space-time

    OpenAIRE

    Pavlov, Dmitry; Kokarev, Sergey

    2014-01-01

    Based on the concept of material event as an elementary material source that is concentrated on metric sphere of zero radius --- light-cone of Minkowski space-time, we deduce the analog of Coulomb's law for hyperbolic space-time field universally acting between the events of space-time. Collective field that enables interaction of world lines of a pair of particles at rest contains a standard 3-dimensional Coulomb's part and logarithmic addendum. We've found that the Coulomb's part depends on...

  7. QCD-instantons and conformal space-time inversion symmetry

    International Nuclear Information System (INIS)

    Klammer, D.

    2008-04-01

    In this paper, we explore the appealing possibility that the strong suppression of large-size QCD instantons - as evident from lattice data - is due to a surviving conformal space-time inversion symmetry. This symmetry is both suggested from the striking invariance of highquality lattice data for the instanton size distribution under inversion of the instanton size ρ→(left angle ρ right angle 2 )/(ρ) and from the known validity of space-time inversion symmetry in the classical instanton sector. We project the instanton calculus onto the four-dimensional surface of a five-dimensional sphere via conformal stereographic mapping, before investigating conformal inversion. This projection to a compact, curved geometry is both to avoid the occurence of divergences and to introduce the average instanton size left angle ρ right angle from the lattice data as a new length scale. The average instanton size is identified with the radius b of this 5d-sphere and acts as the conformal inversion radius. For b= left angle ρ right angle, our corresponding results are almost perfectly symmetric under space-time inversion and in good qualitative agreement with the lattice data. For (ρ)/(b)→0 we recover the familiar results of instanton perturbation theory in flat 4d-space. Moreover, we illustrate that a (weakly broken) conformal inversion symmetry would have significant consequences for QCD beyond instantons. As a further successful test for inversion symmetry, we present striking implications for another instanton dominated lattice observable, the chirality-flip ratio in the QCD vacuum. (orig.)

  8. Newton-Hooke Limit of Beltrami-de Sitter Spacetime, Principles of Galilei-Hooke's Relativity and Postulate on Newton-Hooke Universal Time

    OpenAIRE

    Huang, Chao-Guang; Guo, Han-Ying; Tian, Yu; Xu, Zhan; Zhou, Bin

    2004-01-01

    Based on the Beltrami-de Sitter spacetime, we present the Newton-Hooke model under the Newton-Hooke contraction of the $BdS$ spacetime with respect to the transformation group, algebra and geometry. It is shown that in Newton-Hooke space-time, there are inertial-type coordinate systems and inertial-type observers, which move along straight lines with uniform velocity. And they are invariant under the Newton-Hooke group. In order to determine uniquely the Newton-Hooke limit, we propose the Gal...

  9. Homotheties of cylindrically symmetric static spacetimes

    International Nuclear Information System (INIS)

    Qadir, A.; Ziad, M.; Sharif, M.

    1998-08-01

    In this note we consider the homotheties of cylindrically symmetric static spacetimes. We find that we can provide a complete list of all metrics that admit non-trivial homothetic motions and are cylindrically symmetric static. (author)

  10. Noncommutative geometry and its application to the standard model

    Energy Technology Data Exchange (ETDEWEB)

    Martinetti, Pierre [Georg-August Universitaet, Goettingen (Germany)

    2009-07-01

    We give an overview of the description of the standard model of particle physics minimally coupled to gravity within the framework of noncommutative geometry. Especially we study in detail the metric structure of spacetime that emerges from the spectral triple recently proposed by Chamseddine, Connes and Marcolli. Within this framework points of spacetime acquire an internal structure inherited from the gauge group of the standard model. A distance is defined on this generalized spacetime which is fully encoded by the Yang-Mills gauge fields together with the Higgs field. We focus on some explicit examples, underlying the link between this distance and other distances well known by physicists and mathematicians, such has the Carnot-Caratheodory horizontal distance or the Monge-Kantorovitch transport distance.

  11. Discrete quantum geometries and their effective dimension

    International Nuclear Information System (INIS)

    Thuerigen, Johannes

    2015-01-01

    In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension d on low energy scales to a real number between 0 and d on high energy scales. In the particular case of 1 these results allow to understand the quantum geometry as effectively fractal.

  12. Negative branes, supergroups and the signature of spacetime

    Science.gov (United States)

    Dijkgraaf, Robbert; Heidenreich, Ben; Jefferson, Patrick; Vafa, Cumrun

    2018-02-01

    We study the realization of supergroup gauge theories using negative branes in string theory. We show that negative branes are intimately connected with the possibility of timelike compactification and exotic spacetime signatures previously studied by Hull. Isolated negative branes dynamically generate a change in spacetime signature near their worldvolumes, and are related by string dualities to a smooth M-theory geometry with closed timelike curves. Using negative D3-branes, we show that SU(0| N) supergroup theories are holographically dual to an exotic variant of type IIB string theory on {dS}_{3,2}× {\\overline{S}}^5 , for which the emergent dimensions are timelike. Using branes, mirror symmetry and Nekrasov's instanton calculus, all of which agree, we derive the Seiberg-Witten curve for N=2 SU( N | M ) gauge theories. Together with our exploration of holography and string dualities for negative branes, this suggests that supergroup gauge theories may be non-perturbatively well-defined objects, though several puzzles remain.

  13. Black hole in closed spacetime with an anisotropic fluid

    Science.gov (United States)

    Kim, Hyeong-Chan

    2017-09-01

    We study spherically symmetric geometries made of anisotropic perfect fluid based on general relativity. The purpose of this work is to find and classify black hole solutions in closed spacetime. In a general setting, we find that a static and closed space exists only when the radial pressure is negative but its size is smaller than the density. The Einstein equation is eventually cast into a first-order autonomous equation on a two-dimensional plane of scale-invariant variables, which are equivalent to the Tolman-Oppenheimer-Volkoff equation in general relativity. Then, we display various solution curves numerically. An exact solution describing a black hole solution in a closed spacetime was known in [I. Cho and H. C. Kim, Phys. Rev. D 95, 084052 (2017), 10.1103/PhysRevD.95.084052], which bears a naked singularity and negative-energy era. We find that these two deficits can be remedied when ρ +3 p1>0 and ρ +p1+2 p2<0 , where the second violates the strong energy condition.

  14. Closed Timelike Curves in Type II Non-Vacuum Spacetime

    International Nuclear Information System (INIS)

    Ahmed, Faizuddin

    2017-01-01

    Here we present a cyclicly symmetric non-vacuum spacetime, admitting closed timelike curves (CTCs) which appear after a certain instant of time, i.e., a time-machine spacetime. The spacetime is asymptotically flat, free-from curvature singularities and a four-dimensional extension of the Misner space in curved spacetime. The spacetime is of type II in the Petrov classification scheme and the matter field pure radiation satisfy the energy condition. (paper)

  15. Minkowski space-time is locally extendible

    International Nuclear Information System (INIS)

    Beem, J.K.

    1980-01-01

    An example of a real analytic local extension of Minkowski space-time is given in this note. This local extension is not across points of the b-boundary since Minkowski space-time has an empty b-boundary. Furthermore, this local extension is not across points of the causal boundary. The example indicates that the concept of local inextendibility may be less useful than originally envisioned. (orig.)

  16. Conformal mechanics in Newton-Hooke spacetime

    International Nuclear Information System (INIS)

    Galajinsky, Anton

    2010-01-01

    Conformal many-body mechanics in Newton-Hooke spacetime is studied within the framework of the Lagrangian formalism. Global symmetries and Noether charges are given in a form convenient for analyzing the flat space limit. N=2 superconformal extension is built and a new class on N=2 models related to simple Lie algebras is presented. A decoupling similarity transformation on N=2 quantum mechanics in Newton-Hooke spacetime is discussed.

  17. Spacetimes admitting a universal redshift function

    International Nuclear Information System (INIS)

    Dautcourt, G.

    1987-01-01

    The conditions are given for a velocity congruence in a Riemannian spacetime admitting a universal redshift function R. This function allows to calculate in a simple way (as a quotient of R values taken at the emission and registration event) the redshift or blueshift connected with an emitter and observer both following the congruence. Spacetimes and congruences with an universal redshift function are shortly discussed. (author)

  18. On discrete models of space-time

    International Nuclear Information System (INIS)

    Horzela, A.; Kempczynski, J.; Kapuscik, E.; Georgia Univ., Athens, GA; Uzes, Ch.

    1992-02-01

    Analyzing the Einstein radiolocation method we come to the conclusion that results of any measurement of space-time coordinates should be expressed in terms of rational numbers. We show that this property is Lorentz invariant and may be used in the construction of discrete models of space-time different from the models of the lattice type constructed in the process of discretization of continuous models. (author)

  19. Space-Time Disarray and Visual Awareness

    Directory of Open Access Journals (Sweden)

    Jan Koenderink

    2012-04-01

    Full Text Available Local space-time scrambling of optical data leads to violent jerks and dislocations. On masking these, visual awareness of the scene becomes cohesive, with dislocations discounted as amodally occluding foreground. Such cohesive space-time of awareness is technically illusory because ground truth is jumbled whereas awareness is coherent. Apparently the visual field is a construction rather than a (veridical perception.

  20. Quantum fields in curved space-times

    International Nuclear Information System (INIS)

    Ashtekar, A.; Magnon, A.

    1975-01-01

    The problem of obtaining a quantum description of the (real) Klein-Gordon system in a given curved space-time is discussed. An algebraic approach is used. The *-algebra of quantum operators is constructed explicitly and the problem of finding its *-representation is reduced to that of selecting a suitable complex structure on the real vector space of the solutions of the (classical) Klein-Gordon equation. Since, in a static space-time, there already exists, a satisfactory quantum field theory, in this case one already knows what the 'correct' complex structure is. A physical characterization of this 'correct' complex structure is obtained. This characterization is used to extend quantum field theory to non-static space-times. Stationary space-times are considered first. In this case, the issue of extension is completely straightforward and the resulting theory is the natural generalization of the one in static space-times. General, non-stationary space-times are then considered. In this case the issue of extension is quite complicated and only a plausible extension is presented. Although the resulting framework is well-defined mathematically, the physical interpretation associated with it is rather unconventional. Merits and weaknesses of this framework are discussed. (author)

  1. Space-time foam as the universal regulator

    International Nuclear Information System (INIS)

    Crane, L.; Smolin, L.

    1985-01-01

    A distribution of virtual black holes in the vacuum will induce modifications in the density of states for small perturbations of gravitational and matter fields. If the virtual black holes fill the volume of a typical spacelike surface then perturbation theory becomes more convergent and may even be finite, depending on how fast the number of virtual black holes increases as their size decreases. For distributions of virtual black holes which are scale invariant the effective dimension of space-time is lowered to a noninteger value less than 4, leading to an interpretation in terms of fractal geometry. In this case general relativity is renormalizable in the 1/N expansion without higher derivative terms. As the Hamiltonian is not modified the theory is stable. (author)

  2. Hubble expansion in static spacetime

    International Nuclear Information System (INIS)

    Rossler, Otto E.; Froehlich, Dieter; Movassagh, Ramis; Moore, Anthony

    2007-01-01

    A recently proposed mechanism for light-path expansion in a static spacetime is based on the moving-lenses paradigm. Since the latter is valid independently of whether space expands or not, a static universe can be used to better see the implications. The moving-lenses paradigm is related to the paradigm of dynamical friction. If this is correct, a Hubble-like law is implicit. It is described quantitatively. A bent in the Hubble-like line is predictably implied. The main underlying assumption is Price's Principle (PI 3 ). If the theory is sound, the greatest remaining problem in cosmology becomes the origin of hydrogen. Since Blandford's jet production mechanism for quasars is too weak, a generalized Hawking radiation hidden in the walls of cosmic voids is invoked. A second prediction is empirical: slow pattern changes in the cosmic microwave background. A third is ultra-high redshifts for Giacconi quasars. Bruno's eternal universe in the spirit of Augustine becomes a bit less outlandish

  3. Complex analysis and geometry

    CERN Document Server

    Silva, Alessandro

    1993-01-01

    The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.

  4. Cosmological solutions and finite time singularities in Finslerian geometry

    Science.gov (United States)

    Paul, Nupur; de, S. S.; Rahaman, Farook

    2018-03-01

    We consider a very general scenario of our universe where its geometry is characterized by the Finslerian structure on the underlying spacetime manifold, a generalization of the Riemannian geometry. Now considering a general energy-momentum tensor for matter sector, we derive the gravitational field equations in such spacetime. Further, to depict the cosmological dynamics in such spacetime proposing an interesting equation of state identified by a sole parameter γ which for isotropic limit is simply the barotropic equation of state p = (γ ‑ 1)ρ (γ ∈ ℝ being the barotropic index), we solve the background dynamics. The dynamics offers several possibilities depending on this sole parameter as follows: (i) only an exponential expansion, or (ii) a finite time past singularity (big bang) with late accelerating phase, or (iii) a nonsingular universe exhibiting an accelerating scenario at late time which finally predicts a big rip type singularity. We also discuss several energy conditions and the possibility of cosmic bounce. Finally, we establish the first law of thermodynamics in such spacetime.

  5. Dynamics in non-globally-hyperbolic static spacetimes: III. Anti-de Sitter spacetime

    International Nuclear Information System (INIS)

    Ishibashi, Akihiro; Wald, Robert M

    2004-01-01

    In recent years, there has been considerable interest in theories formulated in anti-de Sitter (AdS) spacetime. However, AdS spacetime fails to be globally hyperbolic, so a classical field satisfying a hyperbolic wave equation on AdS spacetime need not have a well-defined dynamics. Nevertheless, AdS spacetime is static, so the possible rules of dynamics for a field satisfying a linear wave equation are constrained by our previous general analysis-given in paper II-where it was shown that the possible choices of dynamics correspond to choices of positive, self-adjoint extensions of a certain differential operator, A. In the present paper, we reduce the analysis of electromagnetic and gravitational perturbations in AdS spacetime to scalar wave equations. We then apply our general results to analyse the possible dynamics of scalar, electromagnetic and gravitational perturbations in AdS spacetime. In AdS spacetime, the freedom (if any) in choosing self-adjoint extensions of A corresponds to the freedom (if any) in choosing suitable boundary conditions at infinity, so our analysis determines all the possible boundary conditions that can be imposed at infinity. In particular, we show that other boundary conditions besides the Dirichlet and Neumann conditions may be possible, depending on the value of the effective mass for scalar field perturbations, and depending on the number of spacetime dimensions and type of mode for electromagnetic and gravitational perturbations

  6. Calibrated geometries and non perturbative superpotentials in M-theory

    International Nuclear Information System (INIS)

    Hernandez, R.

    1999-12-01

    We consider non perturbative effects in M-theory compactifications on a seven-manifold of G 2 holonomy arising from membranes wrapped on supersymmetric three-cycles. When membranes are wrapped on associative submanifolds they induce a superpotential that can be calculated using calibrated geometry. This superpotential is also derived from compactification on a seven-manifold, to four dimensional Anti-de Sitter spacetime, of eleven dimensional supergravity with non vanishing expectation value of the four-form field strength. (author)

  7. Extended Equivalence Principle: Implications for Gravity, Geometry and Thermodynamics

    OpenAIRE

    Sivaram, C.; Arun, Kenath

    2012-01-01

    The equivalence principle was formulated by Einstein in an attempt to extend the concept of inertial frames to accelerated frames, thereby bringing in gravity. In recent decades, it has been realised that gravity is linked not only with geometry of space-time but also with thermodynamics especially in connection with black hole horizons, vacuum fluctuations, dark energy, etc. In this work we look at how the equivalence principle manifests itself in these different situations where we have str...

  8. Pre-Big Bang, space-time structure, asymptotic Universe. Spinorial space-time and a new approach to Friedmann-like equations

    Science.gov (United States)

    Gonzalez-Mestres, Luis

    2014-04-01

    Planck and other recent data in Cosmology and Particle Physics can open the way to controversial analyses concerning the early Universe and its possible ultimate origin. Alternatives to standard cosmology include pre-Big Bang approaches, new space-time geometries and new ultimate constituents of matter. Basic issues related to a possible new cosmology along these lines clearly deserve further exploration. The Planck collaboration reports an age of the Universe t close to 13.8 Gyr and a present ratio H between relative speeds and distances at cosmic scale around 67.3 km/s/Mpc. The product of these two measured quantities is then slightly below 1 (about 0.95), while it can be exactly 1 in the absence of matter and cosmological constant in patterns based on the spinorial space-time we have considered in previous papers. In this description of space-time we first suggested in 1996-97, the cosmic time t is given by the modulus of a SU(2) spinor and the Lundmark-Lemaître-Hubble (LLH) expansion law turns out to be of purely geometric origin previous to any introduction of standard matter and relativity. Such a fundamental geometry, inspired by the role of half-integer spin in Particle Physics, may reflect an equilibrium between the dynamics of the ultimate constituents of matter and the deep structure of space and time. Taking into account the observed cosmic acceleration, the present situation suggests that the value of 1 can be a natural asymptotic limit for the product H t in the long-term evolution of our Universe up to possible small corrections. In the presence of a spinorial space-time geometry, no ad hoc combination of dark matter and dark energy would in any case be needed to get an acceptable value of H and an evolution of the Universe compatible with observation. The use of a spinorial space-time naturally leads to unconventional properties for the space curvature term in Friedmann-like equations. It therefore suggests a major modification of the standard

  9. On the reconstruction of Lifshitz spacetimes

    International Nuclear Information System (INIS)

    Gentle, Simon A.; Keeler, Cynthia

    2016-01-01

    We consider the reconstruction of a Lifshitz spacetime from three perspectives: differential entropy (or ‘hole-ography’), causal wedges and entanglement wedges. We find that not all time-varying bulk curves in vacuum Lifshitz can be reconstructed via the differential entropy approach, adding a caveat to the general analysis of http://dx.doi.org/10.1007/JHEP10(2014)149. We show that the causal wedge for Lifshitz spacetimes degenerates, while the entanglement wedge requires the additional consideration of a set of boundary-emanating light-sheets. The need to include bulk surfaces with no clear field theory interpretation in the differential entropy construction and the change in the entanglement wedge formation both serve as warnings against a naive application of holographic entanglement entropy proposals in Lifshitz spacetimes.

  10. Scalar fields in black hole spacetimes

    Science.gov (United States)

    Thuestad, Izak; Khanna, Gaurav; Price, Richard H.

    2017-07-01

    The time evolution of matter fields in black hole exterior spacetimes is a well-studied subject, spanning several decades of research. However, the behavior of fields in the black hole interior spacetime has only relatively recently begun receiving some attention from the research community. In this paper, we numerically study the late-time evolution of scalar fields in both Schwarzschild and Kerr spacetimes, including the black hole interior. We recover the expected late-time power-law "tails" on the exterior (null infinity, timelike infinity, and the horizon). In the interior region, we find an interesting oscillatory behavior that is characterized by the multipole index ℓ of the scalar field. In addition, we also study the extremal Kerr case and find strong indications of an instability developing at the horizon.

  11. Tension perturbations of black brane spacetimes

    International Nuclear Information System (INIS)

    Traschen, Jennie; Fox, Daniel

    2004-01-01

    We consider black brane spacetimes that have at least one spatial translation Killing field that is tangent to the brane. A new parameter, the tension of a spacetime, is defined. The tension parameter is associated with spatial translations in much the same way that the ADM mass is associated with the time translation Killing field. In this work, we explore the implications of the spatial translation symmetry for small perturbations around a background black brane. For static-charged black branes we derive a law which relates the tension perturbation to the surface gravity times the change in the horizon area, plus terms that involve variations in the charges and currents. We find that as a black brane evaporates the tension decreases. We also give a simple derivation of a first law for black brane spacetimes. These constructions hold when the background stress-energy is governed by a Hamiltonian, and the results include arbitrary perturbative stress-energy sources

  12. K-causality and degenerate spacetimes

    Science.gov (United States)

    Dowker, H. F.; Garcia, R. S.; Surya, S.

