Canonical formalism of the Relativistic Theory of Gravitation
Soloviev, V O
2008-01-01
The Hamiltonian is derived in the Relativistic Theory of Gravitation with nonzero graviton mass. The second class constraints are excluded and Dirac brackets are obtained. There are no first class constraints in the theory.
Hakim, Rémi
1994-01-01
Il existe à l'heure actuelle un certain nombre de théories relativistes de la gravitation compatibles avec l'expérience et l'observation. Toutefois, la relativité générale d'Einstein fut historiquement la première à fournir des résultats théoriques corrects en accord précis avec les faits.
Poincare algebra realized in Hamiltonian formalism of the Relativistic Theory of Gravitation
Soloviev, V O
2010-01-01
We obtain the Poincare group generators by proper choice of arbitrary functions present in the Relativistic Theory of Gravitation (RTG) Hamiltonian. Their Dirac brackets give the Poincare algebra in accordance with the fact that RTG has 10 integrals of motion.
Gravitationally confined relativistic neutrinos
Vayenas, C. G.; Fokas, A. S.; Grigoriou, D.
2017-09-01
Combining special relativity, the equivalence principle, and Newton’s universal gravitational law with gravitational rather than rest masses, one finds that gravitational interactions between relativistic neutrinos with kinetic energies above 50 MeV are very strong and can lead to the formation of gravitationally confined composite structures with the mass and other properties of hadrons. One may model such structures by considering three neutrinos moving symmetrically on a circular orbit under the influence of their gravitational attraction, and by assuming quantization of their angular momentum, as in the Bohr model of the H atom. The model contains no adjustable parameters and its solution, using a neutrino rest mass of 0.05 eV/c2, leads to composite state radii close to 1 fm and composite state masses close to 1 GeV/c2. Similar models of relativistic rotating electron - neutrino pairs give a mass of 81 GeV/c2, close to that of W bosons. This novel mechanism of generating mass suggests that the Higgs mass generation mechanism can be modeled as a latent gravitational field which gets activated by relativistic neutrinos.
LISA sensitivities to gravitational waves from relativistic metric theories of gravity
Tinto, Massimo; Alves, Márcio Eduardo Da Silva
2010-12-01
The direct observation of gravitational waves will provide a unique tool for probing the dynamical properties of highly compact astrophysical objects, mapping ultrarelativistic regions of space-time, and testing Einstein’s general theory of relativity. LISA (Laser Interferometer Space Antenna), a joint National Aeronautics and Space Administration and European Space Agency mission to be launched in the next decade, will perform these scientific tasks by detecting and studying low-frequency cosmic gravitational waves through their influence on the phases of six modulated laser beams exchanged between three remote spacecraft. By directly measuring the polarization components of the waves LISA will detect, we will be able to test Einstein’s theory of relativity with good sensitivity. Since a gravitational wave signal predicted by the most general relativistic metric theory of gravity accounts for six polarization modes (the usual two Einstein’s tensor polarizations as well as two vector and two scalar wave components), we have derived the LISA time-delay interferometric responses and estimated their sensitivities to vector- and scalar-type waves. We find that (i) at frequencies larger than roughly the inverse of the one-way light time (≈6×10-2Hz), LISA is more than ten times sensitive to scalar-longitudinal and vector signals than to tensor and scalar-transverse waves, and (ii) in the low part of its frequency band is equally sensitive to tensor and vector waves and somewhat less sensitive to scalar signals.
Tiec, Alexandre Le
2016-01-01
The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity. First, we introduce those mathematical concepts that are necessary to properly formulate the physical theory, such as the notions of manifold, vector, tensor, metric, connection and curvature. Second, we motivate, formulate and then discuss Einstein's equation, which relates the geometry of spacetime to its matter content. Gravitational waves are later introduced as solutions of the linearized Einstein equation around flat spacetime. These waves are shown to propagate at the speed of light and to possess two polarization states. Gravitational waves can interact with matter, allowing for their direct detection by means of laser interferometers. Finally, Einstein's quadrupole formulas are derived and used to show that nonspherical compact objects moving at relativistic speeds a...
Relativistic theories of materials
Bressan, Aldo
1978-01-01
The theory of relativity was created in 1905 to solve a problem concerning electromagnetic fields. That solution was reached by means of profound changes in fundamental concepts and ideas that considerably affected the whole of physics. Moreover, when Einstein took gravitation into account, he was forced to develop radical changes also in our space-time concepts (1916). Relativistic works on heat, thermodynamics, and elasticity appeared as early as 1911. However, general theories having a thermodynamic basis, including heat conduction and constitutive equations, did not appear in general relativity until about 1955 for fluids and appeared only after 1960 for elastic or more general finitely deformed materials. These theories dealt with materials with memory, and in this connection some relativistic versions of the principle of material indifference were considered. Even more recently, relativistic theories incorporating finite deformations for polarizable and magnetizable materials and those in which couple s...
Antipin, K V; Silaev, P K
2016-01-01
We use both numerical and analytical approaches to study the dynamics of the gravitational collapse in the framework of the relativistic theory of gravitation (RTG). We use various equations of state for the collapsing matter and relatively realistic initial conditions with smooth matter distribution, which corresponds to static solution for the given equation of state. We also obtain results concerning the influence of the graviton mass on the properties of static solutions. We specify several characteristics of the process of the collapse, in particular, we determine the dependence of the turning point time (when contraction is replaced by inflation) on the graviton mass. We also study the influence of non-zero pressure on the dynamics of the collapse.
Special Relativistic Hydrodynamics with Gravitation
Hwang, Jai-chan; Noh, Hyerim
2016-12-01
Special relativistic hydrodynamics with weak gravity has hitherto been unknown in the literature. Whether such an asymmetric combination is possible has been unclear. Here, the hydrodynamic equations with Poisson-type gravity, considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit, are consistently derived from Einstein’s theory of general relativity. An analysis is made in the maximal slicing, where the Poisson’s equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the general hypersurface condition. Our formulation includes the anisotropic stress.
MALFLIET, R
1993-01-01
We discuss the present status of relativistic transport theory. Special emphasis is put on problems of topical interest: hadronic features, thermodynamical consistent approximations and spectral properties.
Gravitational mass of relativistic matter and antimatter
Tigran Kalaydzhyan
2015-12-01
Full Text Available The universality of free fall, the weak equivalence principle (WEP, is a cornerstone of the general theory of relativity, the most precise theory of gravity confirmed in all experiments up to date. The WEP states the equivalence of the inertial, m, and gravitational, mg, masses and was tested in numerous occasions with normal matter at relatively low energies. However, there is no confirmation for the matter and antimatter at high energies. For the antimatter the situation is even less clear – current direct observations of trapped antihydrogen suggest the limits −65
Workshop on gravitational waves and relativistic astrophysics
Patrick Das Gupta
2004-10-01
Discussions related to gravitational wave experiments viz. LIGO and LISA as well as to observations of supermassive black holes dominated the workshop sessions on gravitational waves and relativistic astrophysics in the ICGC-2004. A summary of seven papers that were presented in these workshop sessions has been provided in this article.
Green, H.S. [Department of Physics and Mathematical Physics, University of Adelaide, Adelaide, SA (Australia)
1998-12-31
It is possible to construct the non-euclidean geometry of space-time from the information carried by neutral particles. Points are identified with the quantal events in which photons or neutrinos are created and annihilated, and represented by the relativistic density matrices of particles immediately after creation or before annihilation. From these, matrices representing subspaces in any number of dimensions are constructed, and the metric and curvature tensors are derived by an elementary algebraic method; these are similar in all respects to those of Riemannian geometry. The algebraic method is extended to obtain solutions of Einstein`s gravitational field equations for empty space, with a cosmological term. General relativity and quantum theory are unified by the quantal embedding of non-euclidean space-time, and the derivation of a generalisation, consistent with Einstein`s equations, of the special relativistic wave equations of particles of any spin within representations of SO(3) SO(4; 2). There are some novel results concerning the dependence of the scale of space-time on properties of the particles by means of which it is observed, and the gauge groups associated with gravitation. Copyright (1998) CSIRO Australia 33 refs.
Gravitational mass of relativistic matter and antimatter
Kalaydzhyan, Tigran
2015-01-01
The universality of free fall, the so-called weak equivalence principle (WEP), is a cornerstone of the general theory of relativity, the most precise theory of gravity confirmed in all experiments up to date. The WEP states the equivalence of the inertial and gravitational masses and was tested in numerous occasions with normal matter at relatively low energies. However, there is no proof for the matter and antimatter at high energies. %coming from ground-based experiments. For the antimatter the situation is even less clear -- current direct observations of trapped antihydrogen suggest the limits -65 < m_g / m < 110 not ruling out antigravity, i.e. repulsion of the antimatter by Earth. Here we demonstrate a bound 1 - 4x10^{-7} < m_g/m < 1 + 2x10^{-7} on the gravitational mass of relativistic electrons and positrons in the potential of the Local Supercluster (LS) coming from the Large Electron-Positron Collider (LEP) and Tevatron accelerator experiments. By considering annual variations of the sol...
Special relativistic hydrodynamics with gravitation
Hwang, Jai-chan
2016-01-01
The special relativistic hydrodynamics with weak gravity is hitherto unknown in the literature. Whether such an asymmetric combination is possible was unclear. Here, the hydrodynamic equations with Poisson-type gravity considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit are consistently derived from Einstein's general relativity. Analysis is made in the maximal slicing where the Poisson's equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the {\\it general} hypersurface condition. Our formulation includes the anisotropic stress.
Theory of gravitational interactions
Gasperini, Maurizio
2017-01-01
This is the second edition of a well-received book that is a modern, self-contained introduction to the theory of gravitational interactions. The new edition includes more details on gravitational waves of cosmological origin, the so-called brane world scenario, and gravitational time-delay effects. The first part of the book follows the traditional presentation of general relativity as a geometric theory of the macroscopic gravitational field, while the second, more advanced part discusses the deep analogies (and differences) between a geometric theory of gravity and the “gauge” theories of the other fundamental interactions. This fills a gap within the traditional approach to general relativity which usually leaves students puzzled about the role of gravity. The required notions of differential geometry are reduced to the minimum, allowing room for aspects of gravitational physics of current phenomenological and theoretical interest, such as the properties of gravitational waves, the gravitational inter...
Theory of gravitational interactions
Gasperini, Maurizio
2013-01-01
This reference textbook is an up-to-date and self-contained introduction to the theory of gravitational interactions. The first part of the book follows the traditional presentation of general relativity as a geometric theory of the macroscopic gravitational field. A second, advanced part then discusses the deep analogies (and differences) between a geometric theory of gravity and the gauge theories of the other fundamental interactions. This fills a gap which is present in the context of the traditional approach to general relativity, and which usually makes students puzzled about the role of gravity. The necessary notions of differential geometry are reduced to the minimum, leaving more room for those aspects of gravitational physics of current phenomenological and theoretical interest, such as the properties of gravitational waves, the gravitational interactions of spinors, and the supersymmetric and higher-dimensional generalization of the Einstein equations. Theory of Gravitational Interactions will be o...
Relativistic stars in bigravity theory
Aoki, Katsuki; Tanabe, Makoto
2016-01-01
Assuming static and spherically symmetric spacetimes in the ghost-free bigravity theory, we find a relativistic star solution, which is very close to that in general relativity. The coupling constants are classified into two classes: Class [I] and Class [II]. Although the Vainshtein screening mechanism is found in the weak gravitational field for both classes, we find that there is no regular solution beyond the critical value of the compactness in Class [I]. This implies that the maximum mass of a neutron star in Class [I] becomes much smaller than that in GR. On the other hand, for the solution in Class [II], the Vainshtein screening mechanism works well even in a relativistic star and the result in GR is recovered.
Relativistic theory of tidal Love numbers
Binnington, Taylor; Poisson, Eric
2009-01-01
In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neut...
Extended Theories of Gravitation
Fatibene Lorenzo
2013-09-01
Full Text Available Extended theories of gravitation are naturally singled out by an analysis inspired by the Ehelers-Pirani-Schild framework. In this framework the structure of spacetime is described by a Weyl geometry which is enforced by dynamics. Standard General Relativity is just one possible theory within the class of extended theories of gravitation. Also all Palatini f(R theories are shown to be extended theories of gravitation. This more general setting allows a more general interpretation scheme and more general possible couplings between gravity and matter. The definitions and constructions of extended theories will be reviewed. A general interpretation scheme will be considered for extended theories and some examples will be considered.
Brun-Battistini, D; Sandoval-Villalbazo, A
2016-01-01
Richard C. Tolman analyzed the relation between a temperature gradient and a gravitational field in an equilibrium situation. In 2012, Tolman\\textquoteright s law was generalized to a non-equilibrium situation for a simple dilute relativistic fluid. The result in that scenario, obtained by introducing the gravitational force through the molecular acceleration, couples the heat flux with the metric coefficients and the gradients of the state variables. In the present paper it is shown, by \\textquotedblleft suppressing\\textquotedblright{} the molecular acceleration in Boltzmann\\textquoteright s equation, that a gravitational field drives a heat flux. This procedure corresponds to the description of particle motion through geodesics, in which a Newtonian limit to the Schwarzschild metric is assumed. The effect vanishes in the non-relativistic regime, as evidenced by the direct evaluation of the corresponding limit.
Relativistic orbits and Gravitational Waves from gravitomagnetic corrections
Capozziello, Salvatore; Forte, Luca; Garufi, Fabio; Milano, Leopoldo
2010-01-01
Corrections to the relativistic theory of orbits are discussed considering higher order approximations induced by gravitomagnetic effects. Beside the standard periastron effect of General Relativity (GR), a new nutation effect was found due to the ${\\displaystyle c^{-3}}$ orbital correction. According to the presence of that new nutation effect we studied the gravitational waveforms emitted through the capture in a gravitational field of a massive black hole (MBH) of a compact object (neutron star (NS) or BH) via the quadrupole approximation. We made a numerical study to obtain the emitted gravitational wave (GW) amplitudes. We conclude that the effects we studied could be of interest for the future space laser interferometric GW antenna LISA.
Relativistic theory of tidal Love numbers
Binnington, Taylor
2009-01-01
In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.
Non-relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity
无
2006-01-01
Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation obtained from this non-relativistic limit, we can see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrodinger equation, which can explain the gravitational phase effects found in COW experiments.And because of this Newtonian gravitational potential, a quantum particle in the earth's gravitational field may form a gravitationally bound quantized state, which has already been detected in experiments. Three different kinds of phase effects related to gravitational interactions are studied in this paper, and these phase effects should be observable in some astrophysical processes. Besides, there exists direct coupling between gravitomagnetic field and quantum spin, and radiation caused by this coupling can be used to directly determine the gravitomagnetic field on the surface of a star.
Koehler, Wolfgang
2011-01-01
A new classical theory of gravitation within the framework of general relativity is presented. It is based on a matrix formulation of four-dimensional Riemann-spaces and uses no artificial fields or adjustable parameters. The geometrical stress-energy tensor is derived from a matrix-trace Lagrangian, which is not equivalent to the curvature scalar R. To enable a direct comparison with the Einstein-theory a tetrad formalism is utilized, which shows similarities to teleparallel gravitation theories, but uses complex tetrads. Matrix theory might solve a 27-year-old, fundamental problem of those theories (sec. 4.1). For the standard test cases (PPN scheme, Schwarzschild-solution) no differences to the Einstein-theory are found. However, the matrix theory exhibits novel, interesting vacuum solutions.
Radiation reaction in a system of relativistic gravitating particles
Galtsov, D. V.
A Lorentz-covariant approach is developed to the description of electromagnetic and gravitational radiation in general relativity. A model of a relativistic system of gravitating point particles is constructed in which energy losses can be interpreted in terms of radiation-reaction forces. These forces are applied not only to the point particles but also to fields generated by these particles in the near zone. It is concluded that radiation friction in a system of relativistic gravitating particles is collective in character.
Blair, D.G.; Buckingham, M.J. (Western Australia Univ., Nedlands (Australia). Dept. of Physics)
1989-01-01
The Marcel Grossmann Meetings have been conceived with the aim of reviewing recent developments in gravitation and general relativity, with major emphasis on mathematical foundations and physical predictions. Their main object is to elicit contributions which deepen our understanding of spacetime structure as well as to review the status of experiments testing Einstein's theory of gravitation.
Emission of gravitational radiation from ultra-relativistic sources
Segalis, E B; Segalis, Ehud B.; Ori, Amos
2001-01-01
Recent observations suggest that blobs of matter are ejected with ultra-relativistic speeds in various astrophysical phenomena such as supernova explosions, quasars, and microquasars. In this paper we analyze the gravitational radiation emitted when such an ultra-relativistic blob is ejected from a massive object. We express the gravitational wave by the metric perturbation in the transverse-traceless gauge, and calculate its amplitude and angular dependence. We find that in the ultra-relativistic limit the gravitational wave has a wide angular distribution, like $1+\\cos\\theta$. The typical burst's frequency is Doppler shifted, with the blue-shift factor being strongly beamed in the forward direction. As a consequence, the energy flux carried by the gravitational radiation is beamed. In the second part of the paper we estimate the anticipated detection rate of such bursts by a gravitational-wave detector, for blobs ejected in supernova explosions. Dar and De Rujula recently proposed that ultra-relativistic bl...
Extended Theories of Gravitation
Fatibene Lorenzo
2013-09-01
Full Text Available Within the framework of extended theories of gravitation we shall discuss physical equivalences among different formalisms and classical tests. As suggested by the Ehlers-Pirani-Schild framework, the conformal invariance will be preserved and its effect on observational protocols discussed. Accordingly, we shall review standard tests showing how Palatini f(R-theories naturally passes solar system tests. Observation protocols will be discussed in this wider framework.
Gravitational mass of relativistic matter and antimatter
Kalaydzhyan, Tigran
2015-12-01
The universality of free fall, the weak equivalence principle (WEP), is a cornerstone of the general theory of relativity, the most precise theory of gravity confirmed in all experiments up to date. The WEP states the equivalence of the inertial, m, and gravitational, mg, masses and was tested in numerous occasions with normal matter at relatively low energies. However, there is no confirmation for the matter and antimatter at high energies. For the antimatter the situation is even less clear - current direct observations of trapped antihydrogen suggest the limits - 65 International Linear Collider (ILC) and Compact Linear Collider (CLIC).
Emergent gravitational dynamics in relativistic Bose--Einstein condensate
Belenchia, Alessio; Mohd, Arif
2014-01-01
Analogue models of gravity have played a pivotal role in the past years by providing a test bench for many open issues in quantum field theory in curved spacetime such as the robustness of Hawking radiation and cosmological particle production. More recently, the same models have offered a valuable framework within which current ideas about the emergence of spacetime and its dynamics could be discussed via convenient toy models. In this context, we study here an analogue gravity system based on a relativistic Bose--Einstein condensate. We show that in a suitable limit this system provides not only an example of an emergent spacetime (with a massive and a massless relativistic fields propagating on it) but also that such spacetime is governed by an equation with geometric meaning that takes the familiar form of Nordstr{\\"o}m theory of gravitation. In this equation the gravitational field is sourced by the expectation value of the trace of the effective stress energy tensor of the quasiparticles while the Newto...
Blagojević, Milutin
2012-01-01
During the last five decades, gravity, as one of the fundamental forces of nature, has been formulated as a gauge field theory of the Weyl-Cartan-Yang-Mills type. The resulting theory, the Poincar\\'e gauge theory of gravity, encompasses Einstein's gravitational theory as well as the teleparallel theory of gravity as subcases. In general, the spacetime structure is enriched by Cartan's torsion and the new theory can accommodate fermionic matter and its spin in a perfectly natural way. The present reprint volume contains articles from the most prominent proponents of the theory and is supplemented by detailed commentaries of the editors. This guided tour starts from special relativity and leads, in its first part, to general relativity and its gauge type extensions a la Weyl and Cartan. Subsequent stopping points are the theories of Yang-Mills and Utiyama and, as a particular vantage point, the theory of Sciama and Kibble. Later, the Poincar\\'e gauge theory and its generalizations are explored and specific topi...
Unification of Relativistic and Quantum Mechanics from Elementary Cycles Theory
Dolce, Donatello
2016-01-01
In Elementary Cycles theory elementary quantum particles are consistently described as the manifestation of ultra-fast relativistic spacetime cyclic dynamics, classical in the essence. The peculiar relativistic geometrodynamics of Elementary Cycles theory yields de facto a unification of ordinary relativistic and quantum physics. In particular its classical-relativistic cyclic dynamics reproduce exactly from classical physics first principles all the fundamental aspects of Quantum Mechanics, such as all its axioms, the Feynman path integral, the Dirac quantisation prescription (second quantisation), quantum dynamics of statistical systems, non-relativistic quantum mechanics, atomic physics, superconductivity, graphene physics and so on. Furthermore the theory allows for the explicit derivation of gauge interactions, without postulating gauge invariance, directly from relativistic geometrodynamical transformations, in close analogy with the description of gravitational interaction in general relativity. In thi...
Radiation reaction in a system of relativistic gravitating particles
Galtsov, D.V.
1983-01-01
A Lorentz-covariant approach is developed to the description of electromagnetic and gravitational radiation in general relativity. A model of a relativistic system of gravitating point particles is constructed in which energy losses can be interpreted in terms of radiation-reaction forces. These forces are applied not only to the point particles but also to fields generated by these particles in the near zone. It is concluded that radiation friction in a system of relativistic gravitating particles is collective in character. 16 references.
Vector Theory in Relativistic Thermodynamics
刘泽文
1994-01-01
It is pointed out that five defects occur in Planck-Einstein’s relativistic thermodynamics (P-E theory). A vector theory in relativistic thermodynamics (VTRT) is established. Defining the internal energy as a 4-vector, and supposing the entropy and the number of. particles to be invariants we have derived the transformations of all quantities, and subsequently got the Lagrangian and 4-D forms of thermodynamic laws. In order to test the new theory, several exact solutions with classical limits are given. The VTRT is free from the defects of the P-E theory.
Exact relativistic theory of geoid's undulation
Kopeikin, Sergei; Karpik, Alexander
2014-01-01
Precise determination of geoid is one of the most important problem of physical geodesy. The present paper extends the Newtonian concept of the geoid to the realm of Einstein's general relativity and derives an exact relativistic equation for the unperturbed geoid and level surfaces under assumption of axisymmetric distribution of background matter in the core and mantle of the Earth. We consider Earth's crust as a small disturbance imposed on the background distribution of matter, and formulate the master equation for the anomalous gravity potential caused by this disturbance. We find out the gauge condition that drastically simplifies the master equation for the anomalous gravitational potential and reduces it to the form closely resembling the one in the Newtonian theory. The master equation gives access to the precise calculation of geoid's undulation with the full account for relativistic effects not limited to the post-Newtonian approximation. The geoid undulation theory, given in the present paper, uti...
Vacaru, Olivia
2013-01-01
Using $3+1$ spacetime fibrations on Lorentz manifolds, we define an analogous W--entropy for gravitational fields. Such F- and W-functionals were introduced in the Ricci flow theory of three dimensional Riemannian metrics by G. Perelman, arXiv: math.DG/0211159. The main goal of this paper is to solve and study one of the mentioned there problems: how associated statistical thermodynamical functions could reproduce in a relativistic manner the black hole thermodynamics and, in a more general context, provide a thermodynamic description of gravitational interactions? In our approach, the gravitational W--entropy characterizes the geometric evolution of three dimensional (3-d) hypersurface metrics nonoholonomically imbedded into certain classes of 4-d solutions of gravitational field equations. A geometric method for generating generic off-diagonal exact solutions for Einstein manifolds of pseudo-Euclidean signature determined by relativistic Ricci flow evolution of 3-d Riemannian metrics is applied. To relate s...
Piran, T.; Ruffini, R.
The following topics were dealt with: conservation laws; exact solutions; inertial forces in general relativity; alternative theories in four dimensions; alternative theories (Kaluza-Klein); hairy black holes; time machines; chaos in general relativity; Einstein Maxwell systems; mass inflation; critical phenomena; numerical relativity; algebraic computations; quantum fields in curved space time; time in quantum gravity; canonical quantum gravity; strings; the Casimir effect; black hole thermodynamics; quantum cosmology; gravitational wave detectors; general relativity in space; experimental tests; equivalence principle in space; observational cosmology; inflation; topological defects; early universe; cosmic microwave background; nonsingular cosmology; dark matter; astro-particles; gravitational lenses; extragalactic sources; astrophysical black holes; QPO's; binary neutron stars; microlenses; gamma ray bursts; boson stars.
Relativistic Motion of Spinning Particles in a Gravitational Field
Chicone, C.; Mashhoon, B.; Punsly, B.
2005-01-01
The relative motion of a classical relativistic spinning test particle is studied with respect to a nearby free test particle in the gravitational field of a rotating source. The effects of the spin-curvature coupling force are elucidated and the implications of the results for the motion of rotating plasma clumps in astrophysical jets are discussed.
Relativistic motion of spinning particles in a gravitational field
Chicone, C.; Mashhoon, B.; Punsly, B.
2005-08-01
The relative motion of a classical relativistic spinning test particle is studied with respect to a nearby free test particle in the gravitational field of a rotating source. The effects of the spin-curvature coupling force are elucidated and the implications of the results for the motion of rotating plasma clumps in astrophysical jets are discussed.
Gravitational and dilaton radiation from a relativistic membrane
Galtsov, D V; Gal'tsov, Dmitri V.; Melkumova, Elena Yu.
2001-01-01
Recent scenarios of the TeV-scale brane cosmology suggest a possibility of existence in the early universe of two-dimensional topological defects: relativistic membranes. Like cosmic strings, oscillating membranes could emit gravitational radiation contributing to a stochastic background of gravitational waves. We calculate dilaton and gravitational radiation from a closed toroidal membrane excited along one homology cycle. The spectral-angular distributions of dilaton and gravitational radiation are obtained in a closed form in terms of Bessel's functions. The angular distributions are affected by oscillating factors due to an interference of radiation from different segments of the membrane. The dilaton radiation power is dominated by a few lower harmonics of the basic frequency, while the spectrum of the gravitational radiation contains also a substantial contribution from higher harmonics. The radiative lifetime of the membrane is determined by its tension and depends weakly on the ratio of two radii of t...
Frontiers in Relativistic Celestial Mechanics, Vol. 1. Theory
Kopeikin, Sergei
2014-10-01
Relativistic celestial mechanics - investigating the motion celestial bodies under the influence of general relativity - is a major tool of modern experimental gravitational physics. With a wide range of prominent authors from the field, this two-volume series consists of reviews on a multitude of advanced topics in the area of relativistic celestial mechanics - starting from more classical topics such as the regime of asymptotically-flat spacetime, light propagation and celestial ephemerides, but also including its role in cosmology and alternative theories of gravity as well as modern experiments in this area. This first volume of a two-volume series is concerned with theoretical foundations such as post-Newtonian solutions to the two-body problem, light propagation through time-dependent gravitational fields, as well as cosmological effects on the movement of bodies in the solar systems. On the occasion of his 80-th birthday, these two volumes honor V. A. Brumberg - one of the pioneers in modern relativistic celestial mechanics. Contributions include: M. Soffel: On the DSX-framework T. Damour: The general relativistic two body problem G. Schaefer: Hamiltonian dynamics of spinning compact binaries through high post-Newtonian approximations A. Petrov and S. Kopeikin: Post-Newtonian approximations in cosmology T. Futamase: On the backreaction problem in cosmology Y. Xie and S. Kopeikin: Covariant theory of the post-Newtonian equations of motion of extended bodies S. Kopeikin and P. Korobkov: General relativistic theory of light propagation in multipolar gravitational fields
Relativistic kinetic theory with applications in astrophysics and cosmology
Vereshchagin, Gregory V
2017-01-01
Relativistic kinetic theory has widespread application in astrophysics and cosmology. The interest has grown in recent years as experimentalists are now able to make reliable measurements on physical systems where relativistic effects are no longer negligible. This ambitious monograph is divided into three parts. It presents the basic ideas and concepts of this theory, equations and methods, including derivation of kinetic equations from the relativistic BBGKY hierarchy and discussion of the relation between kinetic and hydrodynamic levels of description. The second part introduces elements of computational physics with special emphasis on numerical integration of Boltzmann equations and related approaches, as well as multi-component hydrodynamics. The third part presents an overview of applications ranging from covariant theory of plasma response, thermalization of relativistic plasma, comptonization in static and moving media to kinetics of self-gravitating systems, cosmological structure formation and neut...
Diffusion of relativistic gas mixtures in gravitational fields
Kremer, Gilberto M
2013-01-01
A mixture of relativistic gases of non-disparate rest masses in a Schwarzschild metric is studied on the basis of a relativistic Boltzmann equation in the presence of gravitational fields. A BGK-type model equation of the collision operator of the Boltzmann equation is used in order to compute the non-equilibrium distribution functions by the Chapman-Enskog method. The main focus of this work is to obtain Fick's law without the thermal-diffusion cross-effect. Fick's law has four contributions, two of them are the usual terms proportional to the gradients of concentration and pressure. The other two are of the same nature as those which appears in Fourier's law in the presence of gravitational fields and are related with an acceleration and gravitational potential gradient, but unlike Fourier's law these two last terms are of non-relativistic order. Furthermore, it is shown that the coefficients of diffusion depend on the gravitational potential and they become larger than those in the absence of it.