    2000-11-01

    The causal relation K+ was introduced by Sorkin and Woolgar to extend the standard causal analysis of C2 spacetimes to those that are only C0. Most of their results also hold true in the case of metrics with degeneracies which are C0 but vanish at isolated points. In this paper we seek to examine K+ explicitly in the case of topology-changing `Morse histories' which contain degeneracies. We first demonstrate some interesting features of this relation in globally Lorentzian spacetimes. In particular, we show that K+ is robust and the Hawking and Sachs characterization of causal continuity translates into a natural condition in terms of K+. We then examine K+ in topology-changing Morse spacetimes with the degenerate points excised and then for the Morse histories in which the degenerate points are reinstated. We find further characterizations of causal continuity in these cases.

  13. Dynamics of quantum entanglement in de Sitter spacetime and thermal Minkowski spacetime

    Directory of Open Access Journals (Sweden)

    Zhiming Huang

    2017-10-01

    Full Text Available We investigate the dynamics of entanglement between two atoms in de Sitter spacetime and in thermal Minkowski spacetime. We treat the two-atom system as an open quantum system which is coupled to a conformally coupled massless scalar field in the de Sitter invariant vacuum or to a thermal bath in the Minkowski spacetime, and derive the master equation that governs its evolution. We compare the phenomena of entanglement creation, degradation, revival and enhancement for the de Sitter spacetime case with that for the thermal Minkowski spacetime case. We find that the entanglement dynamics of two atoms for these two spacetime cases behave quite differently. In particular, the two atoms interacting with the field in the thermal Minkowski spacetime (with the field in the de Sitter-invariant vacuum, under certain conditions, could be entangled, while they would not become entangled in the corresponding de Sitter case (in the corresponding thermal Minkowski case. Thus, although a single static atom in the de Sitter-invariant vacuum responds as if it were bathed in thermal radiation in a Minkowski universe, with the help of the different dynamic evolution behaviors of entanglement for two atoms one can in principle distinguish these two universes.

  14. Dimensional flow and fuzziness in quantum gravity: Emergence of stochastic spacetime

    Directory of Open Access Journals (Sweden)

    Gianluca Calcagni

    2017-10-01

    Full Text Available We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.

  15. Dirac Hamiltonian and Reissner-Nordström metric: Coulomb interaction in curved space-time

    Science.gov (United States)

    Noble, J. H.; Jentschura, U. D.

    2016-03-01

    We investigate the spin-1 /2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordström space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordström geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational and electrogravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electrogravitational correction terms to the potential proportional to αnG , where α is the fine-structure constant and G is the gravitational coupling constant. The particle-antiparticle symmetry found for the Dirac-Schwarzschild geometry (and for other geometries which do not include electromagnetic interactions) is shown to be explicitly broken due to the electrostatic coupling. The resulting spectrum of radially symmetric, electrostatically bound systems (with gravitational corrections) is evaluated for example cases.

  16. Dimensional flow and fuzziness in quantum gravity: Emergence of stochastic spacetime

    International Nuclear Information System (INIS)

    Calcagni, Gianluca; Ronco, Michele

    2017-01-01

    We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow) and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales) and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.

  17. Dimensional flow and fuzziness in quantum gravity: Emergence of stochastic spacetime

    Science.gov (United States)

    Calcagni, Gianluca; Ronco, Michele

    2017-10-01

    We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow) and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales) and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.

  18. Quasinormal modes in pure de Sitter spacetimes

    International Nuclear Information System (INIS)

    Du Daping; Wang Bin; Su Ruheng

    2004-01-01

    We have studied scalar perturbations as well as fermion perturbations in pure de Sitter spacetimes. For scalar perturbations we have shown that well-defined quasinormal modes in d-dimensions can exist provided that the mass of scalar field m>(d-1/2l). The quasinormal modes of fermion perturbations in three and four dimensional cases have also been investigated. We found that different from other dimensional cases, in the three dimensional pure de Sitter spacetime there is no quasinormal mode for the s-wave. This interesting difference caused by the spacial dimensions is true for both scalar and fermion perturbations

  19. Racing a quantum computer through Minkowski spacetime

    International Nuclear Information System (INIS)

    Biamonte, Jacob D

    2010-01-01

    The Lorentzian length of a timelike curve connecting both endpoints of a computation in Minkowski spacetime is smaller than the Lorentzian length of the corresponding geodesic. In this talk, I will point out some properties of spacetime that allow an inertial classical computer to outperform a quantum one, at the completion of a long journey. We will focus on a comparison between the optimal quadratic Grover speed up from quantum computing and an n=2 speedup using classical computers and relativistic effects. These results are not practical as a new model of computation, but allow us to probe the ultimate limits physics places on computers.

  20. Axiomatics of uniform space-time models

    International Nuclear Information System (INIS)

    Levichev, A.V.

    1983-01-01

    The mathematical statement of space-time axiomatics of the special theory of relativity is given; it postulates that the space-time M is the binding single boundary Hausedorf local-compact four-dimensional topological space with the given order. The theorem is proved: if the invariant order in the four-dimensional group M is given by the semi-group P, which contingency K contains inner points , then M is commutative. The analogous theorem is correct for the group of two and three dimensionalities

  1. Holography and Entanglement in Flat Spacetime

    International Nuclear Information System (INIS)

    Li Wei; Takayanagi, Tadashi

    2011-01-01

    We propose a holographic correspondence of the flat spacetime based on the behavior of the entanglement entropy and the correlation functions. The holographic dual theory turns out to be highly nonlocal. We argue that after most part of the space is traced out, the reduced density matrix gives the maximal entropy and the correlation functions become trivial. We present a toy model for this holographic dual using a nonlocal scalar field theory that reproduces the same property of the entanglement entropy. Our conjecture is consistent with the entropy of Schwarzschild black holes in asymptotically flat spacetimes.

  2. Perturbative spacetimes from Yang-Mills theory

    Energy Technology Data Exchange (ETDEWEB)

    Luna, Andrés [School of Physics and Astronomy, University of Glasgow,Glasgow G12 8QQ, Scotland (United Kingdom); Monteiro, Ricardo [Theoretical Physics Department, CERN,Geneva (Switzerland); Nicholson, Isobel; Ochirov, Alexander; O’Connell, Donal [Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); Westerberg, Niclas [Institute of Photonics and Quantum Sciences,School of Engineering and Physical Sciences, Heriot-Watt University,Edinburgh (United Kingdom); Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); White, Chris D. [Centre for Research in String Theory,School of Physics and Astronomy, Queen Mary University of London,327 Mile End Road, London E1 4NS (United Kingdom)

    2017-04-12

    The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.

  3. Special relativity derived from spacetime magma.

    Science.gov (United States)

    Greensite, Fred

    2014-01-01

    We present a derivation of relativistic spacetime largely untethered from specific physical considerations, in constrast to the many physically-based derivations that have appeared in the last few decades. The argument proceeds from the inherent magma (groupoid) existing on the union of spacetime frame components [Formula: see text] and Euclidean [Formula: see text] which is consistent with an "inversion symmetry" constraint from which the Minkowski norm results. In this context, the latter is also characterized as one member of a class of "inverse norms" which play major roles with respect to various unital [Formula: see text]-algebras more generally.

  4. Special relativity derived from spacetime magma.

    Directory of Open Access Journals (Sweden)

    Fred Greensite

    Full Text Available We present a derivation of relativistic spacetime largely untethered from specific physical considerations, in constrast to the many physically-based derivations that have appeared in the last few decades. The argument proceeds from the inherent magma (groupoid existing on the union of spacetime frame components [Formula: see text] and Euclidean [Formula: see text] which is consistent with an "inversion symmetry" constraint from which the Minkowski norm results. In this context, the latter is also characterized as one member of a class of "inverse norms" which play major roles with respect to various unital [Formula: see text]-algebras more generally.

  5. Spacetime transformations from a uniformly accelerated frame

    International Nuclear Information System (INIS)

    Friedman, Yaakov; Scarr, Tzvi

    2013-01-01

    We use the generalized Fermi–Walker transport to construct a one-parameter family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the weak hypothesis of locality, we obtain local spacetime transformations from a uniformly accelerated frame K′ to an inertial frame K. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame. (paper)

  6. Thin accretion disks in stationary axisymmetric wormhole spacetimes

    International Nuclear Information System (INIS)

    Harko, Tiberiu; Kovacs, Zoltan; Lobo, Francisco S. N.

    2009-01-01

    In this paper, we study the physical properties and the equilibrium thermal radiation emission characteristics of matter forming thin accretion disks in stationary axially symmetric wormhole spacetimes. The thin disk models are constructed by taking different values of the wormhole's angular velocity, and the time averaged energy flux, the disk temperature, and the emission spectra of the accretion disks are obtained. Comparing the mass accretion in a rotating wormhole geometry with the one of a Kerr black hole, we verify that the intensity of the flux emerging from the disk surface is greater for wormholes than for rotating black holes with the same geometrical mass and accretion rate. We also present the conversion efficiency of the accreting mass into radiation, and show that the rotating wormholes provide a much more efficient engine for the transformation of the accreting mass into radiation than the Kerr black holes. Therefore specific signatures appear in the electromagnetic spectrum of thin disks around rotating wormholes, thus leading to the possibility of distinguishing wormhole geometries by using astrophysical observations of the emission spectra from accretion disks.

  7. The space-time model according to dimensional continuous space-time theory

    International Nuclear Information System (INIS)

    Martini, Luiz Cesar

    2014-01-01

    This article results from the Dimensional Continuous Space-Time Theory for which the introductory theoretician was presented in [1]. A theoretical model of the Continuous Space-Time is presented. The wave equation of time into absolutely stationary empty space referential will be described in detail. The complex time, that is the time fixed on the infinite phase time speed referential, is deduced from the New View of Relativity Theory that is being submitted simultaneously with this article in this congress. Finally considering the inseparable Space-Time is presented the duality equation wave-particle.

  8. Constant scalar curvature hypersurfaces in extended Schwarzschild space-time

    International Nuclear Information System (INIS)

    Pareja, M. J.; Frauendiener, J.

    2006-01-01

    We present a class of spherically symmetric hypersurfaces in the Kruskal extension of the Schwarzschild space-time. The hypersurfaces have constant negative scalar curvature, so they are hyperboloidal in the regions of space-time which are asymptotically flat

  9. Geometry of lattice field theory

    International Nuclear Information System (INIS)

    Honan, T.J.

    1986-01-01

    Using some tools of algebraic topology, a general formalism for lattice field theory is presented. The lattice is taken to be a simplicial complex that is also a manifold and is referred to as a simplicial manifold. The fields on this lattice are cochains, that are called lattice forms to emphasize the connections with differential forms in the continuum. This connection provides a new bridge between lattice and continuum field theory. A metric can be put onto this simplicial manifold by assigning lengths to every link or I-simplex of the lattice. Regge calculus is a way of defining general relativity on this lattice. A geometric discussion of Regge calculus is presented. The Regge action, which is a discrete form of the Hilbert action, is derived from the Hilbert action using distribution valued forms. This is a new derivation that emphasizes the underlying geometry. Kramers-Wannier duality in statistical mechanics is discussed in this general setting. Nonlinear field theories, which include gauge theories and nonlinear sigma models are discussed in the continuum and then are put onto a lattice. The main new result here is the generalization to curved spacetime, which consists of making the theory compatible with Regge calculus

  10. Black-hole horizons in modified spacetime structures arising from canonical quantum gravity

    International Nuclear Information System (INIS)

    Bojowald, Martin; Paily, George M; Reyes, Juan D; Tibrewala, Rakesh

    2011-01-01

    Several properties of canonical quantum gravity modify spacetime structures, sometimes to the degree that no effective line elements exist to describe the geometry. An analysis of solutions, for instance in the context of black holes, then requires new insights. In this paper, standard definitions of horizons in spherical symmetry are first reformulated canonically, and then evaluated for solutions of equations and constraints modified by inverse-triad corrections of loop quantum gravity. When possible, a spacetime analysis is performed which reveals a mass threshold for black holes and small changes to Hawking radiation. For more general conclusions, canonical perturbation theory is developed to second order to include back-reaction from matter. The results shed light on the questions of whether renormalization of Newton's constant or other modifications of horizon conditions should be taken into account in computations of black-hole entropy in loop quantum gravity.

  11. The limit space of a Cauchy sequence of globally hyperbolic spacetimes

    Energy Technology Data Exchange (ETDEWEB)

    Noldus, Johan [Universiteit Gent, Vakgroep Wiskundige analyse, Galglaan 2, 9000 Gent (Belgium)

    2004-02-21

    In this second paper, I construct a limit space of a Cauchy sequence of globally hyperbolic spacetimes. In section 2, I work gradually towards a construction of the limit space. I prove that the limit space is unique up to isometry. I also show that, in general, the limit space has quite complicated causal behaviour. This work prepares the final paper in which I shall study in more detail properties of the limit space and the moduli space of (compact) globally hyperbolic spacetimes (cobordisms). As a fait divers, I give in this paper a suitable definition of dimension of a Lorentz space in agreement with the one given by Gromov in the Riemannian case. The difference in philosophy between Lorentzian and Riemannian geometry is one of relativism versus absolutism. In the latter every point distinguishes itself while in the former in general two elements get distinguished by a third, different, one.

  12. Sector models—A toolkit for teaching general relativity: I. Curved spaces and spacetimes

    International Nuclear Information System (INIS)

    Zahn, C; Kraus, U

    2014-01-01

    Teaching the general theory of relativity to high school or undergraduate students must be based on an approach that is conceptual rather than mathematical. In this paper we present such an approach that requires no more than elementary mathematics. The central idea of this introduction to general relativity is the use of so-called sector models. Sector models describe curved spaces the Regge calculus way by subdivision into blocks with euclidean geometry. This procedure is similar to the approximation of a curved surface by flat triangles. We outline a workshop for high school and undergraduate students that introduces the notion of curved space by means of sector models of black holes. We further describe the extension to sector models of curved spacetimes. The spacetime models are suitable for learners with a basic knowledge of special relativity. The teaching materials presented in this paper are available online for teaching purposes at www.spacetimetravel.org. (paper)

  13. The limit space of a Cauchy sequence of globally hyperbolic spacetimes

    International Nuclear Information System (INIS)

    Noldus, Johan

    2004-01-01

    In this second paper, I construct a limit space of a Cauchy sequence of globally hyperbolic spacetimes. In section 2, I work gradually towards a construction of the limit space. I prove that the limit space is unique up to isometry. I also show that, in general, the limit space has quite complicated causal behaviour. This work prepares the final paper in which I shall study in more detail properties of the limit space and the moduli space of (compact) globally hyperbolic spacetimes (cobordisms). As a fait divers, I give in this paper a suitable definition of dimension of a Lorentz space in agreement with the one given by Gromov in the Riemannian case. The difference in philosophy between Lorentzian and Riemannian geometry is one of relativism versus absolutism. In the latter every point distinguishes itself while in the former in general two elements get distinguished by a third, different, one

  14. Thermal particle production in two Taub-Nut type spacetimes

    International Nuclear Information System (INIS)

    Lapedes, A.S.

    1976-01-01

    The Hartle-Hawking method of deriving black hole radiance has been extended to non-asymptotically flat de Sitter spacetime by Gibbons and Hawking. We extend this work to Taub-Nut spacetime and a related and more physical spacetime constructed from it by Siklos. (orig./BJ) [de

  15. Spacetime emergence of the robertson-walker universe from a matrix model.

    Science.gov (United States)

    Erdmenger, Johanna; Meyer, René; Park, Jeong-Hyuck

    2007-06-29

    Using a novel, string theory-inspired formalism based on a Hamiltonian constraint, we obtain a conformal mechanical system for the spatially flat four-dimensional Robertson-Walker Universe. Depending on parameter choices, this system describes either a relativistic particle in the Robertson-Walker background or metric fluctuations of the Robertson-Walker geometry. Moreover, we derive a tree-level M theory matrix model in this time-dependent background. Imposing the Hamiltonian constraint forces the spacetime geometry to be fuzzy near the big bang, while the classical Robertson-Walker geometry emerges as the Universe expands. From our approach, we also derive the temperature of the Universe interpolating between the radiation and matter dominated eras.

  16. Space-time modeling of timber prices

    Science.gov (United States)

    Mo Zhou; Joseph Buongriorno

    2006-01-01

    A space-time econometric model was developed for pine sawtimber timber prices of 21 geographically contiguous regions in the southern United States. The correlations between prices in neighboring regions helped predict future prices. The impulse response analysis showed that although southern pine sawtimber markets were not globally integrated, local supply and demand...

  17. Strings in arbitrary space-time dimensions

    International Nuclear Information System (INIS)

    Fabbrichesi, M.E.; Leviant, V.M.

    1988-01-01

    A modified approach to the theory of a quantum string is proposed. A discussion of the gauge fixing of conformal symmetry by means of Kac-Moody algebrae is presented. Virasoro-like operators are introduced to cancel the conformal anomaly in any number of space-time dimensions. The possibility of massless states in the spectrum is pointed out. 18 refs

  18. Kundt spacetimes minimally coupled to scalar field

    Energy Technology Data Exchange (ETDEWEB)

    Tahamtan, T. [Charles University, Institute of Theoretical Physics, Faculty of Mathematics and Physics, Prague 8 (Czech Republic); Astronomical Institute, Czech Academy of Sciences, Prague (Czech Republic); Svitek, O. [Charles University, Institute of Theoretical Physics, Faculty of Mathematics and Physics, Prague 8 (Czech Republic)

    2017-06-15

    We derive an exact solution belonging to the Kundt class of spacetimes both with and without a cosmological constant that are minimally coupled to a free massless scalar field. We show the algebraic type of these solutions and give interpretation of the results. Subsequently, we look for solutions additionally containing an electromagnetic field satisfying nonlinear field equations. (orig.)

  19. The effective mass of the Kerr spacetime

    International Nuclear Information System (INIS)

    Kulkarni, R.; Chellathurai, V.; Dadhich, N.

    1988-01-01

    The expressions for the effective mass of rotating spacetimes existing in the literature do not incorporate the rotational contribution at all. We generalise a result of Cohen and de Felice [1984, J. Math. Phys. 25, 992] and show how rotational effects can be taken into account. (author)

  20. Construction of spacetimes from initial data

    International Nuclear Information System (INIS)

    Isenberg, J.A.

    1979-01-01

    As relativistic effects become more accessible to physical experiment and observation, it becomes important to be able to theoretically analyze the behavior of relativistic model systems designed to incorporate such measurable effects. This dissertation describes in detail the initial value (IV) procedure for carrying out such analyses (i.e., for ''building spacetimes''). We report progress--of the author as well as others--in all of these areas: (1) The generalized Bergmann-Dirac (BD) procedure can be used to systematically translate any theory into 3+1 form. (2) The York procedure turns the constraints of Einstein's theory into a set of four elliptic equations for four unknowns (with the rest of the initial data ''relatively free''). (3) The maximal and K-foliation schemes appear to give preferred kinematics for the generic spacetimes one might build. We discuss the sense in which these foliations are preferred, and compare them with others. We then show how to find maximal and K-surfaces, both in a given spacetime (e.g. Schwarzschild) and in one being built from scratch. (4) Many physically interesting systems have symmetries which considerably simplify the equations. After discussing how, in general, one can build symmetries into initial data, and how one can use them to simplify the analysis, we look at a particular example symmetry: spacetimes with two space-like translation Killing Vectors. (''2T'')

  1. Spacetime-varying couplings and Lorentz violation

    International Nuclear Information System (INIS)

    Kostelecky, V. Alan; Lehnert, Ralf; Perry, Malcolm J.