Towards Relativistic Atomic Physics and Post-Minkowskian Gravitational Waves
Lusanna, Luca
2009-01-01
A review is given of the formulation of relativistic atomic theory, in which there is an explicit realization of the Poincare' generators, both in the inertial and in the non-inertial rest-frame instant form of dynamics in Minkowski space-time. This implies the need to solve the problem of the relativistic center of mass of an isolated system and to describe the transitions from different conventions for clock synchronization, namely for the identifications of instantaneous 3-spaces, as gauge transformations. These problems, stemming from the Lorentz signature of space-time, are a source of non-locality, which induces a spatial non-separability in relativistic quantum mechanics, with implications for relativistic entanglement. Then the classical system of charged particles plus the electro-magnetic field is studied in the framework of ADM canonical tetrad gravity in asymptotically Minkowskian space-times admitting the ADM Poincare' group at spatial infinity, which allows to get the general relativistic extens...
Exploring gravitational theories beyond Horndeski
Gleyzes, Jérôme; Piazza, Federico; Vernizzi, Filippo
2014-01-01
We have recently proposed a new class of gravitational scalar-tensor theories free from ghost instabilities. As they generalize Horndeski theories, or "generalized" galileons, we call them G$^3$. These theories possess a simple formulation when the time hypersurfaces are chosen to coincide with the uniform scalar field hypersurfaces. We confirm that they do not suffer from Ostrogradski instabilities by presenting the details of the Hamiltonian formulation. We examine the coupling between these theories and matter. Moreover, we investigate how they transform under a disformal redefinition of the metric. Remarkably, these theories are preserved by disformal transformations, which also allow subfamilies of G$^3$ to be mapped into Horndeski theories.
Testing alternate gravitational theories
Standish, E. M.
2010-01-01
The planetary ephemerides are used to examine different suggested forms of the gravitational equations of motion which could possibly cause the observed Pioneer Anomaly. It is shown that most of the forms would be unacceptable, including that generally assumed - a constant acceleration directed toward the Sun. The tests show that three other forms could not exist within 10 au's of the Sun. Only one suggested form would be compatible with the Pioneer Anomaly affecting Saturn or any other more inward planet. Additional planetary observations in the future may possibly eliminate this form also.
Demianski, Marek
2013-01-01
Relativistic Astrophysics brings together important astronomical discoveries and the significant achievements, as well as the difficulties in the field of relativistic astrophysics. This book is divided into 10 chapters that tackle some aspects of the field, including the gravitational field, stellar equilibrium, black holes, and cosmology. The opening chapters introduce the theories to delineate gravitational field and the elements of relativistic thermodynamics and hydrodynamics. The succeeding chapters deal with the gravitational fields in matter; stellar equilibrium and general relativity
Dwarf Galaxies, MOND, and Relativistic Gravitation
Arthur Kosowsky
2010-01-01
Certain limits of these theories can also give the accelerating expansion of the Universe. The standard dark matter cosmology boasts numerous manifest triumphs; however, alternatives should also be pursued as long as outstanding observational issues remain unresolved, including the empirical successes of MOND on galaxy scales and the phenomenology of dark energy.
Relativistic Kinetic Theory: An Introduction
Sarbach, Olivier
2013-01-01
We present a brief introduction to the relativistic kinetic theory of gases with emphasis on the underlying geometric and Hamiltonian structure of the theory. Our formalism starts with a discussion on the tangent bundle of a Lorentzian manifold of arbitrary dimension. Next, we introduce the Poincare one-form on this bundle, from which the symplectic form and a volume form are constructed. Then, we define an appropriate Hamiltonian on the bundle which, together with the symplectic form yields the Liouville vector field. The corresponding flow, when projected onto the base manifold, generates geodesic motion. Whenever the flow is restricted to energy surfaces corresponding to a negative value of the Hamiltonian, its projection describes a family of future-directed timelike geodesics. A collisionless gas is described by a distribution function on such an energy surface, satisfying the Liouville equation. Fibre integrals of the distribution function determine the particle current density and the stress-energy ten...
Extended Theories of Gravitation
Fatibene, Lorenzo
2016-01-01
In this paper we shall review the equivalence between Palatini$-f(\\mathcal R)$ theories and Brans- Dicke (BD) theories at the level of action principles. We shall define the Helmholtz Lagrangian associated to Palatini$-f(\\mathcal R)$ theory and we will define some transformations which will be useful to recover Einstein frame and Brans-Dicke frame. We shall see an explicit example of matter field and we will discuss how the conformal factor affects the physical quantities.
Magnetism and rotation in relativistic field theory
Mameda, Kazuya; Yamamoto, Arata
2016-09-01
We investigate the analogy between magnetism and rotation in relativistic theory. In nonrelativistic theory, the exact correspondence between magnetism and rotation is established in the presence of an external trapping potential. Based on this, we analyze relativistic rotation under external trapping potentials. A Landau-like quantization is obtained by considering an energy-dependent potential.
Thermodynamics of relativistic quantum fields: extracting energy from gravitational waves
Bruschi, David Edward
2016-01-01
We investigate the quantum thermodynamical properties of localised relativistic quantum fields that can be used as quantum thermal machines. We study the efficiency and power of energy transfer between the classical degrees of freedom, such as the energy input due to motion or to an impinging gravitational wave, and the excitations of the confined quantum field. We find that the efficiency of energy transfer depends dramatically on the input initial state of the system. Furthermore, we investigate the ability to extract the energy and to store it in a battery. This process is inefficient in optical cavities but is significantly enhanced when employing trapped Bose Einstein Condensates. Finally, we apply our techniques to a setup where an impinging gravitational wave excites the phononic modes of a Bose Einstein Condensate. We find that, in this case, the amount of energy transfer to the phonons increases with time and quickly approaches unity. These results suggest that, in the future, it might be possible to...
Holographic Aspects of a Relativistic Nonconformal Theory
Chanyong Park
2013-01-01
Full Text Available We study a general D-dimensional Schwarzschild-type black brane solution of the Einstein-dilaton theory and derive, by using the holographic renormalization, its thermodynamics consistent with the geometric results. Using the membrane paradigm, we calculate the several hydrodynamic transport coefficients and compare them with the results obtained by the Kubo formula, which shows the self-consistency of the gauge/gravity duality in the relativistic nonconformal theory. In order to understand more about the relativistic non-conformal theory, we further investigate the binding energy, drag force, and holographic entanglement entropy of the relativistic non-conformal theory.
On the usefulness of relativistic space-times for the description of the Earth's gravitational field
Soffel, Michael; Frutos, Francisco
2016-12-01
The usefulness of relativistic space-times for the description of the Earth's gravitational field is investigated. A variety of exact vacuum solutions of Einstein's field equations (Schwarzschild, Erez and Rosen, Gutsunayev and Manko, Hernández-Pastora and Martín, Kerr, Quevedo, and Mashhoon) are investigated in that respect. It is argued that because of their multipole structure and influences from external bodies, all these exact solutions are not really useful for the central problem. Then, approximate space-times resulting from an MPM or post-Newtonian approximation are considered. Only in the DSX formalism that is of the first post-Newtonian order, all aspects of the problem can be tackled: a relativistic description (a) of the Earth's gravity field in a well-defined geocentric reference system (GCRS), (b) of the motion of solar system bodies in a barycentric reference system (BCRS), and (c) of inertial and tidal terms in the geocentric metric describing the external gravitational field. A relativistic SLR theory is also discussed with respect to our central problem. Orders of magnitude of many effects related to the Earth's gravitational field and SLR are given. It is argued that a formalism with accuracies better than of the first post-Newtonian order is not yet available.
Exploring gravitational theories beyond Horndeski
Gleyzes, Jérôme; Langlois, David; Piazza, Federico; Vernizzi, Filippo
2015-02-01
We have recently proposed a new class of gravitational scalar-tensor theories free from Ostrogradski instabilities, in ref. [1]. As they generalize Horndeski theories, or "generalized" galileons, we call them G3. These theories possess a simple formulation when the time hypersurfaces are chosen to coincide with the uniform scalar field hypersurfaces. We confirm that they contain only three propagating degrees of freedom by presenting the details of the Hamiltonian formulation. We examine the coupling between these theories and matter. Moreover, we investigate how they transform under a disformal redefinition of the metric. Remarkably, these theories are preserved by disformal transformations that depend on the scalar field gradient, which also allow to map subfamilies of G3 into Horndeski theories.
Gravitational Waves Astronomy: a cornerstone for gravitational theories
Corda, Christian
2010-01-01
Realizing a gravitational wave (GW) astronomy in next years is a great challenge for the scientific community. By giving a significant amount of new information, GWs will be a cornerstone for a better understanding of gravitational physics. In this paper we re-discuss that the GW astronomy will permit to solve a captivating issue of gravitation. In fact, it will be the definitive test for Einstein's general relativity (GR), or, alternatively, a strong endorsement for extended theories of gravity (ETG).
Relativistic bound state approach to fundamental forces including gravitation
Morsch H.P.
2012-06-01
Full Text Available To describe the structure of particle bound states of nature, a relativistic bound state formalism is presented, which requires a Lagrangian including scalar coupling of two boson fields. The underlying mechanisms are quite complex and require an interplay of overlapping boson fields and fermion-antifermion production. This gives rise to two potentials, a boson-exchange potential and one identified with the long sought confinement potential in hadrons. With minimal requirements, two elementary massless fermions (quantons - with and without charge - and one gauge boson, hadrons and leptons but also atoms and gravitational systems are described by bound states with electric and magnetic coupling between the charges and spins of quantons. No need is found for colour, Higgs-coupling and supersymmetry.
The theory of space, time and gravitation
Fock, V
2015-01-01
The Theory of Space, Time, and Gravitation, 2nd Revised Edition focuses on Relativity Theory and Einstein's Theory of Gravitation and correction of the misinterpretation of the Einsteinian Gravitation Theory. The book first offers information on the theory of relativity and the theory of relativity in tensor form. Discussions focus on comparison of distances and lengths in moving reference frames; comparison of time differences in moving reference frames; position of a body in space at a given instant in a fixed reference frame; and proof of the linearity of the transformation linking two iner
Non-relativistic twistor theory and Newton--Cartan geometry
Dunajski, Maciej
2015-01-01
We develop a non-relativistic twistor theory, in which Newton--Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle ${\\mathcal O}\\oplus{\\mathcal O}(2)$. We show that the Newton--Cartan space-times are unstable under the general Kodaira deformation of the twistor complex structure. The Newton--Cartan connections can nevertheless be reconstructed from Merkulov's generalisation of the Kodaira map augmented by a choice of a holomorphic line bundle over the twistor space trivial on twistor lines. The Coriolis force may be incorporated by holomorphic vector bundles, which in general are non--trivial on twistor lines. The resulting geometries agree with non--relativistic limits of anti-self-dual gravitational instantons.
Brane in the Relativistic Theory of Gravitation
Naboulsi, R
2003-01-01
It was proven that Logunov RTG predicts a cyclic Universe with no singularities. It is shown in this paper that an additional exotic density term will not affect this important characteristic of the Universe evolution. We assume that this later varies with time according to the law m^2 propto frac{dot{R}^2}{R}. The graviton mass and the density term are of order of Hubble's constant. The classical Einstein's cosmological parameter is excluded to converse the logical structure of the RTG. The age of the Universe and the deceleration parameter agree with recent observational data from BOOMERANG, MAXIMA and COBE.
The Foundations of Einstein's Theory of Gravitation
Freundlich, Erwin; Brose, Translated by Henry L.; Einstein, Preface by Albert; Turner, Introduction by H. H.
2011-06-01
Introduction; 1. The special theory of relativity as a stepping-stone to the general theory of relativity; 2. Two fundamental postulates in the mathematical formulation of physical laws; 3. Concerning the fulfilment of the two postulates; 4. The difficulties in the principles of classical mechanics; 5. Einstein's theory of gravitation; 6. The verification of the new theory by actual experience; Appendix; Index.
Vanishing Vierbein in Gauge Theories of Gravitation
Jadczyk, A
1999-01-01
We discuss the problem of a degenerate vierbein in the framework of gauge theories of gravitation (thus including torsion). We discuss two examples: Hanson-Regge gravitational instanton and Einstein-Rose bridge.We argue that a region of space-time with vanishing vierbein but smooth principal connection can be, in principle, detected by scattering experiments.
Gravitational Waves from Perturbed Black Holes and Relativistic Stars
Rezzolla, Luciano
2003-01-01
These lectures aim at providing an introduction to the properties of gravitational waves and in particular to those gravitational waves that are expected as a consequence of perturbations of black holes and neutron stars. Imprinted in the gravitational radiation emitted by these objects is, in fact, a wealth of physical information. In the case of black holes, a detailed knowledge of the gravitational radiation emitted as a response to perturbations will reveal us important details about thei...
Vacaru, Olivia [National College of Iasi (Romania); Vacaru, Sergiu I. [Quantum Gravity Research, Topanga, CA (United States); University ' ' Al.I. Cuza' ' Iasi, Project IDEI, Iasi (Romania); Werner-Heisenberg-Institute, Max-Planck-Institute for Physics, Munich (Germany); Leibniz University of Hannover, Institute for Theoretical Physics (Germany); Ruchin, Vyacheslav
2017-03-15
Using double 2 + 2 and 3 + 1 nonholonomic fibrations on Lorentz manifolds, we extend the concept of W-entropy for gravitational fields in general relativity (GR). Such F- and W-functionals were introduced in the Ricci flow theory of three dimensional (3-d) Riemannian metrics by Perelman (the entropy formula for the Ricci flow and its geometric applications. arXiv:math.DG/0211159). Non-relativistic 3-d Ricci flows are characterized by associated statistical thermodynamical values determined by W-entropy. Generalizations for geometric flows of 4-d pseudo-Riemannian metrics are considered for models with local thermodynamical equilibrium and separation of dissipative and non-dissipative processes in relativistic hydrodynamics. The approach is elaborated in the framework of classical field theories (relativistic continuum and hydrodynamic models) without an underlying kinetic description, which will be elaborated in other work. The 3 + 1 splitting allows us to provide a general relativistic definition of gravitational entropy in the Lyapunov-Perelman sense. It increases monotonically as structure forms in the Universe. We can formulate a thermodynamic description of exact solutions in GR depending, in general, on all spacetime coordinates. A corresponding 2 + 2 splitting with nonholonomic deformation of linear connection and frame structures is necessary for generating in very general form various classes of exact solutions of the Einstein and general relativistic geometric flow equations. Finally, we speculate on physical macrostates and microstate interpretations of the W-entropy in GR, geometric flow theories and possible connections to string theory (a second unsolved problem also contained in Perelman's work) in Polyakov's approach. (orig.)