    2003-01-01

    Spacetime-varying coupling constants can be associated with violations of local Lorentz invariance and CPT symmetry. An analytical supergravity cosmology with a time-varying fine-structure constant provides an explicit example. Estimates are made for some experimental constraints

  2. Space-time and Local Gauge Symmetries

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 2. Symmetries of Particle Physics: Space-time and Local Gauge Symmetries. Sourendu Gupta. General Article Volume 6 Issue 2 February 2001 pp 29-38. Fulltext. Click here to view fulltext PDF. Permanent link:

  3. Local and nonlocal space-time singularities

    International Nuclear Information System (INIS)

    Konstantinov, M.Yu.

    1985-01-01

    The necessity to subdivide the singularities into two classes: local and nonlocal, each of them to be defined independently, is proved. Both classes of the singularities are defined, and the relation between the definitions introduced and the standard definition of singularities, based on space-time, incompleteness, is established. The relation between definitions introduced and theorems on the singularity existence is also established

  4. Quantum teleportation and Kerr-Newman spacetime

    Institute of Scientific and Technical Information of China (English)

    Ge Xian-Hui; Shen You-Gen

    2005-01-01

    We consider the teleportation in the background of Kerr-Newman spacetime. Because of the Hawking effect, the fidelity of the teleportation is reduced. The results also show the fidelity is closely related to the mass, charge and rotating velocity of the black hole: high fidelity can be reached for massive, slowly rotating Kerr-Newman black holes.

  5. Chaos in Kundt Type-III Spacetimes

    International Nuclear Information System (INIS)

    Sakalli, I.; Halilsoy, M.

    2011-01-01

    We consider geodesic motion in a particular Kundt type-III spacetime in which the Einstein-Yang-Mills equations admit the solutions. On a particular surface as constraint, we project the geodesics into the (x, y) plane and treat the problem as a two-dimensional one. Our numerical study shows that chaotic behavior emerges under reasonable conditions. (general)

  6. Quantum space-time and gravitational consequences

    International Nuclear Information System (INIS)

    Namsrai, K.

    1986-01-01

    Relativistic particle dynamics and basic physical quantities for the general theory of gravity are reconstructed from a quantum space-time point of view. An additional force caused by quantum space-time appears in the equation of particle motion, giving rise to a reformulation of the equivalence principle up to values of O(L 2 ), where L is the fundamental length. It turns out that quantum space-time leads to quantization of gravity, i.e. the metric tensor g/sub uv/ (/ZETA/) becomes operator-valued and is not commutative at different points x/sup micro/ and y/sup micro/ in usual space-time on a large scale, and its commutator depending on the ''vielbein'' field (gaugelike graviton field) is proportional to L 2 multiplied by a translationinvariant wave function propagated between points x/sup micro/ and y/sup micro/. In the given scheme, there appears to be an antigravitational effect in the motion of a particle in the gravitational force. This effect depends on the value of particle mass; when a particle is heavy its free-fall time is long compared to that for a light-weight particle. The problem of the change of time scale and the anisotropy of inertia are discussed. From experimental data from testing of the latter effect it follows that L ≤ 10 -22 cm

  7. The Thermal Entropy Density of Spacetime

    Directory of Open Access Journals (Sweden)

    Rongjia Yang

    2013-01-01

    Full Text Available Introducing the notion of thermal entropy density via the first law of thermodynamics and assuming the Einstein equation as an equation of thermal state, we obtain the thermal entropy density of any arbitrary spacetime without assuming a temperature or a horizon. The results confirm that there is a profound connection between gravity and thermodynamics.

  8. Type III and N universal spacetimes

    Czech Academy of Sciences Publication Activity Database

    Hervik, S.; Pravda, Vojtěch; Pravdová, Alena

    2014-01-01

    Roč. 31, č. 21 (2014), s. 215005 ISSN 0264-9381 R&D Projects: GA ČR GA13-10042S Institutional support: RVO:67985840 Keywords : universal spacetimes * generalized gravity * exact solutions Subject RIV: BA - General Mathematics Impact factor: 3.168, year: 2014 http://iopscience.iop.org/0264-9381/31/21/215005/article

  9. Noncommutative gravity and quantum field theory on noncummutative curved spacetimes

    Energy Technology Data Exchange (ETDEWEB)

    Schenkel, Alexander

    2011-10-24

    The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein's field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of a given symmetric system. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models, for which the noncommutative metric field coincides with the classical one. In the second part we focus on quantum field theory on noncommutative curved spacetimes. We develop a new formalism by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. The result is an algebra of observables for scalar quantum field theories on a large class of noncommutative curved spacetimes. A precise relation to the algebra of observables of the corresponding undeformed quantum field theory is established. We focus on explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories, which is not the case in the simplest example of the Moyal-Weyl deformed Minkowski spacetime. The convergent deformation of simple toy-models is investigated and it is shown that these quantum field theories have many new features compared to formal deformation quantization. In addition to the expected nonlocality, we obtain that the relation between the deformed and the undeformed quantum field theory is affected in a nontrivial way, leading to an improved behavior of the

  10. Noncommutative gravity and quantum field theory on noncummutative curved spacetimes

    International Nuclear Information System (INIS)

    Schenkel, Alexander

    2011-01-01

    The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein's field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of a given symmetric system. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models, for which the noncommutative metric field coincides with the classical one. In the second part we focus on quantum field theory on noncommutative curved spacetimes. We develop a new formalism by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. The result is an algebra of observables for scalar quantum field theories on a large class of noncommutative curved spacetimes. A precise relation to the algebra of observables of the corresponding undeformed quantum field theory is established. We focus on explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories, which is not the case in the simplest example of the Moyal-Weyl deformed Minkowski spacetime. The convergent deformation of simple toy-models is investigated and it is shown that these quantum field theories have many new features compared to formal deformation quantization. In addition to the expected nonlocality, we obtain that the relation between the deformed and the undeformed quantum field theory is affected in a nontrivial way, leading to an improved behavior of the noncommutative

  11. Spacetime Dynamics and Slow Neutrino Background

    Science.gov (United States)

    Zhang, Tianxi

    2018-06-01

    Space is a form of existence of matter, while time is a measure of change of the matter in the space. Issac Newton suggested that the space and time are absolute, not affected by matter and its motion. His first law of motion or the law of inertia says that, without net force acts on it, an object in motion remains the motion in a straight line at a constant speed. Ernest Mach proposed that the inertia of a body results from the gravitational interaction on the body by the rest of the entire universe. As mass is a measure of inertia, Mach’s principle can be simply stated as mass here is affected by matter there. On the basis of Mach’s principle, Albert Einstein considered the space and time to be relative and developed two theories of relativities. One called special relativity describes the effect of motion on spacetime and the other called general relativity describes the effect of matter on spacetime. Recently, the author has further considered reactions of the influenced spacetime on the moving objects, including photons. A moving object including a photon, because of its continuously keeping on displacement, disturbs the rest of the entire universe or distorts/curves the spacetime. The distorted or curved spacetime then generates an effective gravitational force to act back on the moving object or photon, so that reduces the object inertia or photon frequency. Considering the disturbance of spacetime by a photon is extremely weak, the author has modelled the effective gravitational force to be Newtonian and derived a new redshift-distance relation that not only perfectly explained the redshift-distance measurement of distant type Ia supernovae but also inherently obtained Hubble’s law as an approximate at small redshift. In this study, we will further analyse the reaction of the influenced spacetime on moving neutrinos and demonstrate the creation of slow neutrino (or tired neutrino) background that may be gravitationally orbiting around clusters

  12. Geometry and its applications

    CERN Document Server

    Meyer, Walter J

    2006-01-01

    Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...

  13. Algebraic geometry in India

    Indian Academy of Sciences (India)

    algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.

  14. Spinorial Geometry and Branes

    International Nuclear Information System (INIS)

    Sloane, Peter

    2007-01-01

    We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

  15. Spinorial Geometry and Branes

    Energy Technology Data Exchange (ETDEWEB)

    Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)

    2007-09-15

    We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

  16. Global properties of physically interesting Lorentzian spacetimes

    Science.gov (United States)

    Nawarajan, Deloshan; Visser, Matt

    Under normal circumstances most members of the general relativity community focus almost exclusively on the local properties of spacetime, such as the locally Euclidean structure of the manifold and the Lorentzian signature of the metric tensor. When combined with the classical Einstein field equations this gives an extremely successful empirical model of classical gravity and classical matter — at least as long as one does not ask too many awkward questions about global issues, (such as global topology and global causal structure). We feel however that this is a tactical error — even without invoking full-fledged “quantum gravity” we know that the standard model of particle physics is also an extremely good representation of some parts of empirical reality; and we had better be able to carry over all the good features of the standard model of particle physics — at least into the realm of semi-classical quantum gravity. Doing so gives us some interesting global features that spacetime should possess: On physical grounds spacetime should be space-orientable, time-orientable, and spacetime-orientable, and it should possess a globally defined tetrad (vierbein, or in general a globally defined vielbein/n-bein). So on physical grounds spacetime should be parallelizable. This strongly suggests that the metric is not the fundamental physical quantity; a very good case can be made for the tetrad being more fundamental than the metric. Furthermore, a globally-defined “almost complex structure” is almost unavoidable. Ideas along these lines have previously been mooted, but much is buried in the pre-arXiv literature and is either forgotten or inaccessible. We shall revisit these ideas taking a perspective very much based on empirical physical observation.

  17. The topology of geodesically complete space-times

    International Nuclear Information System (INIS)

    Lee, C.W.

    1983-01-01

    Two theorems are given on the topology of geodesically complete space-times which satisfy the energy condition. Firstly, the condition that a compact embedded 3-manifold in space-time be dentless is defined in terms of causal structure. Then it is shown that a dentless 3-manifold must separate space-time, and that it must enclose a compact portion of space-time. Further, it is shown that if the dentless 3-manifold is homeomorphic to S 3 then the part of space-time that it encloses must be simply connected. (author)

  18. On spinless null propagation in five-dimensional space-times with approximate space-like Killing symmetry

    Energy Technology Data Exchange (ETDEWEB)

    Breban, Romulus [Institut Pasteur, Paris Cedex 15 (France)

    2016-09-15

    Five-dimensional (5D) space-time symmetry greatly facilitates how a 4D observer perceives the propagation of a single spinless particle in a 5D space-time. In particular, if the 5D geometry is independent of the fifth coordinate then the 5D physics may be interpreted as 4D quantum mechanics. In this work we address the case where the symmetry is approximate, focusing on the case where the 5D geometry depends weakly on the fifth coordinate. We show that concepts developed for the case of exact symmetry approximately hold when other concepts such as decaying quantum states, resonant quantum scattering, and Stokes drag are adopted, as well. We briefly comment on the optical model of the nuclear interactions and Millikan's oil drop experiment. (orig.)

  19. Geometry essentials for dummies

    CERN Document Server

    Ryan, Mark

    2011-01-01

    Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque

  20. Arithmetic noncommutative geometry

    CERN Document Server

    Marcolli, Matilde

    2005-01-01

    Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...

  1. Geometry of Majorana neutrino and new symmetries

    CERN Document Server

    Volkov, G G

    2006-01-01

    Experimental observation of Majorana fermion matter gives a new impetus to the understanding of the Lorentz symmetry and its extension, the geometrical properties of the ambient space-time structure, matter--antimatter symmetry and some new ways to understand the baryo-genesis problem in cosmology. Based on the primordial Majorana fermion matter assumption, we discuss a possibility to solve the baryo-genesis problem through the the Majorana-Diraco genesis in which we have a chance to understand creation of Q(em) charge and its conservation in our D=1+3 Universe after the Big Bang. In the Majorana-Diraco genesis approach there appears a possibility to check the proton and electron non-stability on the very low energy scale. In particle physics and in our space-time geometry, the Majorana nature of the neutrino can be related to new types of symmetries which are lying beyond the binary Cartan-Killing-Lie algebras/superalgebras. This can just support a conjecture about the non-completeness of the SM in terms of ...

  2. Spin, statistics, and geometry of random walks

    International Nuclear Information System (INIS)

    Jaroszewicz, T.; Kurzepa, P.S.

    1991-01-01

    The authors develop and unify two complementary descriptions of propagation of spinning particles: the directed random walk representation and the spin factor approach. Working in an arbitrary number of dimensions D, they first represent the Dirac propagator in terms of a directed random walk. They then derive the general and explicit form of the gauge connection describing parallel transport of spin and investigate the resulting quantum-mechanical problem of a particle moving on a sphere in the field of a nonabelian SO(D-1) monopole. This construction, generalizing Polyakov's results, enables them to prove the equivalence of the random walk and path-integral (spin factor) representation. As an alternative, they construct and discuss various Wess-Zumino-Witten forms of the spin factor. They clarify the role played by the coupling between the particle's spin and translational degrees of freedom in establishing the geometrical properties of particle's paths in spacetime. To this end, they carefully define and evaluate Hausdorff dimensions of bosonic and fermionic sample paths, in the covariant as well as nonrelativistic formulations. Finally, as an application of the developed formalism, they give an intuitive spacetime interpretation of chiral anomalies in terms of the geometry of fermion trajectories

  3. Massive Vector Fields in Rotating Black-Hole Spacetimes: Separability and Quasinormal Modes.

    Science.gov (United States)

    Frolov, Valeri P; Krtouš, Pavel; Kubizňák, David; Santos, Jorge E

    2018-06-08

    We demonstrate the separability of the massive vector (Proca) field equation in general Kerr-NUT-AdS black-hole spacetimes in any number of dimensions, filling a long-standing gap in the literature. The obtained separated equations are studied in more detail for the four-dimensional Kerr geometry and the corresponding quasinormal modes are calculated. Two of the three independent polarizations of the Proca field are shown to emerge from the separation ansatz and the results are found in an excellent agreement with those of the recent numerical study where the full coupled partial differential equations were tackled without using the separability property.

  4. Splitting spacetime and cloning qubits: linking no-go theorems across the ER=EPR duality

    Energy Technology Data Exchange (ETDEWEB)

    Bao, Ning [Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125 (United States); Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125 (United States); Pollack, Jason; Remmen, Grant N. [Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125 (United States)

    2015-11-15

    We analyze the no-cloning theorem in quantum mechanics through the lens of the proposed ER=EPR (Einstein-Rosen = Einstein-Podolsky-Rosen) duality between entanglement and wormholes. In particular, we find that the no-cloning theorem is dual on the gravity side to the no-go theorem for topology change, violating the axioms of which allows for wormhole stabilization and causality violation. Such a duality between important no-go theorems elucidates the proposed connection between spacetime geometry and quantum entanglement. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  5. Time-dependent gravitating solitons in five dimensional warped space-times

    CERN Document Server

    Giovannini, Massimo

    2007-01-01

    Time-dependent soliton solutions are explicitly derived in a five-dimensional theory endowed with one (warped) extra-dimension. Some of the obtained geometries, everywhere well defined and technically regular, smoothly interpolate between two five-dimensional anti-de Sitter space-times for fixed value of the conformal time coordinate. Time dependent solutions containing both topological and non-topological sectors are also obtained. Supplementary degrees of freedom can be also included and, in this case, the resulting multi-soliton solutions may describe time-dependent kink-antikink systems.

  6. Holographic free energy and thermodynamic geometry

    Science.gov (United States)

    Ghorai, Debabrata; Gangopadhyay, Sunandan

    2016-12-01

    We obtain the free energy and thermodynamic geometry of holographic superconductors in 2+1 dimensions. The gravitational theory in the bulk dual to this 2+1-dimensional strongly coupled theory lives in the 3+1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method.

  7. Holographic free energy and thermodynamic geometry

    International Nuclear Information System (INIS)

    Ghorai, Debabrata; Gangopadhyay, Sunandan

    2016-01-01

    We obtain the free energy and thermodynamic geometry of holographic superconductors in 2 + 1 dimensions. The gravitational theory in the bulk dual to this 2 + 1-dimensional strongly coupled theory lives in the 3 + 1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method. (orig.)

  8. Holographic free energy and thermodynamic geometry

    Energy Technology Data Exchange (ETDEWEB)

    Ghorai, Debabrata [S.N. Bose National Centre for Basic Sciences, Kolkata (India); Gangopadhyay, Sunandan [Indian Institute of Science Education and Research, Kolkata, Nadia (India); West Bengal State University, Department of Physics, Barasat (India); Inter University Centre for Astronomy and Astrophysics, Pune (India)

    2016-12-15

    We obtain the free energy and thermodynamic geometry of holographic superconductors in 2 + 1 dimensions. The gravitational theory in the bulk dual to this 2 + 1-dimensional strongly coupled theory lives in the 3 + 1 dimensions and is that of a charged AdS black hole together with a massive charged scalar field. The matching method is applied to obtain the nature of the fields near the horizon using which the holographic free energy is computed through the gauge/gravity duality. The critical temperature is obtained for a set of values of the matching point of the near horizon and the boundary behaviour of the fields in the probe limit approximation which neglects the back reaction of the matter fields on the background spacetime geometry. The thermodynamic geometry is then computed from the free energy of the boundary theory. From the divergence of the thermodynamic scalar curvature, the critical temperature is obtained once again. We then compare this result for the critical temperature with that obtained from the matching method. (orig.)

  9. Mach's principle and space-time structure

    International Nuclear Information System (INIS)

    Raine, D.J.

    1981-01-01

    Mach's principle, that inertial forces should be generated by the motion of a body relative to the bulk of matter in the universe, is shown to be related to the structure imposed on space-time by dynamical theories. General relativity theory and Mach's principle are both shown to be well supported by observations. Since Mach's principle is not contained in general relativity this leads to a discussion of attempts to derive Machian theories. The most promising of these appears to be a selection rule for solutions of the general relativistic field equations, in which the space-time metric structure is generated by the matter content of the universe only in a well-defined way. (author)

  10. A spacetime cloak, or a history editor

    Science.gov (United States)

    McCall, Martin W.; Favaro, Alberto; Kinsler, Paul; Boardman, Allan

    2011-02-01

    We introduce a new type of electromagnetic cloak, the spacetime cloak (STC), which conceals events rather than objects. Non-emitting events occurring during a restricted period are never suspected by a distant observer. The cloak works by locally manipulating the speed of light of an initially uniform light distribution, whilst the light rays themselves always follow straight paths. Any 'perfect' spacetime cloak would necessarily rely upon the technology of electromagnetic metamaterials, which has already been shown to be capable of deforming light in ways hitherto unforeseen—to produce, for example, an electromagnetic object cloak. Nevertheless, we show how it is possible to use intensity-dependent refractive indices to construct an approximate STC, an implementation that would enable the distinct signature of successful event cloaking to be observed. Potential demonstrations include systems that apparently violate quantum statistics, 'interrupt-without-interrupt' computation on convergent data channels and the illusion of a Star Trek transporter.

  11. Initial data sets for the Schwarzschild spacetime

    International Nuclear Information System (INIS)

    Gomez-Lobo, Alfonso Garcia-Parrado; Kroon, Juan A. Valiente

    2007-01-01

    A characterization of initial data sets for the Schwarzschild spacetime is provided. This characterization is obtained by performing a 3+1 decomposition of a certain invariant characterization of the Schwarzschild spacetime given in terms of concomitants of the Weyl tensor. This procedure renders a set of necessary conditions--which can be written in terms of the electric and magnetic parts of the Weyl tensor and their concomitants--for an initial data set to be a Schwarzschild initial data set. Our approach also provides a formula for a static Killing initial data set candidate--a KID candidate. Sufficient conditions for an initial data set to be a Schwarzschild initial data set are obtained by supplementing the necessary conditions with the requirement that the initial data set possesses a stationary Killing initial data set of the form given by our KID candidate. Thus, we obtain an algorithmic procedure of checking whether a given initial data set is Schwarzschildean or not

  12. Twin paradox in de Sitter spacetime

    International Nuclear Information System (INIS)

    Boblest, Sebastian; Wunner, Guenter; Mueller, Thomas

    2011-01-01

    The 'twin paradox' of special relativity offers the possibility of making interstellar flights within a lifetime. For very long journeys with velocities close to the speed of light, however, we have to take into account the expansion of the universe. Inspired by the work of Rindler on hyperbolic motion in curved spacetime, we study the worldline of a uniformly accelerated observer in de Sitter spacetime and the communication between the travelling observer and an observer at rest. This paper is intended to give graduate students who are familiar with special relativity and have some basic experience of general relativity a deeper insight into accelerated motion in general relativity, into the relationship between the proper times of different observers and the propagation of light signals between them, and into the use of compactification to describe the global structure of a relativistic model.

  13. Topology of classical vacuum space-time

    International Nuclear Information System (INIS)

    Cho, Y.M.

    2007-04-01

    We present a topological classification of classical vacuum space-time. Assuming the 3-dimensional space allows a global chart, we show that the static vacuum space-time of Einstein's theory can be classified by the knot topology π 3 (S 3 ) = π 3 (S 2 ). Viewing Einstein's theory as a gauge theory of Lorentz group and identifying the gravitational connection as the gauge potential of Lorentz group, we construct all possible vacuum gravitational connections which give a vanishing curvature tensor. With this we show that the vacuum connection has the knot topology, the same topology which describes the multiple vacua of SU(2) gauge theory. We discuss the physical implications of our result in quantum gravity. (author)

  14. Approximate spacetime symmetries and conservation laws

    Energy Technology Data Exchange (ETDEWEB)

    Harte, Abraham I [Enrico Fermi Institute, University of Chicago, Chicago, IL 60637 (United States)], E-mail: harte@uchicago.edu

    2008-10-21

    A notion of geometric symmetry is introduced that generalizes the classical concepts of Killing fields and other affine collineations. There is a sense in which flows under these new vector fields minimize deformations of the connection near a specified observer. Any exact affine collineations that may exist are special cases. The remaining vector fields can all be interpreted as analogs of Poincare and other well-known symmetries near timelike worldlines. Approximate conservation laws generated by these objects are discussed for both geodesics and extended matter distributions. One example is a generalized Komar integral that may be taken to define the linear and angular momenta of a spacetime volume as seen by a particular observer. This is evaluated explicitly for a gravitational plane wave spacetime.

  15. Petrov classification and holographic reconstruction of spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Gath, Jakob [Centre de Physique Théorique, Ecole Polytechnique, CNRS UMR 7644,91128 Palaiseau Cedex (France); Mukhopadhyay, Ayan [Department of Physics, University of Crete,Heraklion 71003 (Greece); Petkou, Anastasios C. [Department of Physics, Institute of Theoretical Physics,Aristotle University of Thessaloniki,54124, Thessaloniki (Greece); Petropoulos, P. Marios [Centre de Physique Théorique, Ecole Polytechnique, CNRS UMR 7644,91128 Palaiseau Cedex (France); Siampos, Konstantinos [Albert Einstein Center for Fundamental Physics,Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, 3012 Bern (Switzerland)

    2015-09-01

    Using the asymptotic form of the bulk Weyl tensor, we present an explicit approach that allows us to reconstruct exact four-dimensional Einstein spacetimes which are algebraically special with respect to Petrov’s classification. If the boundary metric supports a traceless, symmetric and conserved complex rank-two tensor, which is related to the boundary Cotton and energy-momentum tensors, and if the hydrodynamic congruence is shearless, then the bulk metric is exactly resummed and captures modes that stand beyond the hydrodynamic derivative expansion. We illustrate the method when the congruence has zero vorticity, leading to the Robinson-Trautman spacetimes of arbitrary Petrov class, and quote the case of non-vanishing vorticity, which captures the Plebański-Demiański Petrov D family.

  16. Swimming versus swinging effects in spacetime

    International Nuclear Information System (INIS)

    Gueron, Eduardo; Maia, Clovis A. S.; Matsas, George E. A.

    2006-01-01

    Wisdom has recently unveiled a new relativistic effect, called 'spacetime swimming', where quasirigid free bodies in curved spacetimes can 'speed up', 'slow down' or 'deviate' their falls by performing local cyclic shape deformations. We show here that for fast enough cycles this effect dominates over a nonrelativistic related one, named here 'space swinging', where the fall is altered through nonlocal cyclic deformations in Newtonian gravitational fields. We expect, therefore, to clarify the distinction between both effects leaving no room to controversy. Moreover, the leading contribution to the swimming effect predicted by Wisdom is enriched with a higher order term and the whole result is generalized to be applicable in cases where the tripod is in large redshift regions

  17. A spacetime cloak, or a history editor

    International Nuclear Information System (INIS)

    McCall, Martin W; Favaro, Alberto; Kinsler, Paul; Boardman, Allan

    2011-01-01

    We introduce a new type of electromagnetic cloak, the spacetime cloak (STC), which conceals events rather than objects. Non-emitting events occurring during a restricted period are never suspected by a distant observer. The cloak works by locally manipulating the speed of light of an initially uniform light distribution, whilst the light rays themselves always follow straight paths. Any 'perfect' spacetime cloak would necessarily rely upon the technology of electromagnetic metamaterials, which has already been shown to be capable of deforming light in ways hitherto unforeseen—to produce, for example, an electromagnetic object cloak. Nevertheless, we show how it is possible to use intensity-dependent refractive indices to construct an approximate STC, an implementation that would enable the distinct signature of successful event cloaking to be observed. Potential demonstrations include systems that apparently violate quantum statistics, 'interrupt-without-interrupt' computation on convergent data channels and the illusion of a Star Trek transporter

  18. Poincare covariance and κ-Minkowski spacetime

    International Nuclear Information System (INIS)

    Dabrowski, Ludwik; Piacitelli, Gherardo

    2011-01-01

    A fully Poincare covariant model is constructed as an extension of the κ-Minkowski spacetime. Covariance is implemented by a unitary representation of the Poincare group, and thus complies with the original Wigner approach to quantum symmetries. This provides yet another example (besides the DFR model), where Poincare covariance is realised a la Wigner in the presence of two characteristic dimensionful parameters: the light speed and the Planck length. In other words, a Doubly Special Relativity (DSR) framework may well be realised without deforming the meaning of 'Poincare covariance'. -- Highlights: → We construct a 4d model of noncommuting coordinates (quantum spacetime). → The coordinates are fully covariant under the undeformed Poincare group. → Covariance a la Wigner holds in presence of two dimensionful parameters. → Hence we are not forced to deform covariance (e.g. as quantum groups). → The underlying κ-Minkowski model is unphysical; covariantisation does not cure this.

  19. The Green functions in curved spacetime

    International Nuclear Information System (INIS)

    Buchbinder, I.L.; Kirillova, E.N.; Odinstov, S.D.

    1987-01-01

    The theory of a free scalar field with conformal coupling in curved spacetime with some special metrics is considered. The integral representations for the green function G-tilde in the form of integrals with Schwinger-De Witt kernel over contours in the complex plane of proper time are obtained. It is shown how the transitions from a unique Green function in Euclidean space to different Green functions in Minkowski space and vice versa can be carried out. (author)

  20. Fermions on spacetimes of spatially closed hypersurfaces

    International Nuclear Information System (INIS)

    Dariescu, Marina-Aura; Dariescu, Ciprian

    2009-01-01

    Using a convenient compact time-like coordinate f element of [0, 1], characterizing the whole big bang-big crunch spacetime history cyclicly evolving with a 2π conformal period, we write down the Dirac-type equation in a FRW matter-dominated Universe. It turns out that, by accepting the idea of existence of an alternative time gauge, as for example in the projected Universe, one is able to derive closed form solutions, for physically meaningful cases.

  1. Born-Infeld gravity in Weitzenboeck spacetime

    International Nuclear Information System (INIS)

    Ferraro, Rafael; Fiorini, Franco

    2008-01-01

    Using the teleparallel equivalent of general relativity formulated in Weitzenboeck spacetime, we thoroughly explore a kind of Born-Infeld regular gravity leading to second order field equations for the vielbein components. We explicitly solve the equations of motion for two examples: the extended Banados-Teitelboim-Zanelli black hole, which exists even if the cosmological constant is positive, and a cosmological model with matter, where the scale factor is well behaved, thus giving a singularity-free solution.

  2. Spacetime and orbits of bumpy black holes

    International Nuclear Information System (INIS)

    Vigeland, Sarah J.; Hughes, Scott A.

    2010-01-01

    Our Universe contains a great number of extremely compact and massive objects which are generally accepted to be black holes. Precise observations of orbital motion near candidate black holes have the potential to determine if they have the spacetime structure that general relativity demands. As a means of formulating measurements to test the black hole nature of these objects, Collins and Hughes introduced ''bumpy black holes'': objects that are almost, but not quite, general relativity's black holes. The spacetimes of these objects have multipoles that deviate slightly from the black hole solution, reducing to black holes when the deviation is zero. In this paper, we extend this work in two ways. First, we show how to introduce bumps which are smoother and lead to better behaved orbits than those in the original presentation. Second, we show how to make bumpy Kerr black holes--objects which reduce to the Kerr solution when the deviation goes to zero. This greatly extends the astrophysical applicability of bumpy black holes. Using Hamilton-Jacobi techniques, we show how a spacetime's bumps are imprinted on orbital frequencies, and thus can be determined by measurements which coherently track the orbital phase of a small orbiting body. We find that in the weak field, orbits of bumpy black holes are modified exactly as expected from a Newtonian analysis of a body with a prescribed multipolar structure, reproducing well-known results from the celestial mechanics literature. The impact of bumps on strong-field orbits is many times greater than would be predicted from a Newtonian analysis, suggesting that this framework will allow observations to set robust limits on the extent to which a spacetime's multipoles deviate from the black hole expectation.

  3. Vector mass in curved space-times

    International Nuclear Information System (INIS)

    Maia, M.D.

    The use of the Poincare-symmetry appears to be incompatible with the presence of the gravitational field. The consequent problem of the definition of the mass operator is analysed and an alternative definition based on constant curvature tangent spaces is proposed. In the case where the space-time has no killing vector fields, four independent mass operators can be defined at each point. (Author) [pt

  4. A Statistical Mechanical Problem in Schwarzschild Spacetime

    OpenAIRE

    Collas, Peter; Klein, David

    2006-01-01

    We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit increases to infinity. We also discuss how the method can be extended to the non ideal gas case.

  5. Anomalies in curved spacetime at finite temperature

    International Nuclear Information System (INIS)

    Boschi-Filho, H.; Natividade, C.P.

    1993-01-01

    We discuss the problem of the breakdown of conformal and gauge symmetries at finite temperature in curved spacetime background, when the changes in the background are gradual. We obtain the expressions for the Seeley's coefficients and the heat kernel expansion in this regime. As applications, we consider the self-interacting lambda phi''4 and chiral Schwinger models in curved backgrounds at finite temperature. (Author) 9 refs

  6. Superstring gravitational wave backgrounds with spacetime supersymmetry

    CERN Document Server

    Kiritsis, Elias B; Lüst, Dieter; Kiritsis, E; Kounnas, C; Lüst, D

    1994-01-01

    We analyse the stringy gravitational wave background based on the current algebra E.sup(c).sub(2). We determine its exact spectrum and construct the modular invariant vacuum energy. The corresponding N=1 extension is also constructed. The algebra is again mapped to free bosons and fermions and we show that this background has N=4 (N=2) unbroken spacetime supersymmetry in the type II (heterotic case).

  7. Temporal and spatial foliations of spacetimes.

    Science.gov (United States)

    Herold, H.

    For the solution of initial-value problems in numerical relativity usually the (3+1) splitting of Einstein's equations is employed. An important part of this splitting is the choice of the temporal gauge condition. In order to estimate the quality of time-evolution schemes, different time slicings of given well-known spherically symmetric spacetimes have been studied. Besides the maximal slicing condition the harmonic slicing prescription has been used to calculate temporal foliations of the Schwarzschild and the Oppenheimer-Snyder spacetime. Additionally, the author has studied a recently proposed, geometrically motivated spatial gauge condition, which is defined by considering the foliations of the three-dimensional space-like hypersurfaces by 2-surfaces of constant mean extrinsic curvature. Apart from the equations for the shift vector, which can be derived for this gauge condition, he has investigated such spatial foliations for well-known stationary axially symmetric spacetimes, namely for the Kerr metric and for numerically determined solutions for rapidly rotating neutron stars.

  8. The manifold model for space-time

    International Nuclear Information System (INIS)

    Heller, M.

    1981-01-01

    Physical processes happen on a space-time arena. It turns out that all contemporary macroscopic physical theories presuppose a common mathematical model for this arena, the so-called manifold model of space-time. The first part of study is an heuristic introduction to the concept of a smooth manifold, starting with the intuitively more clear concepts of a curve and a surface in the Euclidean space. In the second part the definitions of the Csub(infinity) manifold and of certain structures, which arise in a natural way from the manifold concept, are given. The role of the enveloping Euclidean space (i.e. of the Euclidean space appearing in the manifold definition) in these definitions is stressed. The Euclidean character of the enveloping space induces to the manifold local Euclidean (topological and differential) properties. A suggestion is made that replacing the enveloping Euclidean space by a discrete non-Euclidean space would be a correct way towards the quantization of space-time. (author)

  9. Perturbative Critical Behavior from Spacetime Dependent Couplings

    International Nuclear Information System (INIS)

    Torroba, Gonzalo

    2012-01-01

    We find novel perturbative fixed points by introducing mildly spacetime-dependent couplings into otherwise marginal terms. In four-dimensional QFT, these are physical analogues of the small-ε Wilson-Fisher fixed point. Rather than considering 4-ε dimensions, we stay in four dimensions but introduce couplings whose leading spacetime dependence is of the form λx κ μ κ , with a small parameter κ playing a role analogous to ε. We show, in φ 4 theory and in QED and QCD with massless flavors, that this leads to a critical theory under perturbative control over an exponentially wide window of spacetime positions x. The exact fixed point coupling λ * (x) in our theory is identical to the running coupling of the translationally invariant theory, with the scale replaced by 1/x. Similar statements hold for three-dimensional φ 6 theories and two-dimensional sigma models with curved target spaces. We also describe strongly coupled examples using conformal perturbation theory.

  10. Quantum space-time: a review

    International Nuclear Information System (INIS)

    Namsrai, K.

    1988-01-01

    The review presents systematically the results of studies which develop an idea of quantum properties of space-time in the microworld or near exotic objects (black holes, magnetic monopoles and others). On the basis of this idea motion equations of nonrelativistic and relativistic particles are studied. It is shown that introducing concept of quantum space-time at small distances (or near superdense matter) leads to an additional force giving rise to appearance of spiral-like behaviour of a particle along its classical trajectory. Given method is generalized to nonrelativistic quantum mechanics and to motion of a particle in gravitational force. In the latter case, there appears to be an antigravitational effect in the motion of a particle leading to different value of free-fall time (at least for gravitational force of exotic objects) for particles with different masses. Gravitational consequences of quantum space-time and tensor structures of physical quantities are investigated in detail. From experimental data on testing relativity and anisotropy of inertia estimation L ≤ 10 -22 cm on the value of the fundamental length is obtained. (author)

  11. Towards a theory of spacetime theories

    CERN Document Server

    Schiemann, Gregor; Scholz, Erhard

    2017-01-01

    This contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories? How do we judge, objectively, which is the “best” theory? Is there even a unique answer to this question? The goal of the workshop, and of this book, is to contribute to the development of a meta-theory of spacetime theories. Such a meta-theory would reveal insights about specific spacetime theories by distilling their essential similarities and differences, deliver a framework for a class of theories that could be helpful as a blueprint to build other meta-theories, and provide a higher level viewpoint for judging which theory most accurately describes nature. But rather than drawing a map in broad strokes, the focus is on particularly rich regions in the “space of spaceti...

  12. Space-time modeling of soil moisture

    Science.gov (United States)

    Chen, Zijuan; Mohanty, Binayak P.; Rodriguez-Iturbe, Ignacio

    2017-11-01

    A physically derived space-time mathematical representation of the soil moisture field is carried out via the soil moisture balance equation driven by stochastic rainfall forcing. The model incorporates spatial diffusion and in its original version, it is shown to be unable to reproduce the relative fast decay in the spatial correlation functions observed in empirical data. This decay resulting from variations in local topography as well as in local soil and vegetation conditions is well reproduced via a jitter process acting multiplicatively over the space-time soil moisture field. The jitter is a multiplicative noise acting on the soil moisture dynamics with the objective to deflate its correlation structure at small spatial scales which are not embedded in the probabilistic structure of the rainfall process that drives the dynamics. These scales of order of several meters to several hundred meters are of great importance in ecohydrologic dynamics. Properties of space-time correlation functions and spectral densities of the model with jitter are explored analytically, and the influence of the jitter parameters, reflecting variabilities of soil moisture at different spatial and temporal scales, is investigated. A case study fitting the derived model to a soil moisture dataset is presented in detail.

  13. Deduction of Einstein equation from homogeneity of Riemann spacetime

    Science.gov (United States)

    Ni, Jun

    2012-03-01

    The symmetry of spacetime translation leads to the energy-momentum conservation. However, the Lagrange depends on spacetime coordinates, which makes the symmetry of spacetime translation different with other symmetry invariant explicitly under symmetry transformation. We need an equation to guarantee the symmetry of spacetime translation. In this talk, I will show that the Einstein equation can be deduced purely from the general covariant principle and the homogeneity of spacetime in the frame of quantum field theory. The Einstein equation is shown to be the equation to guarantee the symmetry of spacetime translation. Gravity is an apparent force due to the curvature of spacetime resulted from the conservation of energy-momentum. In the action of quantum field, only electroweak-strong interactions appear with curved spacetime metric determined by the Einstein equation.. The general covariant principle and the homogeneity of spacetime are merged into one basic principle: Any Riemann spacetime metric guaranteeing the energy-momentum conservation are equivalent, which can be called as the conserved general covariant principle. [4pt] [1] Jun Ni, Chin. Phys. Lett. 28, 110401 (2011).

  14. The Geometry Conference

    CERN Document Server

    Bárány, Imre; Vilcu, Costin

    2016-01-01

    This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.

  15. On the Penrose inequality for dust null shells in the Minkowski spacetime of arbitrary dimension

    International Nuclear Information System (INIS)

    Mars, Marc; Soria, Alberto

    2012-01-01

    A particular, yet relevant, case of the Penrose inequality involves null shells propagating in the Minkowski spacetime. Despite previous claims in the literature, the validity of this inequality remains open. In this paper, we rewrite this inequality in terms of the geometry of the surface obtained by intersecting the past null cone of the original surface S with a constant time hyperplane and the 'time height' function of S over this hyperplane. We also specialize to the case when S lies in the past null cone of a point and show the validity of the corresponding inequality in any dimension (in four dimensions this inequality was proved by Tod (1985 Class. Quantum Grav. 2 L65-8). Exploiting properties of convex hypersurfaces in the Euclidean space, we write down the Penrose inequality in the Minkowski spacetime of an arbitrary dimension n + 2 as an inequality for two smooth functions on the sphere S n . We finally obtain a sufficient condition for the validity of the Penrose inequality in the four-dimensional Minkowski spacetime and show that this condition is satisfied by a large class of surfaces. (paper)

  16. Generalized wave operators, weighted Killing fields, and perturbations of higher dimensional spacetimes

    Science.gov (United States)

    Araneda, Bernardo

    2018-04-01

    We present weighted covariant derivatives and wave operators for perturbations of certain algebraically special Einstein spacetimes in arbitrary dimensions, under which the Teukolsky and related equations become weighted wave equations. We show that the higher dimensional generalization of the principal null directions are weighted conformal Killing vectors with respect to the modified covariant derivative. We also introduce a modified Laplace–de Rham-like operator acting on tensor-valued differential forms, and show that the wave-like equations are, at the linear level, appropriate projections off shell of this operator acting on the curvature tensor; the projection tensors being made out of weighted conformal Killing–Yano tensors. We give off shell operator identities that map the Einstein and Maxwell equations into weighted scalar equations, and using adjoint operators we construct solutions of the original field equations in a compact form from solutions of the wave-like equations. We study the extreme and zero boost weight cases; extreme boost corresponding to perturbations of Kundt spacetimes (which includes near horizon geometries of extreme black holes), and zero boost to static black holes in arbitrary dimensions. In 4D our results apply to Einstein spacetimes of Petrov type D and make use of weighted Killing spinors.