Neronov, A
2015-01-01
We show that observation of the time-dependent effect of microlensing of relativistically broadened emission lines (such as e.g. the Fe Kalpha line in X-rays) in strongly lensed quasars could provide data on celestial mechanics of circular orbits in the direct vicinity of the horizon of supermassive black holes. This information can be extracted from the observation of evolution of red / blue edge of the magnified line just before and just after the period of crossing of the innermost stable circular orbit by the microlensing caustic. The functional form of this evolution is insensitive to numerous astrophysical parameters of the accreting black hole and of the microlensing caustics network system (as opposed to the evolution the full line spectrum). Measurement of the temporal evolution of the red / blue edge could provide a precision measurement of the radial dependence of the gravitational redshift and of velocity of the circular orbits, down to the innermost stable circular orbit. These measurements could...
A Structurally Relativistic Quantum Theory. Part 1: Foundations
Grgin, Emile
2012-01-01
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A new number system with the properties needed to support an inherently relativistic quantum theory is brought to light and investigated to a point sufficient for applications.
Relativistic-microwave theory of ball lightning
Wu, H.-C.
2016-06-01
Ball lightning, a fireball sometimes observed during lightnings, has remained unexplained. Here we present a comprehensive theory for the phenomenon: At the tip of a lightning stroke reaching the ground, a relativistic electron bunch can be produced, which in turn excites intense microwave radiation. The latter ionizes the local air and the radiation pressure evacuates the resulting plasma, forming a spherical plasma bubble that stably traps the radiation. This mechanism is verified by particle simulations. The many known properties of ball lightning, such as the occurrence site, relation to the lightning channels, appearance in aircraft, its shape, size, sound, spark, spectrum, motion, as well as the resulting injuries and damages, are also explained. Our theory suggests that ball lighting can be created in the laboratory or triggered during thunderstorms. Our results should be useful for lightning protection and aviation safety, as well as stimulate research interest in the relativistic regime of microwave physics.
Relativistic Rotation: A Comparison of Theories
Klauber, R D
2006-01-01
Alternative theories of relativistic rotation considered viable as of 2004 are compared in the light of experiments reported in 2005. En route, the contentious issue of simultaneity choice in rotation is resolved by showing that only one simultaneity choice, the one possessing continuous time, gives rise, via the general relativistic equation of motion, to the correct Newtonian limit Coriolis acceleration. In addition, the widely dispersed argument purporting to justify an absolute Lorentz contraction in rotation is analyzed and found lacking for more than one reason. It is argued that only via experiment can we know whether such absolute contraction exists in rotation or not. The Coriolis/simultaneity correlation, and the results of the 2005 experiments, support the Selleri theory as being closest to the truth, though it is incomplete in a more general applicability sense, because it does not provide a global metric. Two alternatives, a modified Klauber approach and a Selleri-Klauber hybrid, are presented wh...
Relativistic-microwave theory of ball lightning.
Wu, H-C
2016-06-22
Ball lightning, a fireball sometimes observed during lightnings, has remained unexplained. Here we present a comprehensive theory for the phenomenon: At the tip of a lightning stroke reaching the ground, a relativistic electron bunch can be produced, which in turn excites intense microwave radiation. The latter ionizes the local air and the radiation pressure evacuates the resulting plasma, forming a spherical plasma bubble that stably traps the radiation. This mechanism is verified by particle simulations. The many known properties of ball lightning, such as the occurrence site, relation to the lightning channels, appearance in aircraft, its shape, size, sound, spark, spectrum, motion, as well as the resulting injuries and damages, are also explained. Our theory suggests that ball lighting can be created in the laboratory or triggered during thunderstorms. Our results should be useful for lightning protection and aviation safety, as well as stimulate research interest in the relativistic regime of microwave physics.
Non-relativistic Quantum Mechanics versus Quantum Field Theories
Pineda, Antonio
2007-01-01
We briefly review the derivation of a non-relativistic quantum mechanics description of a weakly bound non-relativistic system from the underlying quantum field theory. We highlight the main techniques used.
Classical Gravitational Interactions and Gravitational Lorentz Force
无
2005-01-01
In quantum gauge theory of gravity, the gravitational field is represented by gravitational gauge field.The field strength of gravitational gauge field has both gravitoelectric component and gravitomagnetic component. In classical level, gauge theory of gravity gives classical Newtonian gravitational interactions in a relativistic form. Besides,it gives gravitational Lorentz force, which is the gravitational force on a moving object in gravitomagnetic field The direction of gravitational Lorentz force is not the same as that of classical gravitational Newtonian force. Effects of gravitational Lorentz force should be detectable, and these effects can be used to discriminate gravitomagnetic field from ordinary electromagnetic magnetic field.
A Uniﬁed Theory of Interaction: Gravitation and Electrodynamics
Wagener P.
2008-10-01
Full Text Available A theory is proposed from which the basic equations of gravitation and electromagnetism are derived from a single Lagrangian. The total energy of an atom can be expressed in a power series of the fine structure constant, $alpha$. Specific selections of these terms yield the relativistic correction to the Bohr values of the hydrogen spectrum and the Sommerfeld-Dirac equation for the fine structure spectrum of the hydrogen atom. Expressions for the classical electron radius and some of the Large Number Coincidences are derived. A Lorentz-type force equation is derived for both gravitation and electrodynamics. Electron spin is shown to be an effect of fourth order in $alpha$.
Introduction to the relativistic string theory
Barbashov, B M
1990-01-01
This book presents a systematic and detailed account of the classical and quantum theory of the relativistic string and some of its modifications. Main attention is paid to the first-quantized string theory with possible applications to the string models of hadrons as well as to the superstring approach to unifications of all the fundamental interactions in the elementary particle physics and to the "cosmic" strings. Some new aspects are provided such as the consideration of the string in an external electromagnetic field and in the space-time of constant curvature (the de Sitter universe), th
Planar Gravitational Corrections For Supersymmetric Gauge Theories
Dijkgraaf, R; Ooguri, H; Vafa, C; Zanon, D
2004-01-01
In this paper we discuss the contribution of planar diagrams to gravitational F-terms for N=1 supersymmetric gauge theories admitting a large N description. We show how the planar diagrams lead to a universal contribution at the extremum of the glueball superpotential, leaving only the genus one contributions, as was previously conjectured. We also discuss the physical meaning of gravitational F-terms.
GRAVITATIONAL LENSES AND UNCONVENTIONAL GRAVITY THEORIES
BEKENSTEIN, JD; SANDERS, RH
1994-01-01
We study gravitational lensing by clusters of galaxies in the context of the generic class of unconventional gravity theories which describe gravity in terms of a metric and one or more scalar fields (called here scalar-tensor theories). We conclude that, if the scalar fields have positive energy, t
GRAVITATIONAL LENSES AND UNCONVENTIONAL GRAVITY THEORIES
BEKENSTEIN, JD; SANDERS, RH
1994-01-01
We study gravitational lensing by clusters of galaxies in the context of the generic class of unconventional gravity theories which describe gravity in terms of a metric and one or more scalar fields (called here scalar-tensor theories). We conclude that, if the scalar fields have positive energy,
Approximation methods in gravitational-radiation theory
Will, C. M.
1986-02-01
The observation of gravitational-radiation damping in the binary pulsar PSR 1913+16 and the ongoing experimental search for gravitational waves of extraterrestrial origin have made the theory of gravitational radiation an active branch of classical general relativity. In calculations of gravitational radiation, approximation methods play a crucial role. The author summarizes recent developments in two areas in which approximations are important: (1) the quadrupole approximation, which determines the energy flux and the radiation reaction forces in weak-field, slow-motion, source-within-the-near-zone systems such as the binary pulsar; and (2) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes.
Theory of symmetry for a rotational relativistic Birkhoff system
罗绍凯; 陈向炜; 郭永新
2002-01-01
The theory of symmetry for a rotational relativistic Birkhoff system is studied. In terms of the invariance of therotational relativistic Pfaff-Birkhoff-D'Alembert principle under infinitesimal transformations, the Noether symmetriesand conserved quantities of a rotational relativistic Birkhoff system are given. In terms of the invariance of rotationalrelativistic Birkhoff equations under infinitesimal transformations, the Lie symmetries and conserved quantities of therotational relativistic Birkhoff system are given.
Radiation from relativistic particles in nongeodesic motion in a strong gravitational field
Aliev, A.N. (AN Gruzinskoj SSR, Abastumani. Abastumanskaya Astrofizicheskaya Observatoriya); Galtsov, D.V. (Moskovskij Gosudarstvennyj Univ. (USSR). Kafedra Teoreticheskoj Fiziki)
1981-10-01
The scalar and electromagnetic radiation emitted by relativistic particles moving along the stable nongeodesic trajectories in the Kerr gravitational field are described. Two particular models of the nongeodesic motion are developed involving a slightly charged rotating black hole and a rotating black hole immersed in an external magnetic field.
Moratto, Valdemar; Kremer, Gilberto M.
2015-05-01
In this work we study an r -species mixture of gases within the relativistic kinetic theory point of view. We use the relativistic covariant Boltzmann equation and incorporate the Schwarzschild metric. The method of solution of the Boltzmann equation is a combination of the Chapman-Enskog and Grad representations. The thermodynamic four-fluxes are expressed as functions of the thermodynamic forces so the generalized expressions for the Navier-Stokes, Fick, and Fourier laws are obtained. The constitutive equations for the diffusion and heat four-fluxes of the mixture are functions of thermal and diffusion generalized forces which depend on the acceleration and the gravitational potential gradient. While this dependence is of relativistic nature for the thermal force, this is not the case for the diffusion forces. We show also that the matrix of diffusion coefficients is symmetric, implying that the thermal-diffusion equals the diffusion-thermal effect, proving the Onsager reciprocity relations. The entropy four-flow of the mixture is also expressed in terms of the thermal and diffusion generalized forces, so its dependence on the acceleration and gravitational potential gradient is also determined.
Wiesendanger, C
2011-01-01
Viewing gravitational energy-momentum $p_G^\\mu$ as equal by observation, but different in essence from inertial energy-momentum $p_I^\\mu$ naturally leads to the gauge theory of volume-preserving diffeormorphisms of an inner Minkowski space ${\\bf M}^{\\sl 4}$. To extract its physical content the full gauge group is reduced to its Poincar\\'e subgroup. The respective Poincar\\'e gauge fields, field strengths and Poincar\\'e-covariant field equations are obtained and point-particle source currents are derived. The resulting set of non-linear field equations coupled to point matter is solved in first order resulting in Lienard-Wiechert-like potentials for the Poincar\\'e fields. After numerical identification of gravitational and inertial energy-momentum Newton's inverse square law for gravity in the static non-relativistic limit is recovered. The Weak Equivalence Principle in this approximation is proven to be valid and spacetime geometry in the presence of Poincar\\'e fields is shown to be curved. Finally, the gravit...
Electromagnetism in a nonsymmetric theory of gravitation
Ragusa, S.; Bosquetti, D. [Sao Paulo Univ., Sao Carlos, SP (Brazil). Inst. de Fisica. Dept. de Fisica e Informatica]. E-mail: ragusa@if.sc.usp.br
2000-09-01
The field equations of a proposed nonsymmetric theory of gravitation are derived when electromagnetic fields are present, by adopting a nonminimal coupling which ensures the validity of the equivalence principle. The static and spherically symmetric solution of the field of a charged point particle is obtained. (author)
Isotropic Forms of Dynamics in the Relativistic Direct Interaction Theory
Duviryak, A A; Tretyak, V I
1998-01-01
The Lagrangian relativistic direct interaction theory in the various forms of dynamics is formulated and its connections with the Fokker-type action theory and with the constrained Hamiltonian mechanics are established. The motion of classical two-particle system with relativistic direct interaction is analysed within the framework of isotropic forms of dynamics in the two- and four-dimensional space-time. Some relativistic exactly solvable quantum-mechanical models are also discussed.
Gravitation Field Dynamics in Jeans Theory
A. A. Stupka
2008-09-01
Closed system of time equations for nonrelativistic gravitation field and hydrodynamic medium was obtained by taking into account binary correlations of the field, which is the generalization of Jeans theory. Distribution function of the systemwas built on the basis of the Bogolyubov reduced description method. Calculations were carried out up to the first order of a perturbation theory in interaction. Adiabatic and enthropic types of perturbations were corrected and two new types of perturbations were found.
Gravitation Field Dynamics in Jeans Theory
Stupka, A A
2016-01-01
Closed system of time equations for nonrelativistic gravitation field and hydrodynamic medium was obtained by taking into account binary correlations of the field, which is the generalization of Jeans theory. Distribution function of the systemwas built on the basis of the Bogolyubov reduced description method. Calculations were carried out up to the first order of a perturbation theory in interaction. Adiabatic and enthropic types of perturbations were corrected and two new types of perturbations were found.
Theory of gravitation in flat space with no infinities
Khan, I
2002-01-01
A theory of gravitation is presented. This theory does not relate gravitation to curvature of space-time. It explains the three standard results of general relativity in agreement with observations and suggests new experiments.
Compact objects in relativistic theories of gravity
Okada da Silva, Hector
2017-05-01
In this dissertation we discuss several aspects of compact objects, i.e. neutron stars and black holes, in relativistic theories of gravity. We start by studying the role of nuclear physics (encoded in the so-called equation of state) in determining the properties of neutron stars in general relativity. We show that low-mass neutron stars are potentially useful astrophysical laboratories that can be used to constrain the properties of the equation of state. More specifically, we show that various bulk properties of these objects, such as their quadrupole moment and tidal deformability, are tightly correlated. Next, we develop a formalism that aims to capture how generic modifications from general relativity affect the structure of neutron stars, as predicted by a broad class of gravity theories, in the spirit of the parametrized post-Newtonian formalism (PPN). Our "post-Tolman-Oppenheimer-Volkoff" formalism provides a toolbox to study both stellar structure and the interior/exterior geometries of static, spherically symmetric relativistic stars. We also apply the formalism to parametrize deviations from general relativity in various astrophysical observables related with neutron stars, including surface redshift, apparent radius, Eddington luminosity. We then turn our attention to what is arguably the most well-motivated and well-investigated generalization of general relativity: scalar-tensor theory. We start by considering theories where gravity is mediated by a single extra scalar degree of freedom (in addition to the metric tensor). An interesting class of scalar-tensor theories passes all experimental tests in the weak-field regime of gravity, yet considerably deviates from general relativity in the strong-field regime in the presence of matter. A common assumption in modeling neutron stars is that the pressure within these object is spatially isotropic. We relax this assumption and examine how pressure anisotropy affects the mass, radius and moment of inertia
String theory and relativistic heavy ion collisions
Friess, Joshua J.
It has long been known that string theory describes not only quantum gravity, but also gauge theories with a high degree of supersymmetry. Said gauge theories also have a large number of colors in a regime with a large effective coupling constant that does not depend on energy scale. Supersymmetry is broken in nature, if it is present at all, however the gauge theory described by string theory shares many common features with QCD at temperatures above the quark deconfinement transition. It is generally though not entirely accepted that collisions of gold nuclei at the Relativistic Heavy Ion Collider (RHIC) produce a thermalized Quark-Gluon Plasma (QGP) at temperatures distinctly above the transition temperature as determined from lattice simulations. Hence, we might hope that a string theoretic description of gauge dynamics can elucidate some otherwise intractable physics of the strongly coupled plasma. Here we use string theory to calculate the outgoing energy flux from a RHIC process called "jet quenching", in which a high-momentum quark or gluon traverses a large distance in the QGP. Our setup is in the context of the highly supersymmetric string dual gauge theory, but we nevertheless find that the gross features of the resulting stress-energy tensor match reasonably well with experimental data. We will furthermore discuss the technology behind computations of the leading-order corrections to gauge theory observables that are uniquely string-induced, and we will describe a potential solution to string theory that could resolve a number of discrepancies between the traditional highly supersymmetric setup and QCD---in particular, a significant reduction in the amount of supersymmetry, and a finite effective coupling that is still greater than unity but does depend on energy scale.
Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
Geracie, Michael, E-mail: mgeracie@uchicago.edu; Prabhu, Kartik, E-mail: kartikp@uchicago.edu; Roberts, Matthew M., E-mail: matthewroberts@uchicago.edu [Kadanoff Center for Theoretical Physics, Enrico Fermi Institute and Department of Physics, The University of Chicago, Chicago, Illinois 60637 (United States)
2015-10-15
There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local non-relativistic symmetries which supports massive matter fields. In particular, one cannot impose a priori restrictions on the geometric data if one wants to analyze matter response to a perturbed geometry. In this paper, we construct such a Bargmann spacetime in complete generality without any prior restrictions on the fields specifying the geometry. The resulting spacetime structure includes the familiar Newton-Cartan structure with an additional gauge field which couples to mass. We illustrate the matter coupling with a few examples. The general spacetime we construct also includes as a special case the covariant description of Newtonian gravity, which has been thoroughly investigated in previous works. We also show how our Bargmann spacetimes arise from a suitable non-relativistic limit of Lorentzian spacetimes. In a companion paper [M. Geracie et al., e-print http://arxiv.org/abs/1503.02680 ], we use this Bargmann spacetime structure to investigate the details of matter couplings, including the Noether-Ward identities, and transport phenomena and thermodynamics of non-relativistic fluids.
Relativistic Stars in Beyond Horndeski Theories
Babichev, Eugeny; Langlois, David; Saito, Ryo; Sakstein, Jeremy
2016-01-01
This work studies relativistic stars in beyond Horndeski scalar-tensor theories that exhibit a breaking of the Vainshtein mechanism inside matter, focusing on a model based on the quartic beyond Horndeski Lagrangian. We self-consistently derive the scalar field profile for static spherically symmetric objects in asymptotically de Sitter space-time and show that the Vainshtein breaking branch of the solutions is the physical branch thereby resolving several ambiguities with non-relativistic frameworks. The geometry outside the star is shown to be exactly Schwarzschild-de Sitter and therefore the PPN parameter $\\beta_{\\rm PPN}=1$, confirming that the external screening works at the post-Newtonian level. The Tolman-Oppenheimer-Volkoff (TOV) equations are derived and a new lower bound on the Vainshtein breaking parameter $\\Upsilon_1>-4/9$ is found by requiring the existence of static spherically symmetric stars. Focusing on the unconstrained case where $\\Upsilon_1<0$, we numerically solve the TOV equations for...
Improving LLR Tests of Gravitational Theory
Williams, J G; Williams, James G.; Turyshev, Slava G.; Jr, Thomas W. Murphy
2003-01-01
Accurate analysis of precision ranges to the Moon has provided several tests of gravitational theory including the Equivalence Principle, geodetic precession, parameterized post-Newtonian (PPN) parameters $\\gamma$ and $\\beta$, and the constancy of the gravitational constant {\\it G}. Since the beginning of the experiment in 1969, the uncertainties of these tests have decreased considerably as data accuracies have improved and data time span has lengthened. We are exploring the modeling improvements necessary to proceed from cm to mm range accuracies enabled by the new Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) currently under development in New Mexico. This facility will be able to make a significant contribution to the solar system tests of fundamental and gravitational physics. In particular, the Weak and Strong Equivalence Principle tests would have a sensitivity approaching 10$^{-14}$, yielding sensitivity for the SEP violation parameter $\\eta$ of $\\sim 3\\times 10^{-5}$, $v^2/c^2$ gene...
Time Delay in Gravitational Lensing by a Charged Black Hole of String Theory
Rubio, E A L
2003-01-01
We calculate the time delay between different relativistic images formed by the gravitational lensing produced by the Gibbons-Maeda-Garfinkle-Horowitz-Stromiger (GMGHS) charged black hole of heterotic string theory. Modeling the supermassive central objects of some galaxies as GMGHS black holes, numerical values of the time delays are estimated and compared with the correspondient Reissner-Nordstrom black holes . The time difference amounts to hours, thus being measurable and permiting to distinguish between General Relativity and String Theory charged black holes.
Gallo, Emanuel
2016-01-01
We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. By construction, the model incorporates the back reaction due to gravitational radiation generated by the motion of the particle. Our approach differs from other constructions tackling the same kind of problem.
Universally finite gravitational and gauge theories
Leonardo Modesto
2015-11-01
Full Text Available It is well known that standard gauge theories are renormalizable in D=4 while Einstein gravity is renormalizable in D=2. This is where the research in the field of two derivatives theories is currently standing. We hereby present a class of weakly non-local higher derivative gravitational and gauge theories universally consistent at quantum level in any spacetime dimension. These theories are unitary (ghost-free and perturbatively renormalizable. Moreover, we can always find a simple extension of these theories that is super-renormalizable or finite at quantum level in even and odd spacetime dimensions. Finally, we propose a super-renormalizable or finite theory for gravity coupled to matter laying the groundwork for a “finite standard model of particle physics” and/or a grand unified theory of all fundamental interactions.
Quasiparticle excitations in relativistic quantum field theory
Arteaga, Daniel
2008-01-01
We analyze the particle-like excitations arising in relativistic field theories in states different than the vacuum. The basic properties characterizing the quasiparticle propagation are studied using two different complementary methods. First we introduce a frequency-based approach, wherein the quasiparticle properties are deduced from the spectral analysis of the two-point propagators. Second, we put forward a real-time approach, wherein the quantum state corresponding to the quasiparticle excitation is explicitly constructed, and the time-evolution is followed. Both methods lead to the same result: the energy and decay rate of the quasiparticles are determined by the real and imaginary parts of the retarded self-energy respectively. Both approaches are compared, on the one hand, with the standard field-theoretic analysis of particles in the vacuum and, on the other hand, with the mean-field-based techniques in general backgrounds.
QIAN Shang-Wu
2005-01-01
Based on the new metric theory of gravitation suggested by the author of this article, it gives a possible theoretical interpretation on the famous experiment done by D.R. Long in 1976, i.e. the distance-dependent effect of the gravitational constant in Newton's theory of gravitation.
Relativistic field theories have no `sign problem' with DMRG
Weir, David J
2010-01-01
The density matrix renormalization group (DMRG) is applied to a relativistic complex scalar field at finite chemical potential. The two-point function and various bulk quantities are studied. It is seen that bulk quantities do not change with the chemical potential until it is larger than the minimum excitation energy. The technical limitations of DMRG for treating bosons in relativistic field theories are discussed. Applications to other relativistic models and to non-topological solitons are also suggested.
Relativistic quantum mechanics and introduction to field theory
Yndurain, F.J. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica
1996-12-01
The following topics were dealt with: relativistic transformations, the Lorentz group, Klein-Gordon equation, spinless particles, spin 1/2 particles, Dirac particle in a potential, massive spin 1 particles, massless spin 1 particles, relativistic collisions, S matrix, cross sections, decay rates, partial wave analysis, electromagnetic field quantization, interaction of radiation with matter, interactions in quantum field theory and relativistic interactions with classical sources.
Implications of Cosmic Repulsion for Gravitational Theory
Mannheim, P D
1998-01-01
In this paper we present a general, model independent analysis of a recently detected apparent cosmic repulsion, and discuss its potential implications for gravitational theory. In particular, we show that a negatively spatially curved universe acts like a diverging refractive medium, to thus naturally cause galaxies to accelerate away from each other. Additionally, we show that it is possible for a cosmic acceleration to only be temporary, with some accelerating universes actually being able to subsequently recontract.
BOOK REVIEW: Gravitational Waves, Volume 1: Theory and Experiments
Poisson, Eric
2008-10-01
discussion is helpful, as it clarifies some of the puzzling aspects of general covariance. Next the treatment becomes more sophisticated: the waves are allowed to propagate in an arbitrary background spacetime, and the energy momentum carried by the wave is identified by the second-order perturbation of the Einstein tensor. In chapter 2 the waves are given a field-theoretic foundation that is less familiar (but refreshing) to a relativist, but would appeal to a practitioner of effective field theories. In an interesting section of chapter 2, the author gives a mass to the (classical) graviton and explores the physical consequences of this proposal. In chapter 3 the author returns to the standard linearized theory and develops the multipolar expansion of the gravitational-wave field in the context of slowly-moving sources; at leading order he obtains the famous quadrupole formula. His treatment is very detailed, and it includes a complete account of symmetric-tracefree tensors and tensorial spherical harmonics. It is, however, necessarily limited to sources with negligible internal gravity. Unfortunately (and this is a familiar complaint of relativists) the author omits to warn the reader of this important limitation. In fact, the chapter opens with a statement of the virial theorem of Newtonian gravity, which may well mislead the reader to believe that the linearized theory can be applied to a system bound by gravitational forces. This misconception is confirmed when, in chapter 4, the author applies the quadrupole formula to gravitationally-bound systems such as an inspiraling compact binary, a rigidly rotating body, and a mass falling toward a black hole. This said, the presentation of these main sources of gravitational waves is otherwise irreproachable, and a wealth of useful information is presented in a clear and lucid manner. For example, the discussion of inspiraling compact binaries includes a derivation of the orbital evolution of circular and eccentric orbits
Arun, K G
2013-01-01
Gravitational Wave (GW) observations of coalescing compact binaries will be unique probes of strong-field, dynamical aspects of relativistic gravity. We present a short review of various schemes proposed in the literature to test General Relativity (GR) and alternative theories of gravity using inspiral waveforms. Broadly these schemes may be classified into two types: model dependent and model independent. In the model dependent category, GW observations are compared against a specific waveform model representative of a particular theory or a class of theories like Scalar-Tensor theories, Dynamical Chern-Simons theory and Massive graviton theories. Model independent tests are attempts to write down a parametrised gravitational waveform where the free parameters take different values for different theories and (at least some of) which can be constrained by GW observations. We revisit some of the proposed bounds in the case of downscaled LISA configuration (eLISA) and compare them with the original LISA config...
Continuum dynamics and the electromagnetic field in the scalar ether theory of gravitation
Arminjon Mayeul
2016-01-01
Full Text Available An alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes’ thrust. In it, the gravitational field affects the physical standards of space and time, but motion is governed by an extension of the relativistic form of Newton’s second law. This implies Einstein’s geodesic motion for free particles only in a constant gravitational field. In this work, equations governing the dynamics of a continuous medium subjected to gravitational and non-gravitational forces are derived. Then, the case where the non-gravitational force is the Lorentz force is investigated. The gravitational modification of Maxwell’s equations is obtained under the requirement that a charged continuous medium, subjected to the Lorentz force, obeys the equation derived for continuum dynamics under external forces. These Maxwell equations are shown to be consistent with the dynamics of a “free” photon, and thus with the geometrical optics of this theory. However, these equations do not imply local charge conservation, except for a constant gravitational field.
Continuum dynamics and the electromagnetic field in the scalar ether theory of gravitation
Arminjon, Mayeul
2016-01-01
An alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes' thrust. In it, the gravitational field affects the physical standards of space and time, but motion is governed by an extension of the relativistic form of Newton's second law. This implies Einstein's geodesic motion for free particles only in a constant gravitational field. In this work, equations governing the dynamics of a continuous medium subjected to gravitational and non-gravitational forces are derived. Then, the case where the non-gravitational force is the Lorentz force is investigated. The gravitational modification of Maxwell's equations is obtained under the requirement that a charged continuous medium, subjected to the Lorentz force, obeys the equation derived for continuum dynamics under external forces. These Maxwell equations are shown to be consistent with the dynamics of a "free" photon, and thus with the geometrical optics of this theory. However, these equations do not imply local charge conservation, except for a constant gravitational field.
Gravitational Quantum Foam and Supersymmetric Gauge Theories
Maeda, T; Noma, Y; Tamakoshi, T; Maeda, Takashi; Nakatsu, Toshio; Noma, Yui; Tamakoshi, Takeshi
2005-01-01
We study K\\"{a}hler gravity on local SU(N) geometry and describe precise correspondence with certain supersymmetric gauge theories and random plane partitions. The local geometry is discretized, via the geometric quantization, to a foam of an infinite number of gravitational quanta. We count these quanta in a relative manner by measuring a deviation of the local geometry from a singular Calabi-Yau threefold, that is a A_{N-1} singularity fibred over \\mathbb{P}^1. With such a regularization prescription, the number of the gravitational quanta becomes finite and turns to be the perturbative prepotential for five-dimensional \\mathcal{N}=1 supersymmetric SU(N) Yang-Mills. These quanta are labelled by lattice points in a certain convex polyhedron on \\mathbb{R}^3. The polyhedron becomes obtainable from a plane partition which is the ground state of a statistical model of random plane partition that describes the exact partition function for the gauge theory. Each gravitational quantum of the local geometry is shown...
Gravitational Goldstone fields from affine gauge theory
Tresguerres, R
2000-01-01
In order to facilitate the application of standard renormalization techniques, gravitation should be decribed, if possible, in pure connection formalism, as a Yang-Mills theory of a certain spacetime group, say the Poincare or the affine group. This embodies the translational as well as the linear connection. However, the coframe is not the standard Yang-Mills type gauge field of the translations, since it lacks the inhomogeneous gradient term in the gauge transformations. By explicitly restoring the "hidden" piece responsible for this behavior within the framework of nonlinear realizations, the usual geometrical interpretation of the dynamical theory becomes possible, and in addition one can avoid the metric or coframe degeneracy which would otherwise interfere with the integrations within the path integral. We claim that nonlinear realizations provide a general mathematical scheme clarifying the foundations of gauge theories of spacetime symmetries. When applied to construct the Yang-Mills theory of the aff...