  17. Lorentz invariance violation and electromagnetic field in an intrinsically anisotropic spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Chang, Zhe [Chinese Academy of Sciences, Institute of High Energy Physics, Beijing (China); Chinese Academy of Sciences, Theoretical Physics Center for Science Facilities, Beijing (China); Wang, Sai [Chinese Academy of Sciences, Institute of High Energy Physics, Beijing (China)

    2012-09-15

    Recently, Kostelecky [V.A. Kostelecky, Phys. Lett. B 701, 137 (2011)] proposed that the spontaneous Lorentz invariance violation (sLIV) is related to Finsler geometry. Finsler spacetime is intrinsically anisotropic and naturally induces Lorentz invariance violation (LIV). In this paper, the electromagnetic field is investigated in locally Minkowski spacetime. The Lagrangian is presented explicitly for the electromagnetic field. It is compatible with the one in the standard model extension (SME). We show the Lorentz-violating Maxwell equations as well as the electromagnetic wave equation. The formal plane wave solution is obtained for the electromagnetic wave. The speed of light may depend on the direction of light and the lightcone may be enlarged or narrowed. The LIV effects could be viewed as influence from an anisotropic media on the electromagnetic wave. In addition, birefringence of light will not emerge at the leading order in this model. A constraint on the spacetime anisotropy is obtained from observations on gamma-ray bursts (GRBs). (orig.)

  18. Distribution Function of the Atoms of Spacetime and the Nature of Gravity

    Directory of Open Access Journals (Sweden)

    Thanu Padmanabhan

    2015-10-01

    Full Text Available The fact that the equations of motion for matter remain invariant when a constant is added to the Lagrangian suggests postulating that the field equations of gravity should also respect this symmetry. This principle implies that: (1 the metric cannot be varied in any extremum principle to obtain the field equations; and (2 the stress-tensor of matter should appear in the variational principle through the combination Tabnanb where na is an auxiliary null vector field, which could be varied to get the field equations. This procedure uniquely selects the Lanczos–Lovelock models of gravity in D-dimensions and Einstein’s theory in D = 4. Identifying na with the normals to the null surfaces in the spacetime in the macroscopic limit leads to a thermodynamic interpretation for gravity. Several geometrical variables and the equation describing the spacetime evolution acquire a thermodynamic interpretation. Extending these ideas one level deeper, we can obtain this variational principle from a distribution function for the “atoms of spacetime”, which counts the number of microscopic degrees of freedom of the geometry. This is based on the curious fact that the renormalized spacetime endows each event with zero volume, but finite area!

  19. An analysis of Born–Infeld determinantal gravity in Weitzenböck spacetime

    Directory of Open Access Journals (Sweden)

    Franco Fiorini

    2016-12-01

    Full Text Available The Born–Infeld theory of the gravitational field formulated in Weitzenböck spacetime is studied in detail. The action, constructed quadratically upon the torsion two-form, reduces to Einstein gravity in the low field limit where the Born–Infeld constant λ goes to infinity, and it is described by second order field equations for the vielbein field in D spacetime dimensions. The equations of motion are derived, and a number of properties coming from them are discussed. In particular, we show that under fairly general circumstances, the equations of motion are those of Einstein's General Relativity plus an energy-momentum tensor of purely geometrical character. This tensor is obtained solely from the parallelization defining the spacetime structure, which is encoded in a set of D smooth, everywhere non-null, globally defined 1-forms ea. Spherical symmetry is studied as an example, and we comment on the emergence of the Schwarzschild geometry within this framework. Potential (regular extensions of it are envisioned.

  20. Fermionic vacuum polarization by a cylindrical boundary in the cosmic string spacetime

    International Nuclear Information System (INIS)

    Bezerra de Mello, E. R.; Bezerra, V. B.; Saharian, A. A.; Tarloyan, A. S.

    2008-01-01

    The vacuum expectation values of the energy-momentum tensor and the fermionic condensate are analyzed for a massive spinor field obeying the MIT bag boundary condition on a cylindrical shell in the cosmic string spacetime. Both regions inside and outside the shell are considered. By applying to the corresponding mode sums a variant of the generalized Abel-Plana formula, we explicitly extract the parts in the expectation values corresponding to the cosmic string geometry without boundaries. In this way the renormalization procedure is reduced to that for the boundary-free cosmic string spacetime. The parts induced by the cylindrical shell are presented in terms of integrals rapidly convergent for points away from the boundary. The behavior of the vacuum densities is investigated in various asymptotic regions of the parameters. In the limit of large values of the planar angle deficit, the boundary-induced expectation values are exponentially suppressed. As a special case, we discuss the fermionic vacuum densities for the cylindrical shell on the background of the Minkowski spacetime.

  1. Spinor Casimir densities for a spherical shell in the global monopole spacetime

    International Nuclear Information System (INIS)

    Saharian, A A; Mello, E R Bezerra de

    2004-01-01

    We investigate the vacuum expectation values of the energy-momentum tensor and the fermionic condensate associated with a massive spinor field obeying the MIT bag boundary condition on a spherical shell in the global monopole spacetime. In order to do that, we use the generalized Abel-Plana summation formula. As we shall see, this procedure allows us to extract from the vacuum expectation values the contribution coming from the unbounded spacetime and to explicitly present the boundary induced parts. As regards the boundary induced contribution, two distinct situations are examined: the vacuum average effects inside and outside the spherical shell. The asymptotic behaviour of the vacuum densities is investigated near the sphere centre and near the surface, and at large distances from the sphere. In the limit of strong gravitational field corresponding to small values of the parameter describing the solid angle deficit in the global monopole geometry, the sphere induced expectation values are exponentially suppressed. We discuss, as a special case, the fermionic vacuum densities for the spherical shell on the background of the Minkowski spacetime. Previous approaches to this problem within the framework of the QCD bag models have been global and our calculation is a local extension of these contributions

  2. Representations of spacetime: Formalism and ontological commitment

    Science.gov (United States)

    Bain, Jonathan Stanley

    This dissertation consists of two parts. The first is on the relation between formalism and ontological commitment in the context of theories of spacetime, and the second is on scientific realism. The first part begins with a look at how the substantivalist/relationist debate over the ontological status of spacetime has been influenced by a particular mathematical formalism, that of tensor analysis on differential manifolds (TADM). This formalism has motivated the substantivalist position known as manifold substantivalism. Chapter 1 focuses on the hole argument which maintains that manifold substantivalism is incompatible with determinism. I claim that the realist motivations underlying manifold substantivalism can be upheld, and the hole argument avoided, by adopting structural realism with respect to spacetime. In this context, this is the claim that it is the structure that spacetime points enter into that warrants belief and not the points themselves. In Chapter 2, an elimination principle is defined by means of which a distinction can be made between surplus structure and essential structure with respect to formulations of a theory in two distinct mathematical formulations and some prior ontological commitments. This principle is then used to demonstrate that manifold points may be considered surplus structure in the formulation of field theories. This suggests that, if we are disposed to read field theories literally, then, at most, it should be the essential structure common to all alternative formulations of such theories that should be taken literally. I also investigate how the adoption of alternative formalisms informs other issues in the philosophy of spacetime. Chapter 3 offers a realist position which takes a semantic moral from the preceding investigation and an epistemic moral from work done on reliability. The semantic moral advises us to read only the essential structure of our theories literally. The epistemic moral shows us that such structure

  3. Algorithms in Algebraic Geometry

    CERN Document Server

    Dickenstein, Alicia; Sommese, Andrew J

    2008-01-01

    In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its

  4. Revolutions of Geometry

    CERN Document Server

    O'Leary, Michael

    2010-01-01

    Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull

  5. Fundamental concepts of geometry

    CERN Document Server

    Meserve, Bruce E

    1983-01-01

    Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.

  6. Developments in special geometry

    International Nuclear Information System (INIS)

    Mohaupt, Thomas; Vaughan, Owen

    2012-01-01

    We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.

  7. Global geometry of two-dimensional charged black holes

    International Nuclear Information System (INIS)

    Frolov, Andrei V.; Kristjansson, Kristjan R.; Thorlacius, Larus

    2006-01-01

    The semiclassical geometry of charged black holes is studied in the context of a two-dimensional dilaton gravity model where effects due to pair-creation of charged particles can be included in a systematic way. The classical mass-inflation instability of the Cauchy horizon is amplified and we find that gravitational collapse of charged matter results in a spacelike singularity that precludes any extension of the spacetime geometry. At the classical level, a static solution describing an eternal black hole has timelike singularities and multiple asymptotic regions. The corresponding semiclassical solution, on the other hand, has a spacelike singularity and a Penrose diagram like that of an electrically neutral black hole. Extremal black holes are destabilized by pair-creation of charged particles. There is a maximally charged solution for a given black hole mass but the corresponding geometry is not extremal. Our numerical data exhibits critical behavior at the threshold for black hole formation

  8. F-Theory - From Geometry to Physics and Back

    CERN Multimedia

    CERN. Geneva

    2017-01-01

    Compactifications of string theory have the potential to form a bridge between what we believe is a consistent quantum theory of gravity in 10 spacetime dimensions and observed physics in four dimensions. At the same time, beautiful results from mathematics, especially algebraic geometry, are directly linked to some of the key concepts in modern particle and quantum field theory. This theory colloquium will illustrate some of these ideas in the context of F-theory, which provides a non-perturbative formulation of a class of string compactifications in their geometric regime. Recent applications of F-theory range from very concrete suggestions to address known challenges in physics beyond the Standard Model to the 'physicalization of geometry' to the construction and investigations of strongly coupled quantum field theories in various dimensions. After reviewing examples of such applications we will conclude by demonstrating the close links between geometry and physics in F-theory via some new results on the r...

  9. Tensor analysis and elementary differential geometry for physicists and engineers

    CERN Document Server

    Nguyen-Schäfer, Hung

    2017-01-01

    This book comprehensively presents topics, such as Dirac notation, tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. Additionally, two new chapters of Cartan differential forms and Dirac and tensor notations in quantum mechanics are added to this second edition. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors, differential geometry, and differential forms; and to apply them to the physical and engineering world. Many methods and applications are given in CFD, continuum mechanics, electrodynamics in special relativity, cosmology in the Minkowski four-dimensional spacetime, and relativistic and non-relativistic quantum mechanics. Tensors, differential geometry, differential forms, and Dirac notation are very useful advanced mathematical tools in many fields of modern physics and computational engineering. They are involved in special and general relativity physics, quantum m...

  10. Classification of Near-Horizon Geometries of Extremal Black Holes

    Directory of Open Access Journals (Sweden)

    Hari K. Kunduri

    2013-09-01

    Full Text Available Any spacetime containing a degenerate Killing horizon, such as an extremal black hole, possesses a well-defined notion of a near-horizon geometry. We review such near-horizon geometry solutions in a variety of dimensions and theories in a unified manner. We discuss various general results including horizon topology and near-horizon symmetry enhancement. We also discuss the status of the classification of near-horizon geometries in theories ranging from vacuum gravity to Einstein–Maxwell theory and supergravity theories. Finally, we discuss applications to the classification of extremal black holes and various related topics. Several new results are presented and open problems are highlighted throughout.

  11. Critical gravity on AdS2 spacetimes

    International Nuclear Information System (INIS)

    Myung, Yun Soo; Kim, Yong-Wan; Park, Young-Jai

    2011-01-01

    We study the critical gravity in two-dimensional anti-de Sitter (AdS 2 ) spacetimes, which was obtained from the cosmological topologically massive gravity (TMG Λ ) in three dimensions by using the Kaluza-Klein dimensional reduction. We perform the perturbation analysis around AdS 2 , which may correspond to the near-horizon geometry of the extremal Banados, Teitelboim, and Zanelli (BTZ) black hole obtained from the TMG Λ with identification upon uplifting three dimensions. A massive propagating scalar mode δF satisfies the second-order differential equation away from the critical point of K=l, whose solution is given by the Bessel functions. On the other hand, δF satisfies the fourth-order equation at the critical point. We exactly solve the fourth-order equation, and compare it with the log gravity in two dimensions. Consequently, the critical gravity in two dimensions could not be described by a massless scalar δF ml and its logarithmic partner δF log 4th .

  12. Cosmological applications of algebraic quantum field theory in curved spacetimes

    CERN Document Server

    Hack, Thomas-Paul

    2016-01-01

    This book provides a largely self-contained and broadly accessible exposition on two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology; and a fundamental study of the perturbations in inflation. The two central sections of the book dealing with these applications are preceded by sections providing a pedagogical introduction to the subject. Introductory material on the construction of linear QFTs on general curved spacetimes with and without gauge symmetry in the algebraic approach, physically meaningful quantum states on general curved spacetimes, and the backreaction of quantum fields in curved spacetimes via the semiclassical Einstein equation is also given. The reader should have a basic understanding of General Relativity and QFT on Minkowski spacetime, but no background in QFT on curved spacetimes or the algebraic approach to QFT is required.

  13. Real tunneling geometries and the large-scale topology of the universe

    International Nuclear Information System (INIS)

    Gibbons, G.W.; Hartle, J.B.

    1990-01-01

    If the topology and geometry of spacetime are quantum-mechanically variable, then the particular classical large-scale topology and geometry observed in our universe must be statistical predictions of its initial condition. This paper examines the predictions of the ''no boundary'' initial condition for the present large-scale topology and geometry. Finite-action real tunneling solutions of Einstein's equation are important for such predictions. These consist of compact Riemannian (Euclidean) geometries joined to a Lorentzian cosmological geometry across a spacelike surface of vanishing extrinsic curvature. The classification of such solutions is discussed and general constraints on their topology derived. For example, it is shown that, if the Euclidean Ricci tensor is positive, then a real tunneling solution can nucleate only a single connected Lorentzian spacetime (the unique conception theorem). Explicit examples of real tunneling solutions driven by a cosmological constant are exhibited and their implications for cosmic baldness described. It is argued that the most probable large-scale spacetime predicted by the real tunneling solutions of the ''no-boundary'' initial condition has the topology RxS 3 with the de Sitter metric

  14. Empty space-times with separable Hamilton-Jacobi equation

    International Nuclear Information System (INIS)

    Collinson, C.D.; Fugere, J.

    1977-01-01

    All empty space-times admitting a one-parameter group of motions and in which the Hamilton-Jacobi equation is (partially) separable are obtained. Several different cases of such empty space-times exist and the Riemann tensor is found to be either type D or N. The results presented here complete the search for empty space-times with separable Hamilton-Jacobi equation. (author)

  15. A short history of fractal-Cantorian space-time

    International Nuclear Information System (INIS)

    Marek-Crnjac, L.

    2009-01-01

    The article attempts to give a short historical overview of the discovery of fractal-Cantorian space-time starting from the 17th century up to the present. In the last 25 years a great number of scientists worked on fractal space-time notably Garnet Ord in Canada, Laurent Nottale in France and Mohamed El Naschie in England who gave an exact mathematical procedure for the derivation of the dimensionality and curvature of fractal space-time fuzzy manifold.

  16. Finiteness principle and the concept of space-time

    International Nuclear Information System (INIS)

    Tati, T.

    1984-01-01

    It is shown that the non-space-time description can be given by a system of axioms under the postulate of a certain number of pre-supposed physical concepts in which space-time is not included. It is found that space-time is a compound concept of presupposed concepts of non-space-time description connected by an additional condition called 'space-time condition'. (L.C.) [pt

  17. Smarandache Spaces as a New Extension of the Basic Space-Time of General Relativity

    Directory of Open Access Journals (Sweden)

    Rabounski D.

    2010-04-01

    Full Text Available This short letter manifests how Smarandache geometries can be employed in order to extend the “classical” basis of the General Theory of Relativity (Riemannian geometry through joining the properties of two or more (different geometries in the same single space. Perspectives in this way seem much profitable: the basic space-time of General Relativity can be extended to not only metric geometries, but even to non-metric ones (where no distances can be measured, or to spaces of the mixed kind which possess the properties of both metric and non-metric spaces (the latter should be referred to as “semi-metric spaces”. If both metric and non-metric properties possessed at the same (at least one point of a space, it is one of Smarandache geometries, and should be re- ferred to as “Smarandache semi-metric space”. Such spaces can be introduced accord- ing to the mathematical apparatus of physically observable quantities (chronometric invariants, if we consider a breaking of the observable space metric in the continuous background of the fundamental metric tensor.

  18. Designs and finite geometries

    CERN Document Server

    1996-01-01

    Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.

  19. The Beauty of Geometry

    Science.gov (United States)

    Morris, Barbara H.

    2004-01-01

    This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…

  20. Some Peculiarities of Newton-Hooke Space-Times

    OpenAIRE

    Tian, Yu

    2011-01-01

    Newton-Hooke space-times are the non-relativistic limit of (anti-)de Sitter space-times. We investigate some peculiar facts about the Newton-Hooke space-times, among which the "extraordinary Newton-Hooke quantum mechanics" and the "anomalous Newton-Hooke space-times" are discussed in detail. Analysis on the Lagrangian/action formalism is performed in the discussion of the Newton-Hooke quantum mechanics, where the path integral point of view plays an important role, and the physically measurab...

  1. The global monopole spacetime and its topological charge

    Science.gov (United States)

    Tan, Hongwei; Yang, Jinbo; Zhang, Jingyi; He, Tangmei

    2018-03-01

    We show that the global monopole spacetime is one of the exact solutions of the Einstein equations by treating the matter field as a non-linear sigma model, without the weak field approximation applied in the original derivation by Barriola and Vilenkin. Furthermore, we find the physical origin of the topological charge in the global monopole spacetime. Finally, we generalize the proposal which generates spacetime from thermodynamical laws to the case of spacetime with global monopole charge. Project supported by the National Natural Science Foundation of China (Grant Nos. 11273009 and 11303006).

  2. Stability of generic thin shells in conformally flat spacetimes

    Energy Technology Data Exchange (ETDEWEB)

    Amirabi, Z. [Eastern Mediterranean Univ., Gazimagusa (Turkey). Dept. of Physics

    2017-07-15

    Some important spacetimes are conformally flat; examples are the Robertson-Walker cosmological metric, the Einstein-de Sitter spacetime, and the Levi-Civita-Bertotti-Robinson and Mannheim metrics. In this paper we construct generic thin shells in conformally flat spacetime supported by a perfect fluid with a linear equation of state, i.e., p = ωσ. It is shown that, for the physical domain of ω, i.e., 0 < ω ≤ 1, such thin shells are not dynamically stable. The stability of the timelike thin shells with the Mannheim spacetime as the outer region is also investigated. (orig.)

  3. Black Hole Space-time In Dark Matter Halo

    OpenAIRE

    Xu, Zhaoyi; Hou, Xian; Gong, Xiaobo; Wang, Jiancheng

    2018-01-01

    For the first time, we obtain the analytical form of black hole space-time metric in dark matter halo for the stationary situation. Using the relation between the rotation velocity (in the equatorial plane) and the spherical symmetric space-time metric coefficient, we obtain the space-time metric for pure dark matter. By considering the dark matter halo in spherical symmetric space-time as part of the energy-momentum tensors in the Einstein field equation, we then obtain the spherical symmetr...