Composite spinor bundles in gravitation theory
Sardanashvily, G
1995-01-01
In gravitation theory, the realistic fermion matter is described by spinor bundles associated with the cotangent bundle of a world manifold X. In this case, the Dirac operator can be introduced. There is the 1:1 correspondence between these spinor bundles and the tetrad gravitational fields represented by sections of the quotient \\Si of the linear frame bundle over X by the Lorentz group. The key point lies in the fact that different tetrad fields imply nonequivalent representations of cotangent vectors to X by the Dirac's matrices. It follows that a fermion field must be regarded only in a pair with a certain tetrad field. These pairs can be represented by sections of the composite spinor bundle S\\to\\Si\\to X where values of tetrad fields play the role of parameter coordinates, besides the familiar world coordinates.
Matters of time directionality in gravitation theory
Nickner, Christophe
2016-01-01
Several issues related to time directionality as they arise from a semi-classical perspective are discussed which are all directly or indirectly relevant to gravitation theory. Important clarifications are achieved regarding in particular the concept of negative energy and the associated notion of negative mass. Several difficulties traditionally associated with the possibility for matter to occupy negative energy states are discussed and solutions to the problems they represent are suggested. Generalized gravitational field equations which allow to fulfill the requirements set by the axioms derived from this analysis are provided. A revised formulation of the discrete symmetry operations based on the lessons learned while addressing the problem of negative energy is proposed which gives rise to an improved notion of time reversal. A symmetry operation which allows to provide the missing element needed to obtain a truly complete set of discrete symmetry operations is introduced which involves a reversal of th...
Bancelin, D; Thuillot, W
2016-01-01
The integration of the equations of motion in gravitational dynamical systems -- either in our Solar System or for extra-solar planetary system -- being non integrable in the global case, is usually performed by means of numerical integration. Among the different numerical techniques available for solving ordinary differential equations, the numerical integration using Lie series has shown some advantages. In its original form (Hanslmeier 1984), it was limited to the N-body problem where only gravitational interactions are taken into account. We present in this paper a generalisation of the method by deriving an expression of the Lie-terms when other major forces are considered. As a matter of fact, previous studies had been made but only for objects moving under gravitational attraction. If other perturbations are added, the Lie integrator has to be re-built. In the present work we consider two cases involving position and position-velocity dependent perturbations: relativistic acceleration in the framework ...
CFC+: Improved dynamics and gravitational waveforms from relativistic core collapse simulations
Cerdá-Durán, P; Dimmelmeier, H; Font, J A; Ibáñez, J M; Müller, E; Schäfer, G
2004-01-01
Core collapse supernovae are a promising source of detectable gravitational waves. Most of the existing (multidimensional) numerical simulations of core collapse in general relativity have been done using approximations of the Einstein field equations. As recently shown by Dimmelmeier et al (2002a,b), one of the most interesting such approximation is the so-called conformal flatness condition (CFC) of Isenberg, Wilson and Mathews. Building on this previous work we present here new results from numerical simulations of relativistic rotational core collapse in axisymmetry, aiming at improving the dynamics and the gravitational waveforms. The computer code used for these simulations evolves the coupled system of metric and fluid equations using the 3+1 formalism, specialized to a new framework for the gravitational field equations which we call CFC+. In this approach we add new degrees of freedom to the original CFC equations, which extend them by terms of second post-Newtonian order. The corrections for CFC+ ar...
Chifu E. N.
2009-07-01
Full Text Available General Relativistic metric tensors for gravitational fields exterior to homogeneous spherical mass distributions rotating with constant angular velocity about a fixed di- ameter are constructed. The coeffcients of affine connection for the gravitational field are used to derive equations of motion for test particles. The laws of conservation of energy and angular momentum are deduced using the generalized Lagrangian. The law of conservation of angular momentum is found to be equal to that in Schwarzschild’s gravitational field. The planetary equation of motion and the equation of motion for a photon in the vicinity of the rotating spherical mass distribution have rotational terms not found in Schwarzschild’s field.
Local Existence of Solutions of Self Gravitating Relativistic Perfect Fluids
Brauer, Uwe; Karp, Lavi
2014-01-01
This paper deals with the evolution of the Einstein gravitational fields which are coupled to a perfect fluid. We consider the Einstein-Euler system in asymptotically flat spacestimes and therefore use the condition that the energy density might vanish or tend to zero at infinity, and that the pressure is a fractional power of the energy density. In this setting we prove local in time existence, uniqueness and well-posedness of classical solutions. The zero order term of our system contains an expression which might not be a C ∞ function and therefore causes an additional technical difficulty. In order to achieve our goals we use a certain type of weighted Sobolev space of fractional order. In Brauer and Karp (J Diff Eqs 251:1428-1446, 2011) we constructed an initial data set for these of systems in the same type of weighted Sobolev spaces. We obtain the same lower bound for the regularity as Hughes et al. (Arch Ratl Mech Anal 63(3):273-294, 1977) got for the vacuum Einstein equations. However, due to the presence of an equation of state with fractional power, the regularity is bounded from above.
Local Existence of Solutions of Self Gravitating Relativistic Perfect Fluids
Brauer, Uwe
2011-01-01
This paper deals with the evolution of the Einstein gravitational fields which are coupled to a perfect fluid. We consider the Einstein--Euler system in asymptotically flat spacestimes and therefore use the condition that the energy density might vanish or tend to zero at infinity, and that the pressure is a fractional power of the energy density. In this setting we prove a local in time existence, uniqueness and well-posedness of classical solutions. The zero order term of our system contains an expression which might not be a $C^\\infty$ function and therefore causes an additional technical difficulty. In order to achieve our goals we use a certain type of weighted Sobolev space of fractional order. Previously the authors constructed an initial data set for these of systems in the same type of weighted Sobolev spaces. We obtain the same lower bound for the regularity as the one of the classical result of Hughes, Kato and Marsden for the vacuum Einstein equations. However, due to the presence of an equation o...
Theory and Applications of Non-Relativistic and Relativistic Turbulent Reconnection
Lazarian, A; Takamoto, M; Pino, E M de Gouveia Dal; Cho, J
2015-01-01
Realistic astrophysical environments are turbulent due to the extremely high Reynolds numbers. Therefore, the theories of reconnection intended for describing astrophysical reconnection should not ignore the effects of turbulence on magnetic reconnection. Turbulence is known to change the nature of many physical processes dramatically and in this review we claim that magnetic reconnection is not an exception. We stress that not only astrophysical turbulence is ubiquitous, but also magnetic reconnection itself induces turbulence. Thus turbulence must be accounted for in any realistic astrophysical reconnection setup. We argue that due to the similarities of MHD turbulence in relativistic and non-relativistic cases the theory of magnetic reconnection developed for the non-relativistic case can be extended to the relativistic case and we provide numerical simulations that support this conjecture. We also provide quantitative comparisons of the theoretical predictions and results of numerical experiments, includi...
Convexity and symmetrization in relativistic theories
Ruggeri, T.
1990-09-01
There is a strong motivation for the desire to have symmetric hyperbolic field equations in thermodynamics, because they guarantee well-posedness of Cauchy problems. A generic quasi-linear first order system of balance laws — in the non-relativistic case — can be shown to be symmetric hyperbolic, if the entropy density is concave with respect to the variables. In relativistic thermodynamics this is not so. This paper shows that there exists a scalar quantity in relativistic thermodynamics whose concavity guarantees a symmetric hyperbolic system. But that quantity — we call it —bar h — is not the entropy, although it is closely related to it. It is formed by contracting the entropy flux vector — ha with a privileged time-like congruencebar ξ _α . It is also shown that the convexity of h plus the requirement that all speeds be smaller than the speed of light c provide symmetric hyperbolic field equations for all choices of the direction of time. At this level of generality the physical meaning of —h is unknown. However, in many circumstances it is equal to the entropy. This is so, of course, in the non-relativistic limit but also in the non-dissipative relativistic fluid and even in relativistic extended thermodynamics for a non-degenerate gas.
Solar-System Tests of Gravitational Theories
Shapiro, Irwin
1997-01-01
We are engaged in testing gravitational theory by means of observations of objects in the solar system. These tests include an examination of the Principle Of Equivalence (POE), the Shapiro delay, the advances of planetary perihelia, the possibility of a secular variation G in the "gravitational constant" G, and the rate of the de Sitter (geodetic) precession of the Earth-Moon system. These results are consistent with our preliminary results focusing on the contribution of Lunar Laser Ranging (LLR), which were presented at the seventh Marcel Grossmann meeting on general relativity. The largest improvement over previous results comes in the uncertainty for (eta): a factor of five better than our previous value. This improvement reflects the increasing strength of the LLR data. A similar analysis presented at the same meeting by a group at the Jet Propulsion Laboratory gave a similar result for (eta). Our value for (beta) represents our first such result determined simultaneously with the solar quadrupole moment from the dynamical data set. These results are being prepared for publication. We have shown how positions determined from different planetary ephemerides can be compared and how the combination of VLBI and pulse timing information can yield a direct tie between planetary and radio frames. We have continued to include new data in our analysis as they became available. Finally, we have made improvement in our analysis software (PEP) and ported it to a network of modern workstations from its former home on a "mainframe" computer.
Cardoso, V; Cardoso, Vitor; Lemos, Jos\\'e P. S.
2003-01-01
In this paper, we consider the gravitational radiation generated by the collision of highly relativistic particles with rotating Kerr black holes. We use the Sasaki-Nakamura formalism to compute the waveform, energy spectra and total energy radiated during this process. We show that the gravitational spectrum for high-energy collisions has definite characteristic universal features, which are independent of the spin of the colliding objects. We also discuss possible connections between these results and the black hole-black hole collision at the speed of light process. With these results at hand, we predict that during the high speed collision of a non-rotating hole with a rotating one, about 35% of the total energy gets converted into gravitational waves. Thus, if one is able to produce black holes at the Large Hadron Collider, 35% of the partons' energy should be emitted during the so called balding phase. This energy will be missing, since we don't have gravitational wave detectors able to measure such amp...
Relativistic stars in scalar-tensor theories with disformal coupling
Silva, Hector O.; Minamitsuji, Masato
2017-01-01
We discuss a general formulation to study the structure of slowly-rotating relativistic stars in a broad class of scalar-tensor theories including disformal coupling to matter. Our approach includes as particular cases theories with generalized kinetic terms and generic scalar field potentials, and contains theories with conformal coupling as particular limits. We propose a minimal model to investigate the role of the disformal coupling on the non-perturbative effect known as spontaneous scalarization, which causes relativistic star solutions in certain classes of scalar-tensor theories to differ dramatically from their general relativistic counterparts. Moreover, we show that the moment of inertia and compactness of stars are equation of state independent, which can potentially be used to constrain the model observationally.
Electric and magnetic aspects of gravitational theories
Dehouck, François
2011-01-01
This thesis deals with the construction of conserved charges for asymptotically flat spacetimes at spatial infinity in four spacetime dimensions in a hopefully pedagogical way. As a first motivation of this work, it highlights the difficulties one encounters when trying to understand the gravitational duality, present at the linearized level, in the full non-linear Einstein's theory or even just in an asymptotic regime of it. In the first part, we restrict the discussion to the Noetherian surface charges, called "electric charges", and study the existence of a larger phase space, than previously known in the literature, where the awkward parity boundary conditions, firstly imposed by T. Regge and C. Teitelboim, are relaxed. In the absence of these parity conditions, we show how the Einstein-Hilbert action is a correct variational principle when it is supplemented by an anomalous counter-term and construct conserved and finite charges associated to the larger asymptotic symmetry group. The second and third par...
Workshop on foundations of the relativistic theory of atomic structure
None
1981-03-01
The conference is an attempt to gather state-of-the-art information to understand the theory of relativistic atomic structure beyond the framework of the original Dirac theory. Abstracts of twenty articles from the conference were prepared separately for the data base. (GHT)
Bags in relativistic quantum field theory with spontaneously broken symmetry
Wadati, M.; Matsumoto, H.; Umezawa, H.
1978-08-15
Presented is a microscopic derivation of bags from a relativistic quantum theory with spontaneously broken symmetry. The static energy of a bag whose singularity is the surface of a sphere coincides with the volume tension in the MIT bag theory. A similarity between the bags and the point defects in crystals is pointed out.
Recent progresses in relativistic beam-plasma instability theory
A. Bret
2010-11-01
Full Text Available Beam-plasma instabilities are a key physical process in many astrophysical phenomena. Within the fireball model of Gamma ray bursts, they first mediate a relativistic collisionless shock before they produce upstream the turbulence needed for the Fermi acceleration process. While non-relativistic systems are usually governed by flow-aligned unstable modes, relativistic ones are likely to be dominated by normally or even obliquely propagating waves. After reviewing the basis of the theory, results related to the relativistic kinetic regime of the poorly-known oblique unstable modes will be presented. Relevant systems besides the well-known electron beam-plasma interaction are presented, and it is shown how the concept of modes hierarchy yields a criterion to assess the proton to electron mass ratio in Particle in cell simulations.
Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
Damour, Thibault
2016-01-01
A novel approach to the Effective One-Body description of gravitationally interacting two-body systems is introduced. This approach is based on the post-Minkowskian approximation scheme (perturbation theory in G, without assuming small velocities), and employs a new dictionary focussing on the functional dependence of the scattering angle on the total energy and the total angular momentum of the system. Using this approach, we prove to all orders in v/c two results that were previously known to hold only to a limited post-Newtonian accuracy: (i) the relativistic gravitational dynamics of a two-body system is equivalent, at first post-Minkowskian order, to the relativistic dynamics of an effective test particle moving in a Schwarzschild metric; and (ii) this equivalence requires the existence of an exactly quadratic map between the real (relativistic) two-body energy and the (relativistic) energy of the effective particle. The same energy map is also shown to apply to the effective one-body description of two ...
Post-relativistic gravity a hidden variable theory for general relativity
Schmelzer, I
1996-01-01
Post-relativistic gravity is a hidden variable theory for general relativity. It introduces the pre-relativistic notions absolute space, absolute time, and ether as hidden variables into general relativity. Evolution is defined by the equations of general relativity and the harmonic coordinate condition interpreted as a physical equation. There are minor differences in predictions compared with general relativity (i.e. trivial topology of the universe is predicted). The unobservable absolute time is designed to solve the problem of time in quantization of general relativity. Background space and time define a Newtonian frame for the quantization of the gravitational field. By the way, a lot of other conceptual problems of quantization will be solved (i.e. no constraints, no topological foam, no black hole and bib bang singularities, natural vacuum definition for quantum fields on classical background).
Statistical Gauge Theory for Relativistic Finite Density Problems
YING Shu-Qian
2001-01-01
A relativistic quantum field theory is presented for finite density problems based on the principle of locality. It is shown that, in addition to the conventional ones, a local approach to the relativistic quantum field theories at both zero and finite densities consistent with the violation of Bell-like inequalities should contain and provide solutions to at least three additional problems, namely, i) the statistical gauge invariance; ii) the dark components of the local observables; and iii) the fermion statistical blocking effects, based upon an asymptotic nonthermal ensemble. An application to models is presented to show the importance of the discussions.