  4. Methods of information geometry

    CERN Document Server

    Amari, Shun-Ichi

    2000-01-01

    Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...

  5. Geometry on the space of geometries

    International Nuclear Information System (INIS)

    Christodoulakis, T.; Zanelli, J.

    1988-06-01

    We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs

  6. A line source in Minkowski for the de Sitter spacetime scalar Green's function: Massless minimally coupled case

    International Nuclear Information System (INIS)

    Chu, Yi-Zen

    2014-01-01

    Motivated by the desire to understand the causal structure of physical signals produced in curved spacetimes – particularly around black holes – we show how, for certain classes of geometries, one might obtain its retarded or advanced minimally coupled massless scalar Green's function by using the corresponding Green's functions in the higher dimensional Minkowski spacetime where it is embedded. Analogous statements hold for certain classes of curved Riemannian spaces, with positive definite metrics, which may be embedded in higher dimensional Euclidean spaces. The general formula is applied to (d ≥ 2)-dimensional de Sitter spacetime, and the scalar Green's function is demonstrated to be sourced by a line emanating infinitesimally close to the origin of the ambient (d + 1)-dimensional Minkowski spacetime and piercing orthogonally through the de Sitter hyperboloids of all finite sizes. This method does not require solving the de Sitter wave equation directly. Only the zero mode solution to an ordinary differential equation, the “wave equation” perpendicular to the hyperboloid – followed by a one-dimensional integral – needs to be evaluated. A topological obstruction to the general construction is also discussed by utilizing it to derive a generalized Green's function of the Laplacian on the (d ≥ 2)-dimensional sphere

  7. A short essay on quantum black holes and underlying noncommutative quantized space-time

    International Nuclear Information System (INIS)

    Tanaka, Sho

    2017-01-01

    We emphasize the importance of noncommutative geometry or Lorenz-covariant quantized space-time towards the ultimate theory of quantum gravity and Planck scale physics. We focus our attention on the statistical and substantial understanding of the Bekenstein–Hawking area-entropy law of black holes in terms of the kinematical holographic relation (KHR). KHR manifestly holds in Yang’s quantized space-time as the result of kinematical reduction of spatial degrees of freedom caused by its own nature of noncommutative geometry, and plays an important role in our approach without any recourse to the familiar hypothesis, so-called holographic principle. In the present paper, we find a unified form of KHR applicable to the whole region ranging from macroscopic to microscopic scales in spatial dimension d   =  3. We notice a possibility of nontrivial modification of area-entropy law of black holes which becomes most remarkable in the extremely microscopic system close to Planck scale. (paper)

  8. Aspects of space-time dualities

    CERN Document Server

    Giveon, Amit

    1996-01-01

    Duality groups of Abelian gauge theories on four manifolds and their reduction to two dimensions are considered. The duality groups include elements that relate different space-times in addition to relating different gauge-coupling matrices. We interpret (some of) such dualities as the geometrical symmetries of compactified theories in higher dimensions. In particular, we consider compactifications of a (self-dual) 2-form in 6-D, and compactifications of a self-dual 4-form in 10-D. Relations with a self-dual superstring in 6-D and with the type IIB superstring are discussed.

  9. The emergence of spacetime in string theory

    CERN Document Server

    Vistarini, Tiziana

    2018-01-01

    The nature of space and time is one of the most fascinating and fundamental philosophical issues which presently engages at the deepest level with physics. During the last thirty years this notion has been object of an intense critical review in the light of new scientific theories which try to combine the principles of both general relativity and quantum theory—called theories of quantum gravity. This book considers the way string theory shapes its own account of spacetime disappearance from the fundamental level.

  10. Electromagnetic radiation due to spacetime oscillations

    International Nuclear Information System (INIS)

    Chitre, D.M.; Price, R.H.; Sandberg, V.D.

    1975-01-01

    Wave equations are derived in the Newman-Penrose formalism for mixed electromagnetic and gravitational perturbations on both a flat spacetime background and a slightly charged (Q 2 very-much-less-than GM 2 ) Reissner-Nordstroem background. The physical meaning of these equations is discussed and analytical results are derived for nonrelativistic sources and for ultrarelativistic particle motions. The relationship between even-parity (TM) electromagnetic radiation multipoles in the long-wavelength approximation and static multipoles is shown to be the same as for classical radiation, suggesting a simple picture for electromagnetic radiation induced by gravitational perturbations

  11. Quantum mechanics, stochasticity and space-time

    International Nuclear Information System (INIS)

    Ramanathan, R.

    1986-04-01

    An extended and more rigorous version of a recent proposal for an objective stochastic formulation of quantum mechanics along with its extension to the relativistic case without spin is presented. The relativistic Klein-Gordon equation is shown to be a particular form of the relativistic Kolmogorov-Fokker-Planck equation which is derived from a covariant formulation of the Chapman-Kolmogorov condition. Complexification of probability amplitudes is again achieved only through a conformal rotation of Minkowski space-time M 4 . (author)

  12. Entanglement redistribution in the Schwarzschild spacetime

    International Nuclear Information System (INIS)

    Wang, Jieci; Pan, Qiyuan; Jing, Jiliang

    2010-01-01

    The effect of Hawking radiation on the redistribution of the entanglement and mutual information in the Schwarzschild spacetime is investigated. Our analysis shows that the physically accessible correlations degrade while the unaccessible correlations increase as the Hawking temperature increases because the initial correlations described by inertial observers are redistributed between all the bipartite modes. It is interesting to note that, in the limit case that the temperature tends to infinity, the accessible mutual information equals to just half of its initial value, and the unaccessible mutual information between mode A and II also equals to the same value.

  13. Classification of supersymmetric spacetimes in eleven dimensions

    International Nuclear Information System (INIS)

    Cariglia, Marco; Mac Conamhna, Oisin A.P.

    2005-01-01

    We derive, for spacetimes admitting a Spin(7) structure, the general local bosonic solution of the Killing spinor equation of 11-dimensional supergravity. The metric, four-form, and Killing spinors are determined explicitly, up to an arbitrary eight-manifold of Spin(7) holonomy. It is sufficient to impose the Bianchi identity and one particular component of the four-form field equation to ensure that the solution of the Killing spinor equation also satisfies all the field equations, and we give these conditions explicitly

  14. Spacetime Curvature and Higgs Stability after Inflation.

    Science.gov (United States)

    Herranen, M; Markkanen, T; Nurmi, S; Rajantie, A

    2015-12-11

    We investigate the dynamics of the Higgs field at the end of inflation in the minimal scenario consisting of an inflaton field coupled to the standard model only through the nonminimal gravitational coupling ξ of the Higgs field. Such a coupling is required by renormalization of the standard model in curved space, and in the current scenario also by vacuum stability during high-scale inflation. We find that for ξ≳1, rapidly changing spacetime curvature at the end of inflation leads to significant production of Higgs particles, potentially triggering a transition to a negative-energy Planck scale vacuum state and causing an immediate collapse of the Universe.

  15. Perturbations of spacetimes in general relativity

    International Nuclear Information System (INIS)

    Walker, M.

    1977-01-01

    In the case of gravitation, the differential equation of interest is Einstein's equation. Being a tensor equation, this is rather complicated. Moreover, gravitational theory throws up its own peculiar difficulty, the lack of a fixed background space on which to expand things. The plan of these lecture notes is therefore to discuss linear vs. nonlinear differential equations, perturbation theory for ordinary differential equations (ODE), partial differential equations (PDE), and finally, spacetimes. In this way, the basic ideas can be introduced without interference from non-essential complications. (orig.) [de

  16. Space-time as a causal set

    International Nuclear Information System (INIS)

    Bombelli, L.; Lee, J.; Meyer, D.; Sorkin, R.D.

    1987-01-01

    We propose that space-time at the smallest scales is in reality a causal set: a locally finite set of elements endowed with a partial order corresponding to the macroscopic relation that defines past and future. We explore how a Lorentzian manifold can approximate a causal set, noting in particular that the thereby defined effective dimensionality of a given causal set can vary with length scale. Finally, we speculate briefly on the quantum dynamics of causal sets, indicating why an appropriate choice of action can reproduce general relativity in the classical limit

  17. Deformations of spacetime and internal symmetries

    Directory of Open Access Journals (Sweden)

    Gresnigt Niels G.

    2017-01-01

    Full Text Available Algebraic deformations provide a systematic approach to generalizing the symmetries of a physical theory through the introduction of new fundamental constants. The applications of deformations of Lie algebras and Hopf algebras to both spacetime and internal symmetries are discussed. As a specific example we demonstrate how deforming the classical flavor group S U(3 to the quantum group S Uq(3 ≡ U q (su(3 (a Hopf algebra and taking into account electromagnetic mass splitting within isospin multiplets leads to new and exceptionally accurate baryon mass sum rules that agree perfectly with experimental data.

  18. Space-Time Discrete KPZ Equation

    Science.gov (United States)

    Cannizzaro, G.; Matetski, K.

    2018-03-01

    We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures (Hairer in Invent Math 198(2):269-504, 2014) as well as its discrete counterpart (Hairer and Matetski in Discretizations of rough stochastic PDEs, 2015. arXiv:1511.06937). Since the discretization is in both space and time and we allow non-standard discretization for the product, the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study.

  19. Rotating spacetimes of Goedel-type

    International Nuclear Information System (INIS)

    Reboucas, M.J.; Teixeira, A.F.F.

    1986-01-01

    The Goedel-type Riemannian manifolds are examined under two different assumptions on the algebraic structure of the energy-momentum tensor. All Goedel-type manifolds of either Segre type [1,(1,111)] or [(1,11)1] are shown to be spacetime-homogeneous. A generalization of Bampi-Zordan theorem is presented. All Goedel-type Riemannian manifolds of the algebric tachyon fluid type are shown to be conformally flat and isometric to Reboucas-Tiomno model. The conformal form of Reboucas-Tiomno is given. (Author) [pt

  20. Spacetime Discontinuous Galerkin FEM: Spectral Response

    International Nuclear Information System (INIS)

    Abedi, R; Omidi, O; Clarke, P L

    2014-01-01

    Materials in nature demonstrate certain spectral shapes in terms of their material properties. Since successful experimental demonstrations in 2000, metamaterials have provided a means to engineer materials with desired spectral shapes for their material properties. Computational tools are employed in two different aspects for metamaterial modeling: 1. Mircoscale unit cell analysis to derive and possibly optimize material's spectral response; 2. macroscale to analyze their interaction with conventional material. We compare two different approaches of Time-Domain (TD) and Frequency Domain (FD) methods for metamaterial applications. Finally, we discuss advantages of the TD method of Spacetime Discontinuous Galerkin finite element method (FEM) for spectral analysis of metamaterials

  1. Discrete symmetries and de Sitter spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Cotăescu, Ion I., E-mail: gpascu@physics.uvt.ro; Pascu, Gabriel, E-mail: gpascu@physics.uvt.ro [West University of Timişoara, V. Pârvan Ave. 4, RO-300223 Timişoara (Romania)

    2014-11-24

    Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries- a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries- states between which exists a well-known thermality relation.

  2. Generalized Vaidya spacetime for cubic gravity

    Science.gov (United States)

    Ruan, Shan-Ming

    2016-03-01

    We present a kind of generalized Vaidya solution of a new cubic gravity in five dimensions whose field equations in spherically symmetric spacetime are always second order like the Lovelock gravity. We also study the thermodynamics of its spherically symmetric apparent horizon and get its entropy expression and generalized Misner-Sharp energy. Finally, we present the first law and second law hold in this gravity. Although all the results are analogous to those in Lovelock gravity, we in fact introduce the contribution of a new cubic term in five dimensions where the cubic Lovelock term is just zero.

  3. Spinorial space-time and the origin of Quantum Mechanics. The dynamical role of the physical vacuum

    International Nuclear Information System (INIS)

    Gonzalez-Mestres, Luis

    2016-01-01

    Is Quantum Mechanics really and ultimate principle of Physics described by a set of intrinsic exact laws? Are standard particles the ultimate constituents of matter? The two questions appear to be closely related, as a preonic structure of the physical vacuum would have an influence on the properties of quantum particles. Although the first preon models were just « quark-like » and assumed preons to be direct constituents of the conventional « elementary » particles, we suggested in 1995 that preons could instead be constituents of the physical vacuum (the superbradyon hypothesis). Standard particles would then be excitations of the preonic vacuum and have substantially different properties from those of preons themselves (critical speed…). The standard laws of Particle Physics would be approximate expressions generated from basic preon dynamics. In parallel, the mathematical properties of space-time structures such as the spinoral space-time (SST) we introduced in 1996-97 can have strong implications for Quantum Mechanics and even be its real origin. We complete here our recent discussion of the subject by pointing out that: i) Quantum Mechanics corresponds to a natural set of properties of vacuum excitations in the presence of a SST geometry ; ii) the recently observed entanglement at long distances would be a logical property if preons are superluminal (superbradyons), so that superluminal signals and correlations can propagate in vacuum ; iii) in a specific description, the function of space-time associated to the extended internal structure of a spin-1/2 particle at very small distances may be incompatible with a continuous motion at space and time scales where the internal structure of vacuum can be felt. In the dynamics associated to iii), and using the SST approach to space-time, a contradiction can appear between macroscopic and microscopic space-times due to an overlap in the time variable directly related to the fact that a spinorial function takes

  4. Complex and symplectic geometry

    CERN Document Server

    Medori, Costantino; Tomassini, Adriano

    2017-01-01

    This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.

  5. Non-Euclidean geometry

    CERN Document Server

    Kulczycki, Stefan

    2008-01-01

    This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff

  6. The continuous determination of spacetime geometry by the Riemann curvature tensor

    International Nuclear Information System (INIS)

    Rendall, A.D.

    1988-01-01

    It is shown that generically the Riemann tensor of a Lorentz metric on an n-dimensional manifold (n ≥ 4) determines the metric up to a constant factor and hence determines the associated torsion-free connection uniquely. The resulting map from Riemann tensors to connections is continuous in the Whitney Csup(∞) topology but, at least for some manifolds, constant factors cannot be chosen so as to make the map from Riemann tensors to metrics continuous in that topology. The latter map is, however, continuous in the compact open Csup(∞) topology so that estimates of the metric and its derivatives on a compact set can be obtained from similar estimates on the curvature and its derivatives. (author)

  7. Charged thin-shell gravastars in noncommutative geometry

    Energy Technology Data Exchange (ETDEWEB)

    Oevguen, Ali [Pontificia Universidad Catolica de Valparaiso, Instituto de Fisica, Valparaiso (Chile); Eastern Mediterranean University, Physics Department, Famagusta, Northern Cyprus (Turkey); Banerjee, Ayan [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India); Jusufi, Kimet [State University of Tetovo, Physics Department, Tetovo (Macedonia, The Former Yugoslav Republic of); Institute of Physics, Ss. Cyril and Methodius University, Faculty of Natural Sciences and Mathematics, Skopje (Macedonia, The Former Yugoslav Republic of)

    2017-08-15

    In this paper we construct a charged thin-shell gravastar model within the context of noncommutative geometry. To do so, we choose the interior of the nonsingular de Sitter spacetime with an exterior charged noncommutative solution by cut-and-paste technique and apply the generalized junction conditions. We then investigate the stability of a charged thin-shell gravastar under linear perturbations around the static equilibrium solutions as well as the thermodynamical stability of the charged gravastar. We find the stability regions, by choosing appropriate parameter values, located sufficiently close to the event horizon. (orig.)

  8. Quantum κ-deformed differential geometry and field theory

    Science.gov (United States)

    Mercati, Flavio

    2016-03-01

    I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-∗ and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.

  9. New geometries for black hole horizons

    Energy Technology Data Exchange (ETDEWEB)

    Armas, Jay [Physique Théorique et Mathématique,Université Libre de Bruxelles and International Solvay Institutes, ULB-Campus Plaine CP231, B-1050 Brussels (Belgium); Blau, Matthias [Albert Einstein Center for Fundamental Physics, University of Bern,Sidlerstrasse 5, 3012 Bern (Switzerland)

    2015-07-10

    We construct several classes of worldvolume effective actions for black holes by integrating out spatial sections of the worldvolume geometry of asymptotically flat black branes. This provides a generalisation of the blackfold approach for higher-dimensional black holes and yields a map between different effective theories, which we exploit by obtaining new hydrodynamic and elastic transport coefficients via simple integrations. Using Euclidean minimal surfaces in order to decouple the fluid dynamics on different sections of the worldvolume, we obtain local effective theories for ultraspinning Myers-Perry branes and helicoidal black branes, described in terms of a stress-energy tensor, particle currents and non-trivial boost vectors. We then study in detail and present novel compact and non-compact geometries for black hole horizons in higher-dimensional asymptotically flat space-time. These include doubly-spinning black rings, black helicoids and helicoidal p-branes as well as helicoidal black rings and helicoidal black tori in D≥6.

  10. Macroscopic Spacetime Shortcuts in the Manyfold Universe

    CERN Document Server

    Loup, F

    2004-01-01

    Recently the idea of a Manyfold Universe was proposed by some authors to explain Dark Matter . In this study we assume that the Standard Model(SM) of particles and fields with gravity propagating in the Higher Dimensional Spacetime(Bulk) while other interactions are confined to 3+1 Einsteinian spacetime(Brane) is not due to open strings and closed loops but instead is due to the capability of gravity as the weakest and "smallest" interaction to penetrate these small Bulk size ($10^{-31}$m to $10^{-35}$m) while protons,neutrons and other interactions stronger and "larger" than gravity do not "fits" in the size of the Bulk and remains trapped on the Brane and we present a equation to justify this point of view. Our picture relies over the geometrical beauty of the Manyfold Universe proposal that Dark Matter is chemically identical to ordinary matter but lies on other Folds. Also the geometrical point of view for the small size of the Bulk eliminates the need of trapping mechanisms to confine matter in the Brane...

  11. Spacetime replication of continuous variable quantum information

    International Nuclear Information System (INIS)

    Hayden, Patrick; Nezami, Sepehr; Salton, Grant; Sanders, Barry C

    2016-01-01

    The theory of relativity requires that no information travel faster than light, whereas the unitarity of quantum mechanics ensures that quantum information cannot be cloned. These conditions provide the basic constraints that appear in information replication tasks, which formalize aspects of the behavior of information in relativistic quantum mechanics. In this article, we provide continuous variable (CV) strategies for spacetime quantum information replication that are directly amenable to optical or mechanical implementation. We use a new class of homologically constructed CV quantum error correcting codes to provide efficient solutions for the general case of information replication. As compared to schemes encoding qubits, our CV solution requires half as many shares per encoded system. We also provide an optimized five-mode strategy for replicating quantum information in a particular configuration of four spacetime regions designed not to be reducible to previously performed experiments. For this optimized strategy, we provide detailed encoding and decoding procedures using standard optical apparatus and calculate the recovery fidelity when finite squeezing is used. As such we provide a scheme for experimentally realizing quantum information replication using quantum optics. (paper)

  12. Inflationary scenario from higher curvature warped spacetime

    International Nuclear Information System (INIS)

    Banerjee, Narayan; Paul, Tanmoy

    2017-01-01

    We consider a five dimensional warped spacetime, in presence of the higher curvature term like F(R) = R + αR 2 in the bulk, in the context of the two-brane model. Our universe is identified with the TeV scale brane and emerges as a four dimensional effective theory. From the perspective of this effective theory, we examine the possibility of ''inflationary scenario'' by considering the on-brane metric ansatz as an FRW one. Our results reveal that the higher curvature term in the five dimensional bulk spacetime generates a potential term for the radion field. Due to the presence of radion potential, the very early universe undergoes a stage of accelerated expansion and, moreover, the accelerating period of the universe terminates in a finite time. We also find the spectral index of curvature perturbation (n s ) and the tensor to scalar ratio (r) in the present context, which match with the observational results based on the observations of Planck (Astron. Astrophys. 594, A20, 2016). (orig.)

  13. Inflationary scenario from higher curvature warped spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Banerjee, Narayan [Indian Institute of Science Education and Research Kolkata, Department of Physical Sciences, Nadia, West Bengal (India); Paul, Tanmoy [Indian Association for the Cultivation of Science, Department of Theoretical Physics, Kolkata (India)

    2017-10-15

    We consider a five dimensional warped spacetime, in presence of the higher curvature term like F(R) = R + αR{sup 2} in the bulk, in the context of the two-brane model. Our universe is identified with the TeV scale brane and emerges as a four dimensional effective theory. From the perspective of this effective theory, we examine the possibility of ''inflationary scenario'' by considering the on-brane metric ansatz as an FRW one. Our results reveal that the higher curvature term in the five dimensional bulk spacetime generates a potential term for the radion field. Due to the presence of radion potential, the very early universe undergoes a stage of accelerated expansion and, moreover, the accelerating period of the universe terminates in a finite time. We also find the spectral index of curvature perturbation (n{sub s}) and the tensor to scalar ratio (r) in the present context, which match with the observational results based on the observations of Planck (Astron. Astrophys. 594, A20, 2016). (orig.)

  14. Global embedding of D-dimensional black holes with a cosmological constant in Minkowskian spacetimes: Matching between Hawking temperature and Unruh temperature

    International Nuclear Information System (INIS)

    Santos, Nuno Loureiro; Dias, Oscar J.C.; Lemos, Jose P.S.

    2004-01-01

    We study the matching between the Hawking temperature of a large class of static D-dimensional black holes and the Unruh temperature of the corresponding higher dimensional Rindler spacetime. In order to accomplish this task we find the global embedding of the D-dimensional black holes into a higher dimensional Minkowskian spacetime, called the global embedding Minkowskian spacetime procedure (GEMS procedure). These global embedding transformations are important on their own, since they provide a powerful tool that simplifies the study of black hole physics by working instead, but equivalently, in an accelerated Rindler frame in a flat background geometry. We discuss neutral and charged Tangherlini black holes with and without cosmological constant, and in the negative cosmological constant case, we consider the three allowed topologies for the horizons (spherical, cylindrical/toroidal, and hyperbolic)

  15. Lectures on coarse geometry

    CERN Document Server

    Roe, John

    2003-01-01

    Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...

  16. Lectures on Symplectic Geometry

    CERN Document Server

    Silva, Ana Cannas

    2001-01-01

    The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...

  17. Complex algebraic geometry

    CERN Document Server

    Kollár, János

    1997-01-01

    This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.

  18. Geometry and Combinatorics

    DEFF Research Database (Denmark)

    Kokkendorff, Simon Lyngby

    2002-01-01

    The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...

  19. The geometry of geodesics

    CERN Document Server

    Busemann, Herbert

    2005-01-01

    A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.

  20. Geometry and billiards

    CERN Document Server

    Tabachnikov, Serge

    2005-01-01

    Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...

  1. Introduction to tropical geometry

    CERN Document Server

    Maclagan, Diane

    2015-01-01

    Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...

  2. Rudiments of algebraic geometry

    CERN Document Server

    Jenner, WE

    2017-01-01

    Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.

  3. Class of continuous timelike curves determines the topology of spacetime

    International Nuclear Information System (INIS)

    Malament, D.B.

    1977-01-01

    The title assertion is proven, and two corollaries are established. First, the topology of every past and future distinguishing spacetime is determined by its causal structure. Second, in every spacetime the path topology of Hawking, King, and McCarthy codes topological, differential, and conformal structure

  4. Conserved quantities for stationary Einstein-Maxwell space-times

    International Nuclear Information System (INIS)

    Esposito, F.P.; Witten, L.

    1978-01-01

    It is shown that every stationary Einstein-Maxwell space-time has eight divergence-free vector fields and these are isolated in general form. The vector fields and associated conserved quantities are calculated for several families of space-times. (Auth.)

  5. Quantum space-times in the year 2002

    Indian Academy of Sciences (India)

    These ideas of space-time are suggested from developments in fuzzy physics, string theory, and deformation quantization. The review focuses on the ideas coming from fuzzy physics. We find models of quantum space-time like fuzzy 4 on which states cannot be localized, but which fluctuate into other manifolds like CP3.

  6. Covariant Theory of Gravitation in the Spacetime with Finsler Structure

    OpenAIRE

    Huang, Xin-Bing

    2007-01-01

    The theory of gravitation in the spacetime with Finsler structure is constructed. It is shown that the theory keeps general covariance. Such theory reduces to Einstein's general relativity when the Finsler structure is Riemannian. Therefore, this covariant theory of gravitation is an elegant realization of Einstein's thoughts on gravitation in the spacetime with Finsler structure.

  7. The scalar wave equation in a Schwarzschild spacetime

    International Nuclear Information System (INIS)

    Stewart, J.M.; Schmidt, B.G.

    1978-09-01

    This paper studies the asymptotic behaviour of solutions of the zero rest mass scalar wave equation in the Schwarzschild spacetime in a neighbourhood of spatial infinity, which includes parts of future and past null infinity. The behaviour of such fields is essentially different from that which accurs in a flat spacetime. (orig.) [de

  8. Backreaction in the future behavior of an expanding vacuum spacetime

    Science.gov (United States)

    Lott, John

    2018-02-01

    We perform a rescaling analysis to analyze the future behavior of a class of T 2-symmetric vacuum spacetimes. We show that on the universal cover, there is C 0-convergence to a spatially homogeneous spacetime that does not satisfy the vacuum Einstein equations. Research partially supported by NSF grant DMS-1510192.

  9. Feynman propagator and space-time transformation technique

    International Nuclear Information System (INIS)

    Nassar, A.B.

    1987-01-01

    We evaluate the exact propagator for the time-dependent two-dimensional charged harmonic oscillator in a time-varying magnetic field, by taking direct recourse to the corresponding Schroedinger equation. Through the usage of an appropriate space-time transformation, we show that such a propagator can be obtained from the free propagator in the new space-time coordinate system. (orig.)

  10. Space-time algebra for the generalization of gravitational field

    Indian Academy of Sciences (India)

    The Maxwell–Proca-like field equations of gravitolectromagnetism are formulated using space-time algebra (STA). The gravitational wave equation with massive gravitons and gravitomagnetic monopoles has been derived in terms of this algebra. Using space-time algebra, the most generalized form of ...

  11. Implosions and hypertoric geometry

    DEFF Research Database (Denmark)

    Dancer, A.; Kirwan, F.; Swann, A.

    2013-01-01

    The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....

  12. Intermediate algebra & analytic geometry

    CERN Document Server

    Gondin, William R

    1967-01-01

    Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system

  13. d-geometries revisited

    CERN Document Server

    Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio

    2013-01-01

    We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.

  14. CMS geometry through 2020

    International Nuclear Information System (INIS)

    Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J

    2014-01-01

    CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.

  15. Software Geometry in Simulations

    Science.gov (United States)

    Alion, Tyler; Viren, Brett; Junk, Tom

    2015-04-01

    The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).

  16. Introduction to combinatorial geometry

    International Nuclear Information System (INIS)

    Gabriel, T.A.; Emmett, M.B.

    1985-01-01

    The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity

  17. Accelerated observers and the notion of singular spacetime

    Science.gov (United States)

    Olmo, Gonzalo J.; Rubiera-Garcia, Diego; Sanchez-Puente, Antonio

    2018-03-01

    Geodesic completeness is typically regarded as a basic criterion to determine whether a given spacetime is regular or singular. However, the principle of general covariance does not privilege any family of observers over the others and, therefore, observers with arbitrary motions should be able to provide a complete physical description of the world. This suggests that in a regular spacetime, all physically acceptable observers should have complete paths. In this work we explore this idea by studying the motion of accelerated observers in spherically symmetric spacetimes and illustrate it by considering two geodesically complete black hole spacetimes recently described in the literature. We show that for bound and locally unbound accelerations, the paths of accelerated test particles are complete, providing further support to the regularity of such spacetimes.

  18. Causal boundary for stably causal space-times

    International Nuclear Information System (INIS)

    Racz, I.

    1987-12-01

    The usual boundary constructions for space-times often yield an unsatisfactory boundary set. This problem is reviewed and a new solution is proposed. An explicit identification rule is given on the set of the ideal points of the space-time. This construction leads to a satisfactory boundary point set structure for stably causal space-times. The topological properties of the resulting causal boundary construction are examined. For the stably causal space-times each causal curve has a unique endpoint on the boundary set according to the extended Alexandrov topology. The extension of the space-time through the boundary is discussed. To describe the singularities the defined boundary sets have to be separated into two disjoint sets. (D.Gy.) 8 refs

  19. Thick domain wall spacetimes with and without reflection symmetry

    International Nuclear Information System (INIS)

    Melfo, Alejandra; Pantoja, Nelson; Skirzewski, Aureliano

    2003-01-01

    We show that different thick domain wall spacetimes, for which the scalar field configuration and the potential are the same, can be found as solutions to the coupled Einstein-scalar field equations, depending on whether or not reflection symmetry on the wall is imposed. Spacetimes with reflection symmetry may be dynamic or static, while the asymmetric ones are static. Asymmetric walls are asymptotically flat on one side and reduce to the Taub spacetime on the other. Examples of asymmetric thick walls in D-dimensional spacetimes are given, and previous analysis on the distributional thin-wall limit of the dynamic symmetric thick walls are extended to the asymmetric case. A new family of reflection symmetric, static thick domain wall spacetimes, including previously known Bogomol'nyi-Prasad-Sommerfield walls, is presented

  20. Quantum Space-Time Deformed Symmetries Versus Broken Symmetries

    CERN Document Server

    Amelino-Camelia, G

    2002-01-01

    Several recent studies have concerned the faith of classical symmetries in quantum space-time. In particular, it appears likely that quantum (discretized, noncommutative,...) versions of Minkowski space-time would not enjoy the classical Lorentz symmetries. I compare two interesting cases: the case in which the classical symmetries are "broken", i.e. at the quantum level some classical symmetries are lost, and the case in which the classical symmetries are "deformed", i.e. the quantum space-time has as many symmetries as its classical counterpart but the nature of these symmetries is affected by the space-time quantization procedure. While some general features, such as the emergence of deformed dispersion relations, characterize both the symmetry-breaking case and the symmetry-deformation case, the two scenarios are also characterized by sharp differences, even concerning the nature of the new effects predicted. I illustrate this point within an illustrative calculation concerning the role of space-time symm...

  1. Quantum Dynamics of Test Particle in Curved Space-Time

    International Nuclear Information System (INIS)

    Piechocki, W.

    2002-01-01

    To reveal the nature of space-time singularities of removable type we examine classical and quantum dynamics of a free particle in the Sitter type spacetimes. Consider space-times have different topologies otherwise are isometric. Our systems are integrable and we present analytic solutions of the classical dynamics. We quantize the systems by making use of the group theoretical method: we find an essentially self-adjoint representation of the algebra of observables integrable to the irreducible unitarity representation of the symmetry group of each consider gravitational system. The massless particle dynamics is obtained in the zero-mass limit of the massive case. Global properties of considered gravitational systems are of primary importance for the quantization procedure. Systems of a particle in space-times with removable singularities appear to be quantizable. We give specific proposal for extension of our analysis to space-times with essential type singularities. (author)

  2. Stochastic quantization of geometrodynamic curved space-time

    International Nuclear Information System (INIS)

    Prugovecki, E.

    1981-01-01

    It is proposed that quantum rather than classical test particles be used in recent operational definitions of space-time. In the resulting quantum space-time the role of test particle trajectories is taken over by propagators. The introduced co-ordinate values are stochastic rather than deterministic, the afore-mentioned propagators providing probability amplitudes describing fluctuations of measured co-ordinates around their mean values. It is shown that, if a geometrodynamic point of view based on 3 + 1 foliations of space-time is adopted, self-consistent families of propagators for quantum test particles in free fall can be constructed. The resulting formalism for quantum space-time is outlined and the quantization of spatially flat Robertson-Walker space-times is provided as an illustration. (author)

  3. Global spacetime symmetries in the functional Schroedinger picture

    International Nuclear Information System (INIS)

    Halliwell, J.J.

    1991-01-01

    In the conventional functional Schroedinger quantization of field theory, the background spacetime manifold is foliated into a set of three-surfaces and the quantum state of the field is represented by a wave functional of the field configurations on each three-surface. Although this procedure may be covariantly described, the wave functionals generally fail to carry a representation of the complete spacetime symmetry group of the background, such as the Poincare group in Minkowski spacetime, because spacetime symmetries generally involve distortions or motions of the three-surfaces themselves within that spacetime. In this paper, we show that global spacetime symmetries in the functional Schroedinger picture may be represented by parametrizing the field theory---raising to the status of dynamical variables the embedding variables describing the spacetime location of each three-surface. In particular, we show that the embedding variables provide a connection between the purely geometrical operation of an isometry group on the spacetime and the operation of the usual global symmetry generators (constructed from the energy-momentum tensor) on the wave functionals of the theory. We study the path-integral representation of the wave functionals of the parametrized field theory. We show how to construct, from the path integral, wave functionals that are annihilated by the global symmetry generators, i.e., that are invariant under global spacetime symmetry groups. The invariance of the class of histories summed over in the path integral is identified as the source of the invariance of the wave functionals. We apply this understanding to a study of vacuum states in the de Sitter spacetime. We make mathematically precise a previously given heuristic argument for the de Sitter invariance of the matter wave functionals defined by the no-boundary proposal of Hartle and Hawking

  4. The Euclidean scalar Green function in the five-dimensional Kaluza-Klein magnetic monopole space-time

    International Nuclear Information System (INIS)

    Bezerra de Mello, E.R.

    2006-01-01

    In this paper we present, in a integral form, the Euclidean Green function associated with a massless scalar field in the five-dimensional Kaluza-Klein magnetic monopole superposed to a global monopole, admitting a nontrivial coupling between the field with the geometry. This Green function is expressed as the sum of two contributions: the first one related with uncharged component of the field, is similar to the Green function associated with a scalar field in a four-dimensional global monopole space-time. The second contains the information of all the other components. Using this Green function it is possible to study the vacuum polarization effects on this space-time. Explicitly we calculate the renormalized vacuum expectation value * (x)Φ(x)> Ren , which by its turn is also expressed as the sum of two contributions

  5. Global aspects of complex geometry

    CERN Document Server

    Catanese, Fabrizio; Huckleberry, Alan T

    2006-01-01

    Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.

  6. Coordinates system adapted to non-inertial frames in Minkowski spacetime

    International Nuclear Information System (INIS)

    Felix, Patricio; Dahia, F.

    2011-01-01

    Full text: Static observers in curved spacetimes may interpret their proper acceleration as the opposite of a local gravitation Field (in the Newtonian sense). Based on this interpretation and the equivalence principle, we are led to investigate congruences of timelike curves in Minkowski spacetime whose acceleration field coincides with the acceleration field of static observers of curved spaces. The congruences give rise to non-inertial frames that are examined. Specifically we find, based on the locality principle, the embedding of simultaneity hypersurfaces adapted to the non-inertial frame in an explicit form for arbitrary acceleration fields. This work has motivated the fact that according to the principle of equivalence, it is expected that some physical features of gravity cam be mimicked by accelerated frames in Minkowski spacetime. The Rindler frame, which is adapted to a family of uniformly accelerated observers, is a famous example of a non-inertial system that simulates some characteristics of a black hole's geometry. This frame has been widely investigated in the literature and here we are going to start our discussion pointing out a peculiar aspect of the Rindler frame. It is related to the remarkable characteristic that the proper acceleration 'a' of Rindler observers, which is constant along their world lines, varies according to the law a = 1/ρ in relation to the observers, where ρ corresponds to the initial distance of the observers with respect to the origin of an inertial frame. This particular dependence of a ρ is connected to the behavior of static observers in Schwarzschild geometry in the vicinity of the horizon. Indeed, if ρ denotes the radial distance of an observer to the horizon, then, the proper acceleration the observers need in order to stay at rest in their position close to the horizon is proportional to 1/ρ. Therefore the Rindler congruence and the static Schwarzschild observers have the same acceleration field a(ρ). However

  7. Coordinates system adapted to non-inertial frames in Minkowski spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Felix, Patricio; Dahia, F. [Universidade Federal de Campo Grande (UFCG), PB (Brazil)

    2011-07-01

    Full text: Static observers in curved spacetimes may interpret their proper acceleration as the opposite of a local gravitation Field (in the Newtonian sense). Based on this interpretation and the equivalence principle, we are led to investigate congruences of timelike curves in Minkowski spacetime whose acceleration field coincides with the acceleration field of static observers of curved spaces. The congruences give rise to non-inertial frames that are examined. Specifically we find, based on the locality principle, the embedding of simultaneity hypersurfaces adapted to the non-inertial frame in an explicit form for arbitrary acceleration fields. This work has motivated the fact that according to the principle of equivalence, it is expected that some physical features of gravity cam be mimicked by accelerated frames in Minkowski spacetime. The Rindler frame, which is adapted to a family of uniformly accelerated observers, is a famous example of a non-inertial system that simulates some characteristics of a black hole's geometry. This frame has been widely investigated in the literature and here we are going to start our discussion pointing out a peculiar aspect of the Rindler frame. It is related to the remarkable characteristic that the proper acceleration 'a' of Rindler observers, which is constant along their world lines, varies according to the law a = 1/ρ in relation to the observers, where ρ corresponds to the initial distance of the observers with respect to the origin of an inertial frame. This particular dependence of a ρ is connected to the behavior of static observers in Schwarzschild geometry in the vicinity of the horizon. Indeed, if ρ denotes the radial distance of an observer to the horizon, then, the proper acceleration the observers need in order to stay at rest in their position close to the horizon is proportional to 1/ρ. Therefore the Rindler congruence and the static Schwarzschild observers have the same acceleration field

  8. Sources of hyperbolic geometry

    CERN Document Server

    Stillwell, John

    1996-01-01

    This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...

  9. Entropy of Vaidya-deSitter Spacetime

    Institute of Scientific and Technical Information of China (English)

    LI Xiang; ZHAO Zheng

    2001-01-01

    As a statistical model of black hole entropy, the brick-wall method based on the thermal equilibrium in a large scale cannot be applied to the cases out of equilibrium, such as the non-static hole or the case with two horizons.However, the leading term of hole entropy called the Bekenstein-Hawking entropy comes from the contribution of the field near the horizon. According to this idea, the entropy of Vaidya-deSitter spacetime is calculated. A difference from the static case is that the result proportional to the area of horizon relies on a time-dependent cut-off. The condition of local equilibrium near the horizon is used as a working postulate.

  10. On static and radiative space-times

    International Nuclear Information System (INIS)

    Friedrich, H.

    1988-01-01

    The conformal constraint equations on space-like hypersurfaces are discussed near points which represent either time-like or spatial infinity for an asymptotically flat solution of Einstein's vacuum field equations. In the case of time-like infinity a certain 'radiativity condition' is derived which must be satisfied by the data at that point. The case of space-like infinity is analysed in detail for static space-times with non-vanishing mass. It is shown that the conformal structure implied here on a slice of constant Killing time, which extends analytically through infinity, satisfies at spatial infinity the radiativity condition. Thus to any static solution exists a certain 'radiative solution' which has a smooth structure at past null infinity and is regular at past time-like infinity. A characterization of these solutions by their 'free data' is given and non-symmetry properties are discussed. (orig.)

  11. Electromagnetic waves in gravitational wave spacetimes

    International Nuclear Information System (INIS)

    Haney, M.; Bini, D.; Ortolan, A.; Fortini, P.