Tensor-tensor theory of gravitation
Gogberashvili, Merab
1996-01-01
We consider the standard gauge theory of Poincar\\'{e} group, realizing as a subgroup of GL(5. R). The main problem of this theory was appearing of the fields connected with non-Lorentz symmetries, whose physical sense was unclear. In this paper we treat the gravitation as a Higgs-Goldstone field, and the translation gauge field as a new tensor field. The effective metric tensor in this case is hybrid of two tensor fields. In the linear approximation the massive translation gauge field can give the Yukava type correction to the Newtons potential. Also outer potentials of a sphere and ball of the same mass are different in this case. Corrections to the standard Einshtein post Newtonian formulas of the light deflection and radar echo delay is obtained. The string like solution of the nonlinear equations of the translation gauge fields is found. This objects can results a Aharonov-Bohm type effect even for the spinless particles. They can provide density fluctuations in the early universe, necessary for galaxy fo...
Gravitational Shielding Effect in Gauge Theory of Gravity
WU Ning
2004-01-01
In 1992,E.E.Podkletnov and R.Nieminen found that under certain conditions,ceramic superconductor with composite structure reveals weak shielding properties against gravitational force.In classical Newton's theory of gravity and even in Einstein's general theory of gravity,there are no grounds of gravitational shielding effects.But in quantum gauge theory of gravity,the gravitational shielding effects can be explained in a simple and natural way.In quantum gauge theory of gravity,gravitational gauge interactions of complex scalar field can be formulated based on gauge principle.After spontaneous symmetry breaking,if the vacuum of the complex scalar field is not stable and uniform,there will be a mass term of gravitational gauge field.When gravitational gauge field propagates in this unstable vacuum of the complex scalar field,it will decays exponentially,which is the nature of gravitational shielding effects.The mechanism of gravitational shielding effects is studied in this paper,and some main properties of gravitational shielding effects are discussed.
Newtonian self-gravitating system in a relativistic huge void universe model
Nishikawa, Ryusuke; Nakao, Ken-ichi; Yoo, Chul-Moon
2016-12-01
We consider a test of the Copernican Principle through observations of the large-scale structures, and for this purpose we study the self-gravitating system in a relativistic huge void universe model which does not invoke the Copernican Principle. If we focus on the the weakly self-gravitating and slowly evolving system whose spatial extent is much smaller than the scale of the cosmological horizon in the homogeneous and isotropic background universe model, the cosmological Newtonian approximation is available. Also in the huge void universe model, the same kind of approximation as the cosmological Newtonian approximation is available for the analysis of the perturbations contained in a region whose spatial size is much smaller than the scale of the huge void: the effects of the huge void are taken into account in a perturbative manner by using the Fermi-normal coordinates. By using this approximation, we derive the equations of motion for the weakly self-gravitating perturbations whose elements have relative velocities much smaller than the speed of light, and show the derived equations can be significantly different from those in the homogeneous and isotropic universe model, due to the anisotropic volume expansion in the huge void. We linearize the derived equations of motion and solve them. The solutions show that the behaviors of linear density perturbations are very different from those in the homogeneous and isotropic universe model.
Zhu, Hongyu; Alam, Shadab; Croft, Rupert A. C.; Ho, Shirley; Giusarma, Elena
2017-10-01
Large redshift surveys of galaxies and clusters are providing the first opportunities to search for distortions in the observed pattern of large-scale structure due to such effects as gravitational redshift. We focus on non-linear scales and apply a quasi-Newtonian approach using N-body simulations to predict the small asymmetries in the cross-correlation function of two galaxy different populations. Following recent work by Bonvin et al., Zhao and Peacock and Kaiser on galaxy clusters, we include effects which enter at the same order as gravitational redshift: the transverse Doppler effect, light-cone effects, relativistic beaming, luminosity distance perturbation and wide-angle effects. We find that all these effects cause asymmetries in the cross-correlation functions. Quantifying these asymmetries, we find that the total effect is dominated by the gravitational redshift and luminosity distance perturbation at small and large scales, respectively. By adding additional subresolution modelling of galaxy structure to the large-scale structure information, we find that the signal is significantly increased, indicating that structure on the smallest scales is important and should be included. We report on comparison of our simulation results with measurements from the SDSS/BOSS galaxy redshift survey in a companion paper.
Toward a fully relativistic theory of quantum information
Adami, Christoph
2011-01-01
Information theory is a statistical theory dealing with the relative state of detectors and physical systems. Because of this physicality of information, the classical framework of Shannon needs to be extended to deal with quantum detectors, perhaps moving at relativistic speeds, or even within curved space-time. Considerable progress toward such a theory has been achieved in the last fifteen years, while much is still not understood. This review recapitulates some milestones along this road, and speculates about future ones.
Foundations for proper-time relativistic quantum theory
Gill, Tepper L.; Morris, Trey; Kurtz, Stewart K.
2015-05-01
This paper is a progress report on the foundations for the canonical proper-time approach to relativistic quantum theory. We first review the the standard square-root equation of relativistic quantum theory, followed by a review of the Dirac equation, providing new insights into the physical properties of both. We then introduce the canonical proper-time theory. For completeness, we give a brief outline of the canonical proper-time approach to electrodynamics and mechanics, and then introduce the canonical proper-time approach to relativistic quantum theory. This theory leads to three new relativistic wave equations. In each case, the canonical generator of proper-time translations is strictly positive definite, so that it represents a particle. We show that the canonical proper-time extension of the Dirac equation for Hydrogen gives results that are consistently closer to the experimental data, when compared to the Dirac equation. However, these results are not sufficient to account for either the Lamb shift or the anomalous magnetic moment.
The case for hyperbolic theories of dissipation in relativistic fluids
Anile, A M; Romano, V; Anile, Angelo Marcello; Pavon, Diego; Romano, Vittorio
1998-01-01
In this paper we higlight the fact that the physical content of hyperbolic theories of relativistic dissipative fluids is, in general, much broader than that of the hyperbolic ones. This is substantiated by presenting an ample range of dissipative fluids whose behavior noticeably departs from Navier-Stokes.
Nucleon self-energy in the relativistic Brueckner theory
Waindzoch, T.; Fuchs, C.; Faessler, A. [Inst. fuer Theoretische Physik, Univ. Tuebingen (Germany)
1998-06-01
The self-energy of the nucleon in nuclear matter is calculated in the relativistic Brueckner theory. We solve the Thompson equation for the two nucleon scattering in the medium using different Bonn potentials. The self-energy has a rather strong momentum dependence while the equation of state compares well with previous calculations. (orig.)
Relativistic Aberration and the Cosmological Constant in Gravitational Lensing I: Introduction
Lebedev, Dmitri
2016-01-01
An analysis of null geodesics in Schwarzschild de Sitter space is presented with special attention to their global `bending angles', local measurable angles, and the involvement of the cosmological constant. We make use of a general technique which allows for finding observable intersection angles of null trajectories analytically. A general relativistic aberration relationship is established as one of its applications. The question of whether or not the cosmological constant, $\\Lambda$, contributes to orbits of light and to related observable quantities is addressed in detail. We also discuss the ongoing debate on this issue and respond to some recent papers on the topic. The dependence of measurable quantities on the motion of observers is stressed throughout. Exact formulas for measurable intersection angles, as well as gravitational lens equations for observers in the Schwarzschild de Sitter background are provided.
Relativistic stars in scalar-tensor theories with disformal coupling
Minamitsuji, Masato
2016-01-01
We present a general formulation to analyze the structure of slowly rotating relativistic stars in a broad class of scalar-tensor theories with disformal coupling to matter. Our approach includes theories with generalized kinetic terms, generic scalar field potentials and contains theories with conformal coupling as particular limits. In order to investigate how the disformal coupling affects the structure of relativistic stars, we propose a minimal model of a massless scalar-tensor theory and investigate in detail how the disformal coupling affects the spontaneous scalarization of slowly rotating neutron stars. We show that for negative values of the disformal coupling parameter between scalar field and matter, scalarization can be suppressed, while for large positive values of the disformal coupling parameter stellar models cannot be obtained. This allows us to put a mild upper bound on this parameter. We also show that these properties can be qualitatively understood by linearizing the scalar field equatio...
Relativistic semi-classical theory of atom ionization in ultra-intense laser
无
2001-01-01
A relativistic semi-classical theory (RSCT) of H-atom ionizationin ultra-intense laser (UIL) is proposed. A relativistic analytical expression for ionization probability of H-atom in its ground state is given. This expression, compared with non-relativistic expression, clearly shows the effects of the magnet vector in the laser, the non-dipole approximation and the relativistic mass-energy relation on the ionization processes. At the same time, we show that under some conditions the relativistic expression reduces to the non-relativistic expression of non-dipole approximation. At last, some possible applications of the relativistic theory are briefly stated.
General Relativistic Mean Field Theory for rotating nuclei
Madokoro, Hideki [Kyushu Univ., Fukuoka (Japan). Dept. of Physics; Matsuzaki, Masayuki
1998-03-01
The {sigma}-{omega} model Lagrangian is generalized to an accelerated frame by using the technique of general relativity which is known as tetrad formalism. We apply this model to the description of rotating nuclei within the mean field approximation, which we call General Relativistic Mean Field Theory (GRMFT) for rotating nuclei. The resulting equations of motion coincide with those of Munich group whose formulation was not based on the general relativistic transformation property of the spinor fields. Some numerical results are shown for the yrast states of the Mg isotopes and the superdeformed rotational bands in the A {approx} 60 mass region. (author)
Four Poission-Laplace Theory of Gravitation (I)
Nyambuya, Golden Gadzirayi
2015-08-01
The Poisson-Laplace equation is a working and acceptable equation of gravitation which is mostly used or applied in its differential form in Magneto-Hydro-Dynamic (MHD) modelling of e.g. molecular clouds. From a general relativistic standpoint, it describes gravitational fields in the region of low spacetime curvature as it emerges in the weak field limit. For non-static gravitational fields, this equation is not generally covariant. On the requirements of general covariance, this equation can be extended to include a time-dependent component, in which case one is led to the Four Poisson-Laplace equation. We solve the Four Poisson-Laplace equation for radial solutions, and apart from the Newtonian gravitational component, we obtain four new solutions leading to four new gravitational components capable (in-principle) of explaining e.g. the Pioneer anomaly, the Titius-Bode Law and the formation of planetary rings. In this letter, we focus only on writing down these solutions. The task showing that these new solutions might explain the aforesaid gravitational anomalies has been left for separate future readings.
Arun, K. G.; Pai, Archana
2013-01-01
Gravitational wave (GW) observations of coalescing compact binaries will be unique probes of strong-field, dynamical aspects of relativistic gravity. We present a short review of various schemes proposed in the literature to test general relativity (GR) and alternative theories of gravity using inspiral waveforms. Broadly these schemes may be classified into two types: model dependent and model independent. In the model dependent category, GW observations are compared against a specific waveform model representative of a particular theory or a class of theories such as scalar-tensor theories, dynamical Chern-Simons theory and massive graviton theories. Model independent tests are attempts to write down a parametrized gravitational waveform where the free parameters take different values for different theories and (at least some of) which can be constrained by GW observations. We revisit some of the proposed bounds in the case of downscaled LISA configuration (eLISA) and compare them with the original LISA configuration. We also compare the expected bounds on alternative theories of gravity from ground-based and space-based detectors and find that space-based GW detectors can test GR and other theories of gravity with unprecedented accuracies. We then focus on a recent proposal to use singular value decomposition of the Fisher information matrix to improve the accuracies with which post-Newtonian theory can be tested. We extend those results to the case of space-based detector eLISA and discuss its implications.
Tensor-multi-scalar theories: relativistic stars and 3+1 decomposition
Horbatsch, Michael; Gerosa, Davide; Pani, Paolo; Berti, Emanuele; Gualtieri, Leonardo; Sperhake, Ulrich
2015-01-01
Gravitational theories with multiple scalar fields coupled to the metric and each other - a natural extension of the well studied single-scalar-tensor theories - are interesting phenomenological frameworks to describe deviations from general relativity in the strong-field regime. In these theories, the N-tuple of scalar fields takes values in a coordinate patch of an N-dimensional Riemannian target-space manifold whose properties are poorly constrained by weak-field observations. Here we introduce for simplicity a non-trivial model with two scalar fields and a maximally symmetric target-space manifold. Within this model we present a preliminary investigation of spontaneous scalarization for relativistic, perfect fluid stellar models in spherical symmetry. We find that the scalarization threshold is determined by the eigenvalues of a symmetric scalar-matter coupling matrix, and that the properties of strongly scalarized stellar configurations additionally depend on the target-space curvature radius. In prepara...
The cosmology of the nonsymmetric theory of gravitation
Prokopec, Tomislav [Institute for Theoretical Physics (ITP) and Spinoza Institute, Minnaertgebouw, Leuvenlaan 4, Utrecht University 3584 CE Utrecht (Netherlands)]. E-mail: t.prokopec@phys.uu.nl; Valkenburg, Wessel [Institute for Theoretical Physics (ITP) and Spinoza Institute, Minnaertgebouw, Leuvenlaan 4, Utrecht University 3584 CE Utrecht (Netherlands)]. E-mail: w.valkenburg@phys.uu.nl
2006-04-27
We show that during cosmological inflation the nonsymmetric metric tensor theory of gravitation develops a spectrum which is potentially observable by cosmic microwave background observations, and may be the most sensitive probe of the scale of cosmic inflation.
Gravitational duality in General Relativity and Supergravity theories
Dehouck, F. [Service de physique mathematique et interactions fondamentales. Universite Libre de Bruxelles, Campus Plaine CP-231, 1050 Bruxelles (Belgium)
2011-07-15
We quickly review the current status of gravitational duality in General Relativity. We summarize and comment some recent work on constructing dual (topological) charges and understanding how this duality acts in supergravity theories.
Dirac equation in gauge and affine-metric gravitation theories
Giachetta, G
1995-01-01
We show that the covariant derivative of Dirac fermion fields in the presence of a general linear connection on a world manifold is universal for Einstein's, gauge and affine-metric gravitation theories.
Dynamical Gravitational Coupling as a Modified Theory of General Relativity
Finster, Felix
2016-01-01
A modified theory of general relativity is proposed, where the gravitational constant is replaced by a dynamical variable in space-time. The dynamics of the gravitational coupling is described by a family of parametrized null geodesics, implying that the gravitational coupling at a space-time point is determined by solving transport equations along all null geodesics through this point. General relativity with dynamical gravitational coupling (DGC) is introduced. We motivate DGC from general considerations and explain how it arises in the context of causal fermion systems. The underlying physical idea is that the gravitational coupling is determined by microscopic structures on the Planck scale which propagate with the speed of light. In order to clarify the mathematical structure, we analyze the conformal behavior and prove local existence and uniqueness of the time evolution. The differences to Einstein's theory are worked out in the examples of the Friedmann-Robertson-Walker model and the spherically symme...