    2013-01-01

    We have considered the propagation of electromagnetic waves in a space-time representing an exact gravitational plane wave and calculated the induced changes on the four-potential field Aμ of a plane electromagnetic wave. By choosing a suitable photon round-trip in a Michelson interferometer, we have been able to identify the physical effects of the exact gravitational wave on the electromagnetic field, i.e. phase shift, change of the polarization vector, angular deflection and delay. These results have been exploited to study the response of an interferometric gravitational wave detector beyond the linear approximation of the general theory of relativity. A much more detailed examination of this problem can be found in our paper recently published in Classical and Quantum Gravity (28 (2011) 235007).

  12. Dirac equation in Kerr space-time

    Energy Technology Data Exchange (ETDEWEB)

    Iyer, B R; Kumar, Arvind [Bombay Univ. (India). Dept. of Physics

    1976-06-01

    The weak-field low-velocity approximation of Dirac equation in Kerr space-time is investigated. The interaction terms admit of an interpretation in terms of a 'dipole-dipole' interaction in addition to coupling of spin with the angular momentum of the rotating source. The gravitational gyro-factor for spin is identified. The charged case (Kerr-Newman) is studied using minimal prescription for electromagnetic coupling in the locally intertial frame and to the leading order the standard electromagnetic gyro-factor is retrieved. A first order perturbation calculation of the shift of the Schwarzchild energy level yields the main interesting result of this work: the anomalous Zeeman splitting of the energy level of a Dirac particle in Kerr metric.

  13. Stochastic space-time and quantum theory

    International Nuclear Information System (INIS)

    Frederick, C.

    1976-01-01

    Much of quantum mechanics may be derived if one adopts a very strong form of Mach's principle such that in the absence of mass, space-time becomes not flat, but stochastic. This is manifested in the metric tensor which is considered to be a collection of stochastic variables. The stochastic-metric assumption is sufficient to generate the spread of the wave packet in empty space. If one further notes that all observations of dynamical variables in the laboratory frame are contravariant components of tensors, and if one assumes that a Lagrangian can be constructed, then one can obtain an explanation of conjugate variables and also a derivation of the uncertainty principle. Finally the superposition of stochastic metrics and the identification of root -g in the four-dimensional invariant volume element root -g dV as the indicator of relative probability yields the phenomenon of interference as will be described for the two-slit experiment

  14. Equatorial circular motion in Kerr spacetime

    International Nuclear Information System (INIS)

    Pugliese, Daniela; Quevedo, Hernando; Ruffini, Remo

    2011-01-01

    We analyze the properties of circular orbits of test particles on the equatorial plane of a rotating central mass whose gravitational field is described by the Kerr spacetime. For rotating black holes and naked singularities we explore all the spatial regions where circular orbits can exist and analyze the behavior of the energy and the angular momentum of the corresponding test particles. In particular, we find all the radii at which a test particle can have zero angular momentum due to the repulsive gravity effects generated by naked singularities. We classify all the stability zones of circular orbits. It is shown that the geometric structure of the stability zones of black holes is completely different from that of naked singularities.

  15. Radion stabilization in higher curvature warped spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Das, Ashmita [Indian Institute of Technology, Department of Physics, Guwahati, Assam (India); Mukherjee, Hiya; Paul, Tanmoy; SenGupta, Soumitra [Indian Association for the Cultivation of Science, Department of Theoretical Physics, Kolkata (India)

    2018-02-15

    We consider a five dimensional AdS spacetime in presence of higher curvature term like F(R) = R + αR{sup 2} in the bulk. In this model, we examine the possibility of modulus stabilization from the scalar degrees of freedom of higher curvature gravity free of ghosts. Our result reveals that the model stabilizes itself and the mechanism of modulus stabilization can be argued from a geometric point of view. We determine the region of the parametric space for which the modulus (or radion) can to be stabilized. We also show how the mass and coupling parameters of radion field are modified due to higher curvature term leading to modifications of its phenomenological implications on the visible 3-brane. (orig.)

  16. Spacetime coverings and the casual boundary

    Energy Technology Data Exchange (ETDEWEB)

    Aké, Luis Alberto [Departamento de Álgebra, Geometría y Topología, Facultad de Ciencias, Universidad de Málaga,Campus Teatinos, Málaga (Spain); Herrera, Jónatan [Departamento de Matemática, Universidade Federal de Santa Catarina,Campus Universitario de Trindade, Florianopolis (Brazil)

    2017-04-10

    We consider the relation between the c-completion of a Lorentz manifold V and its quotient M=V/G, where G is an isometry group acting freely and properly discontinuously. First, we consider the future causal completion case, characterizing virtually when such a quotient is well behaved with the future chronological topology and improving the existing results on the literature. Secondly, we show that under some general assumptions, there exists a homeomorphism and chronological isomorphism between both, the c-completion of M and some adequate quotient of the c-completion of V defined by G. Our results are optimal, as we show in several examples. Finally, we give a practical application by considering isometric actions over Robertson-Walker spacetimes, including in particular the Anti-de Sitter model.

  17. Quantum electrodynamics in curved space-time

    International Nuclear Information System (INIS)

    Buchbinder, I.L.; Gitman, D.M.; Fradkin, E.S.

    1981-01-01

    The lagrangian of quantum electrodynamics in curved space-time is constructed and the interaction picture taking into account the external gravitational field exactly is introduced. The transform from the Heisenberg picture to the interaction picture is carried out in a manifestly covariant way. The properties of free spinor and electromagnetic quantum fields are discussed and conditions under which initial and final creation and annihilation operators are connected by unitarity transformation are indicated. The derivation of Feynman's rules for quantum processes are calculated on the base of generalized normal product of operators. The way of reduction formula derivations is indicated and the suitable Green's functions are introduced. A generating functional for this Green's function is defined and the system of functional equations for them is obtained. The representation of different generating funcationals by means of functional integrals is introduced. Some consequences of S-matrix unitary condition are considered which leads to the generalization of the optic theorem

  18. Intrinsic and extrinsic geometries of a tidally deformed black hole

    International Nuclear Information System (INIS)

    Vega, Ian; Poisson, Eric; Massey, Ryan

    2011-01-01

    A description of the event horizon of a perturbed Schwarzschild black hole is provided in terms of the intrinsic and extrinsic geometries of the null hypersurface. This description relies on a Gauss-Codazzi theory of null hypersurfaces embedded in spacetime, which extends the standard theory of spacelike and timelike hypersurfaces involving the first and second fundamental forms. We show that the intrinsic geometry of the event horizon is invariant under a reparameterization of the null generators, and that the extrinsic geometry depends on the parameterization. Stated differently, we show that while the extrinsic geometry depends on the choice of gauge, the intrinsic geometry is gauge invariant. We apply the formalism to solutions to the vacuum field equations that describe a tidally deformed black hole. In a first instance, we consider a slowly varying, quadrupolar tidal field imposed on the black hole, and in a second instance, we examine the tide raised during a close parabolic encounter between the black hole and a small orbiting body.

  19. Torsional Newton–Cartan geometry from Galilean gauge theory

    International Nuclear Information System (INIS)

    Banerjee, Rabin; Mukherjee, Pradip

    2016-01-01

    Using the recently advanced Galilean gauge theory (GGT) we give a comprehensive construction of torsional Newton–Cartan (NC) geometry. The coupling of a Galilean symmetric model with background NC geometry following GGT is illustrated by a free nonrelativistic scalar field theory. The issue of spatial diffeomorphism (Son and Wingate 2006 Ann. Phys. 321 197–224; Banerjee et al 2015 Phys. Rev. D 91 084021) is focussed from a new angle. The expression of the torsionful connection is worked out, which is in complete parallel with the relativistic theory. Also, smooth transition of the connection to its well known torsionless expression is demonstrated. A complete (implicit) expression of the torsion tensor for the NC spacetime is provided where the first-order variables occur in a suggestive way. The well known result for the temporal part of torsion is reproduced from our expression. (paper)

  20. Computational synthetic geometry

    CERN Document Server

    Bokowski, Jürgen

    1989-01-01

    Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...

  1. Discrete and computational geometry

    CERN Document Server

    Devadoss, Satyan L

    2011-01-01

    Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...

  2. Geometry and Cloaking Devices

    Science.gov (United States)

    Ochiai, T.; Nacher, J. C.

    2011-09-01

    Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.

  3. Lectures on discrete geometry

    CERN Document Server

    2002-01-01

    Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...

  4. Complex differential geometry

    CERN Document Server

    Zheng, Fangyang

    2002-01-01

    The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...

  5. Collision-free gases in spatially homogeneous space-times

    International Nuclear Information System (INIS)

    Maartens, R.; Maharaj, S.D.

    1985-01-01

    The kinematical and dynamical properties of one-component collision-free gases in spatially homogeneous, locally rotationally symmetric (LRS) space-times are analyzed. Following Ray and Zimmerman [Nuovo Cimento B 42, 183 (1977)], it is assumed that the distribution function f of the gas inherits the symmetry of space-time, in order to construct solutions of Liouville's equation. The redundancy of their further assumption that f be based on Killing vector constants of the motion is shown. The Ray and Zimmerman results for Kantowski--Sachs space-time are extended to all spatially homogeneous LRS space-times. It is shown that in all these space-times the kinematic average four-velocity u/sup i/ can be tilted relative to the homogeneous hypersurfaces. This differs from the perfect fluid case, in which only one space-time admits tilted u/sup i/, as shown by King and Ellis [Commun. Math. Phys. 31, 209 (1973)]. As a consequence, it is shown that all space-times admit nonzero acceleration and heat flow, while a subclass admits nonzero vorticity. The stress π/sub i/j is proportional to the shear sigma/sub i/j by virtue of the invariance of the distribution function. The evolution of tilt and the existence of perfect fluid solutions is also discussed

  6. Quantization of spacetime and the corresponding quantum mechanics

    International Nuclear Information System (INIS)

    Banai, M.

    1983-11-01

    An axiomatic framework for describing general space-time models is outlined. Space-time models to which irreducible propositional systems belong as causal logics are quantum(q) theoretically interpretable and their event spaces are Hilbert spaces. As a basic assumption, the time t and the radial coordinate r of a q particle satisfy the CCR (t, r)=+-i(h/2π). The two cases will be considered simultaneously. In that case the even space is the Hilbert space L 2 (IR 3 ). Unitary symmetries consist of Poincare-like symmetries: translations, rotations and inversion, and of gauge-like symmetries. Space inversion implies the time inversion. This q space-time reveals a confinement phenomenon: the q particle is 'confined' in a (h/2π) size region of Minkowski space IM 4 at any time. One particle mechanics over q space-time provides mass eigenvalue equations for elementary particles. Prugovecki's stochastic q mechanics and q space-time offer a natural way for introducing and interpreting consistently such a q space-time and q particles living in it. The mass eigenstates of q particles generate Prugovecki's extended elementary particles. When (h/2π) → 0, these particles shrink to point particles and IM 4 is recovered as the classical (c) limit of q space-time. Conceptual considerations prefer the case (t, r)=+i(h/2π) and applications in hadron physics give the fit (h/2π) approx.2/5 fermi/GeV. (author)

  7. Geometry and symmetry

    CERN Document Server

    Yale, Paul B

    2012-01-01

    This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi

  8. Hadamard States for the Klein-Gordon Equation on Lorentzian Manifolds of Bounded Geometry

    Science.gov (United States)

    Gérard, Christian; Oulghazi, Omar; Wrochna, Michał

    2017-06-01

    We consider the Klein-Gordon equation on a class of Lorentzian manifolds with Cauchy surface of bounded geometry, which is shown to include examples such as exterior Kerr, Kerr-de Sitter spacetime and the maximal globally hyperbolic extension of the Kerr outer region. In this setup, we give an approximate diagonalization and a microlocal decomposition of the Cauchy evolution using a time-dependent version of the pseudodifferential calculus on Riemannian manifolds of bounded geometry. We apply this result to construct all pure regular Hadamard states (and associated Feynman inverses), where regular refers to the state's two-point function having Cauchy data given by pseudodifferential operators. This allows us to conclude that there is a one-parameter family of elliptic pseudodifferential operators that encodes both the choice of (pure, regular) Hadamard state and the underlying spacetime metric.

  9. Stability analysis of lower dimensional gravastars in noncommutative geometry

    Energy Technology Data Exchange (ETDEWEB)

    Banerjee, Ayan [Jadavpur University, Department of Mathematics, Kolkata (India); Hansraj, Sudan [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)

    2016-11-15

    The Banados et al. (Phys. Rev. Lett 69:1849, 1992), black hole solution is revamped from the Einstein field equations in (2 + 1)-dimensional anti-de Sitter spacetime, in a context of noncommutative geometry (Phys. Rev. D 87:084014, 2013). In this article, we explore the exact gravastar solutions in three-dimensional anti-de Sitter space given in the same geometry. As a first step we derive BTZ solution assuming the source of energy density as point-like structures in favor of smeared objects, where the particle mass M, is diffused throughout a region of linear size √(α) and is described by a Gaussian function of finite width rather than a Dirac delta function. We matched our interior solution to an exterior BTZ spacetime at a junction interface situated outside the event horizon. Furthermore, a stability analysis is carried out for the specific case when χ < 0.214 under radial perturbations about the static equilibrium solutions. To give theoretical support we are also trying to explore their physical properties and characteristics. (orig.)

  10. Metric space construction for the boundary of space-time

    International Nuclear Information System (INIS)

    Meyer, D.A.

    1986-01-01

    A distance function between points in space-time is defined and used to consider the manifold as a topological metric space. The properties of the distance function are investigated: conditions under which the metric and manifold topologies agree, the relationship with the causal structure of the space-time and with the maximum lifetime function of Wald and Yip, and in terms of the space of causal curves. The space-time is then completed as a topological metric space; the resultant boundary is compared with the causal boundary and is also calculated for some pertinent examples

  11. Some spacetimes with higher rank Killing-Staeckel tensors

    International Nuclear Information System (INIS)

    Gibbons, G.W.; Houri, T.; Kubiznak, D.; Warnick, C.M.

    2011-01-01

    By applying the lightlike Eisenhart lift to several known examples of low-dimensional integrable systems admitting integrals of motion of higher-order in momenta, we obtain four- and higher-dimensional Lorentzian spacetimes with irreducible higher-rank Killing tensors. Such metrics, we believe, are first examples of spacetimes admitting higher-rank Killing tensors. Included in our examples is a four-dimensional supersymmetric pp-wave spacetime, whose geodesic flow is superintegrable. The Killing tensors satisfy a non-trivial Poisson-Schouten-Nijenhuis algebra. We discuss the extension to the quantum regime.

  12. Killing spinors as a characterisation of rotating black hole spacetimes

    International Nuclear Information System (INIS)

    Cole, Michael J; Kroon, Juan A Valiente

    2016-01-01

    We investigate the implications of the existence of Killing spinors in a spacetime. In particular, we show that in vacuum and electrovacuum a Killing spinor, along with some assumptions on the associated Killing vector in an asymptotic region, guarantees that the spacetime is locally isometric to the Kerr or Kerr–Newman solutions. We show that the characterisation of these spacetimes in terms of Killing spinors is an alternative expression of characterisation results of Mars (Kerr) and Wong (Kerr–Newman) involving restrictions on the Weyl curvature and matter content. (paper)

  13. On de Sitter-like and Minkowski-like spacetimes

    International Nuclear Information System (INIS)

    Luebbe, Christian; Kroon, Juan Antonio Valiente

    2009-01-01

    Friedrich's proofs for the global existence results of de Sitter-like spacetimes and of semi-global existence of Minkowski-like spacetimes (Friedrich 1986 Commun. Math. Phys. 107 587) are re-examined and discussed, making use of the extended conformal field equations and a gauge based on conformal geodesics. In this gauge, the location of the conformal boundary of the spacetimes is known a priori once the initial data have been prescribed. Thus, it provides an analysis which is conceptually and calculationally simpler.

  14. A composite model of the space-time and 'colors'

    International Nuclear Information System (INIS)

    Terazawa, Hidezumi.

    1987-03-01

    A pregeometric and pregauge model of the space-time and ''colors'' in which the space-time metric and ''color'' gauge fields are both composite is presented. By the non-triviality of the model, the number of space-time dimensions is restricted to be not larger than the number of ''colors''. The long conjectured space-color correspondence is realized in the model action of the Nambu-Goto type which is invariant under both general-coordinate and local-gauge transformations. (author)

  15. Approaching space-time through velocity in doubly special relativity

    International Nuclear Information System (INIS)

    Aloisio, R.; Galante, A.; Grillo, A.F.; Luzio, E.; Mendez, F.

    2004-01-01

    We discuss the definition of velocity as dE/d vertical bar p vertical bar, where E, p are the energy and momentum of a particle, in doubly special relativity (DSR). If this definition matches dx/dt appropriate for the space-time sector, then space-time can in principle be built consistently with the existence of an invariant length scale. We show that, within different possible velocity definitions, a space-time compatible with momentum-space DSR principles cannot be derived

  16. Circular motion and Polish Doughnuts in NUT spacetime

    Science.gov (United States)

    Jefremov, Paul I.

    The astrophysical relevance of the NUT spacetime(s) is a matter of debate due to pathological properties exhibited by this solution. However, if it is realised in nature, then we should look for the characteristic imprints of it on possible observations. One of the major sources of data on black hole astrophysics is the accretion process. Using a simple but fully analytical ``Polish Doughnuts'' model of accretion disk one gets both qualitative and quantitative differences from the Kerr spacetime produced by the presence of the gravitomagnetic charge. The present paper is based on our work Jefremov & Perlick (2016).

  17. The classification of static plane-symmetric spacetimes

    International Nuclear Information System (INIS)

    Ziad, M.

    1999-01-01

    According to the classical literature, here a complete classification of static plane-symmetric spacetimes according to their isometries and metrics is provided,without imposing any restriction on the stress-energy tensor. It turns out that these spacetimes admit G r as the maximal isometry groups whereas their Killing vector fields are obtained. The Einstein field equations are used to discuss the stress energy tensors of the spacetimes admitting higher symmetries along with their Segre' and Plebanski types and finally results are compared with those of Taub, Hall and Steele

  18. Ghost neutrinos as test fields in curved space-time

    International Nuclear Information System (INIS)

    Audretsch, J.

    1976-01-01

    Without restricting to empty space-times, it is shown that ghost neutrinos (their energy-momentum tensor vanishes) can only be found in algebraically special space-times with a neutrino flux vector parallel to one of the principal null vectors of the conformal tensor. The optical properties are studied. There are no ghost neutrinos in the Kerr-Newman and in spherically symmetric space-times. The example of a non-vacuum gravitational pp-wave accompanied by a ghost neutrino pp-wave is discussed. (Auth.)

  19. Classical black holes: the nonlinear dynamics of curved spacetime.

    Science.gov (United States)

    Thorne, Kip S

    2012-08-03

    Numerical simulations have revealed two types of physical structures, made from curved spacetime, that are attached to black holes: tendexes, which stretch or squeeze anything they encounter, and vortexes, which twist adjacent inertial frames relative to each other. When black holes collide, their tendexes and vortexes interact and oscillate (a form of nonlinear dynamics of curved spacetime). These oscillations generate gravitational waves, which can give kicks up to 4000 kilometers per second to the merged black hole. The gravitational waves encode details of the spacetime dynamics and will soon be observed and studied by the Laser Interferometer Gravitational Wave Observatory and its international partners.

  20. Quaternion wave equations in curved space-time

    Science.gov (United States)

    Edmonds, J. D., Jr.

    1974-01-01

    The quaternion formulation of relativistic quantum theory is extended to include curvilinear coordinates and curved space-time in order to provide a framework for a unified quantum/gravity theory. Six basic quaternion fields are identified in curved space-time, the four-vector basis quaternions are identified, and the necessary covariant derivatives are obtained. Invariant field equations are derived, and a general invertable coordinate transformation is developed. The results yield a way of writing quaternion wave equations in curvilinear coordinates and curved space-time as well as a natural framework for solving the problem of second quantization for gravity.