Sources of Gravitational Waves: Theory and Observations
Buonanno, Alessandra
2014-01-01
Gravitational-wave astronomy will soon become a new tool for observing the Universe. Detecting and interpreting gravitational waves will require deep theoretical insights into astronomical sources. The past three decades have seen remarkable progress in analytical and numerical computations of the source dynamics, development of search algorithms and analysis of data from detectors with unprecedented sensitivity. This Chapter is devoted to examine the advances and future challenges in understanding the dynamics of binary and isolated compact-object systems, expected cosmological sources, their amplitudes and rates, and highlights of results from gravitational-wave observations. All of this is a testament to the readiness of the community to open a new window for observing the cosmos, a century after gravitational waves were first predicted by Albert Einstein.
Universal Spin Structure in Gauge Gravitation Theory
Giachetta, G; Sardanashvily, G
1997-01-01
Building on the universal covering group of the general linear group, we introduce the composite spinor bundle whose subbundles are Lorentz spin structures associated with different gravitational fields. General covariant transformations of this composite spinor bundle are canonically defined.
Theory of photospheric emission from relativistic outflows
Ruffini, R; Vereshchagin, G V
2013-01-01
(shortened) In this paper we reexamine the optical depth of ultrarelativistic spherically symmetric outflows and reevaluate the photospheric radius for each model during both the acceleration and coasting phases. It is shown that for both the wind and the shell models there are two asymptotic solutions for the optical depth during the coasting phase of the outflow. In particular we show that quite counterintuitively a geometrically thin shell may appear as a thick wind for photons propagating inside it. For this reason we introduce notions of photon thick and photon thin outflows, which appear more general and better physically motivated with respect to winds and shells. Photosphere of relativistic outflow is a dynamic surface. We study its geometry and find that the photosphere of photon thin outflow has always a convex shape, while in the photon thick one it is initially convex (there is always a photon thin layer in any outflow) and then it becomes concave asymptotically approaching the photosphere of an i...
SL(2,C) Gauge Theory of Gravitation and the Quantization of the Gravitational Field
Carmeli, M; Carmeli, Moshe; Malin, Shimon
1998-01-01
A new approach to quantize the gravitational field is presented. It is based on the observation that the quantum character of matter becomes more significant as one gets closer to the big bang. As the metric loses its meaning, it makes sense to consider Schrodinger's three generic types of manifolds - unconnected differentiable, affinely connected, and metrically connected - as a temporal sequence following the big bang. Hence one should quantize the gravitational field on general differentiable manifolds or on affinely connected manifolds. The SL(2,C) gauge theory of gravitation is employed to explore this possibility. Within this framework, the quantization itself may well be canonical.
De Felice, Antonio, E-mail: antoniod@nu.ac.th [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); TPTP and NEP, The Institute for Fundamental Study, Naresuan University, Phitsanulok, 65000 (Thailand); Thailand Center of Excellence in Physics, Ministry of Education, Bangkok 10400 (Thailand); Kobayashi, Tsutomu [Hakubi Center, Kyoto University, Kyoto 606-8302 (Japan); Department of Physics, Kyoto University, Kyoto 606-8502 (Japan); Tsujikawa, Shinji [Department of Physics, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan)
2011-12-06
In the Horndeski's most general scalar-tensor theories the equations of scalar density perturbations are derived in the presence of non-relativistic matter minimally coupled to gravity. Under a quasi-static approximation on sub-horizon scales we obtain the effective gravitational coupling G{sub eff} associated with the growth rate of matter perturbations as well as the effective gravitational potential {Phi}{sub eff} relevant to the deviation of light rays. We then apply our formulas to a number of modified gravitational models of dark energy - such as those based on f(R) theories, Brans-Dicke theories, kinetic gravity braidings, covariant Galileons, and field derivative couplings with the Einstein tensor. Our results are useful to test the large-distance modification of gravity from the future high-precision observations of large-scale structure, weak lensing, and cosmic microwave background.
De Felice, Antonio; Tsujikawa, Shinji
2011-01-01
In the Horndeski's most general scalar-tensor theories the equations of scalar density perturbations are derived in the presence of non-relativistic matter minimally coupled to gravity. Under a quasi-static approximation on sub-horizon scales we obtain the effective gravitational coupling $G_{eff}$ associated with the growth rate of matter perturbations as well as the effective gravitational potential $\\Phi_{eff}$ relevant to the deviation of light rays. We then apply our formulas to a number of modified gravitational models of dark energy--such as those based on f(R) theories, Brans-Dicke theories, kinetic gravity braidings, covariant Galileons, and field derivative couplings with the Einstein tensor. Our results are useful to test the large-distance modification of gravity from the future high-precision observations of large-scale structure, weak lensing, and cosmic microwave background.
Relativistic quantum theories and neutrino oscillations
Keister, B D [Physics Division, 1015N, National Science Foundation, 4201 Wilson Blvd., Arlington, VA 22230 (United States); Polyzou, W N, E-mail: polyzou@uiowa.ed [Department of Physics and Astronomy, The University of Iowa, Iowa City, IA 52242 (United States)
2010-05-01
Neutrino oscillations are examined under the broad requirements of Poincare-invariant scattering theory in an S-matrix formulation. This approach can be consistently applied to theories with either field or particle degrees of freedom. The aim of this paper is to use this general framework to identify all of the unique physical properties of this problem that lead to a simple oscillation formula. We discuss what is in principle observable and how many factors that are important in principle end up being negligible in practice.
Relativistic quantum chemistry the fundamental theory of molecular science
Reiher, Markus
2014-01-01
Einstein proposed his theory of special relativity in 1905. For a long time it was believed that this theory has no significant impact on chemistry. This view changed in the 1970s when it was realized that (nonrelativistic) Schrödinger quantum mechanics yields results on molecular properties that depart significantly from experimental results. Especially when heavy elements are involved, these quantitative deviations can be so large that qualitative chemical reasoning and understanding is affected. For this to grasp the appropriate many-electron theory has rapidly evolved. Nowadays relativist
Fokas, Athanassios S; Grigoriou, D
2015-01-01
Let $r(\\varphi)$ denote the orbit of Mercury and other planets. We compare the formula of General Relativity (GR) for $r(\\varphi)$, as well as the formula for the corresponding perihelion precession angle $\\Delta \\varphi$, with the formulae obtained via the relativistic gravitational law, $F=GMm\\gamma^3/r^2$. The latter law can be derived from Newton's gravitational law by employing the gravitational rather than the rest mass of the rotating body and using special relativity (SR) together with the equivalence principle to compute the inertial and hence the gravitational, mass. Remarkably, it is found that the two expressions for $r(\\varphi)$ differ only by a factor of 2 and by an additive constant. This constant does not affect the formula for the $\\Delta \\varphi$, thus the two expressions for $\\Delta\\varphi$ differ only by a factor of 2.
Gravity theories, Transverse Doppler and Gravitational Redshifts in Galaxy Clusters
Zhao, Hongsheng; Li, Baojiu
2012-01-01
There is growing interest in testing alternative gravity theories using the subtle Gravitational Redshifts in clusters of galaxies. However, current models all neglect a Transverse Doppler redshift of similar magnitude, and some models are not self-consistent. An equilibrium model would fix the Gravitational and Transverse Doppler velocity shifts to be about 6\\sigma^2/c and 3\\sigma^2/2c in order to fit the observed velocity dispersion \\sigma self-consistently. This result is from the Virial Theorem for a spherical isotropic cluster, and is insensitive to the theory of gravity. In any case, a gravitational redshift signal cannot directly distinguish between the Einsteinian and f(R) gravity theories, because the mass of the cluster dark halo must be treated as an unknown fitting parameter, whose value must vary according to the theory adopted, otherwise the system would be in equilibrium in one gravity theory and out of equilibrium in another.
Relativistic Multichannel Theory: Theoretical Study of C+ Autoionization States
XIA Dan; ZHANG Shi-Zhong; PENG Yong-Lun; LI Jia-Ming
2003-01-01
Based on relativistic multichannel theory, the autoionization states of C+ are studied. We calculate all the autoionization states in the energy region of 193900 ~ 231700cm"1, and the results are in good agreement with the experimental data. The energy structure we obtain will be important in the dielectronic recombination processes, which plays a key role in determining the abundance of carbon in a nebula.
Novak, Jerome; Dimmelmeier, Harrald; Font-Roda, Jose A.
2004-12-01
We present a new three-dimensional general relativistic hydrodynamics code which can be applied to study stellar core collapses and the resulting gravitational radiation. This code uses two different numerical techniques to solve partial differential equations arising in the model: high-resolution shock capturing (HRSC) schemes for the evolution of hydrodynamic quantities and spectral methods for the solution of Einstein equations. The equations are written and solved using spherical polar coordinates, best suited to stellar topology. Einstein equations are formulated within the 3+1 formalism and conformal flat condition (CFC) for the 3-metric and gravitational radiation is extracted using Newtonian quadrupole formulation.
Covariant theory of gravitation in the framework of special relativity
Vieira, R S
2016-01-01
Purely from covariance requirements regarding the special theory of relativity, we show that a moving body necessarily generates a gravitational magnetic field. Then, from the Lorentz transformations, we deduce the exact formul{\\ae} describing these gravitomagnetic fields in a flat spacetime. We also show that the gravitational mass should be regarded as an invariant quantity in the same foot as the electric charge. Thus, the differential equations satisfied by the gravitomagnetic fields are deduced, which proved to be similar to the Maxwell equations. This allowed us to show that gravitational waves indeed spread out with the speed of light, confirming a result that usually is only guessed. We also show that the gravitational vector potential can be associated to the momentum of interaction between the matter and the gravitomagnetic fields. The energy and momentum stored in the gravitomagnetic fields are also discussed. We highlight that nothing is assumed from the electromagnetic theory in our approach, nev...
Magnetized cosmological models in bimetric theory of gravitation
S D Katore; R S Rane
2006-08-01
Bianchi type-III magnetized cosmological model when the field of gravitation is governed by either a perfect fluid or cosmic string is investigated in Rosen's [1] bimetric theory of gravitation. To complete determinate solution, the condition, viz., = (), where is a constant, between the metric potentials is used. We have assumed different equations of state for cosmic string [2] for the complete solution of the model. Some physical and geometrical properties of the exhibited model are discussed and studied.
Cosmological constant and gravitational theory on D-brane
Shiromizu, T; Torii, T; Shiromizu, Tetsuya; Koyama, Kazuya; Torii, Takashi
2003-01-01
In a toy model we derive the gravitational equation on a self-gravitating curved D-brane. The effective theory on the brane is drastically changed from the ordinal Einstein equation. The net cosmological constant on the brane depends on a tuning between the brane tension and the brane charges. Moreover, non-zero matter stress tensor exists if the net cosmological constant is not zero. This fact indicates a direct connection between matters on the brane and the dark energy.
Two Quantum Effects In The Theory Of Gravitation
Robinson, S P
2005-01-01
We will discuss two methods by which the formalism of quantum field theory can be included in calculating the physical effects of gravitation. In the first of these, the consequences of treating general relativity as an effective quantum field theory will be examined. The primary result will be the calculation of the first-order quantum gravity corrections to the β functions of arbitrary Yang-Mills theories. These corrections will effect the high-energy phenomenology of such theories, including the details of coupling constant unification. Following this, we will address the question of how to form effective quantum field theories in classical gravitational backgrounds. We follow the prescription that effective theories should provide a description of experimentally accessible degrees of freedom with all other degrees of freedom integrated out of the theory. We will show that this prescription appears to fail for a scalar field in a black hole background because of an anomaly generated in general cov...
Relativistic quantum information theory and quantum reference frames
Palmer, Matthew C
2013-01-01
This thesis is a compilation of research in relativistic quantum information theory, and research in quantum reference frames. The research in the former category provides a fundamental construction of quantum information theory of localised qubits in curved spacetimes. For example, this concerns quantum experiments on free-space photons and electrons in the vicinity of the Earth. From field theory a description of localised qubits that traverse classical trajectories in curved spacetimes is obtained, for photons and massive spin-1/2 fermions. The equations governing the evolution of the two-dimensional quantum state and its absolute phase are determined. Quantum information theory of these qubits is then developed. The Stern-Gerlach measurement formalism for massive spin-1/2 fermions is also derived from field theory. In the latter category of research, the process of changing reference frames is considered for the case where the reference frames are quantum systems. As part of this process, it is shown that...
Noteworthy dimensionless constant in gravitation theory
Fayos, F.; Lobo, J.A.; Llanta, E.
1986-01-01
A simple problem of gravitation is studied classically and in the Schwarzchild framework. A relationship is found between the parameters that define the trajectories of two particles (the first in radial motion and the second in a circular orbit) which are initially together and meet again after one revolution of particle 2. Dimensional analysis is the clue to explain the appearance of a dimensionless constant in the Newtonian case.
Gravitational curvature an introduction to Einstein's theory
Frankel, Theodore
2011-01-01
This classic text and reference monograph applies modern differential geometry to general relativity. A brief mathematical introduction to gravitational curvature, it emphasizes the subject's geometric essence, replacing the often-tedious analytical computations with geometric arguments. Clearly presented and physically motivated derivations express the deflection of light, Schwarzchild's exterior and interior solutions, and the Oppenheimer-Volkoff equations. A perfect choice for advanced students of mathematics, this volume will also appeal to mathematicians interested in physics. It stresses
Relativistic quantum transport theory for electrodynamics
Zhuang, P; Zhuang, P; Heinz, U
1995-01-01
We investigate the relationship between the covariant and the three-dimensional (equal-time) formulations of quantum kinetic theory. We show that the three-dimensional approach can be obtained as the energy average of the covariant formulation. We illustrate this statement in scalar and spinor QED. For scalar QED we derive Lorentz covariant transport and constraint equations directly from the Klein-Gordon equation rather than through the previously used Feshbach-Villars representation. We then consider pair production in a spatially homogeneous but time-dependent electric field and show that the pair density is derived much more easily via the energy averaging method than in the equal-time representation. Proceeding to spinor QED, we derive the covariant version of the equal-time equation derived by Bialynicki-Birula et al. We show that it must be supplemented by another self-adjoint equation to obtain a complete description of the covariant spinor Wigner operator. After spinor decomposition and energy averag...
Quantum Theory and the Nature of Gravitation
Mazur, Pawel O
2009-01-01
This is an essay sketching the line of thinking which has led the present author to propose the constituent or atomic model of gravitation more than a decade ago. It turns out that viewing the problem of gravitation as a quantum many body problem could be quite useful when addressing some old unsolved problems such as the cosmological constant problem. I have applied this idea in 1996 to the problem of the largest cold gravitating system, the finite Universe itself. The result was the prediction of a small, positive vacuum energy density, now known, after its experimental discovery in 1998, as `dark energy'. The smallness of this quantity was understood as the finite size effect in the cold quantum many body system, and I quote here from \\cite{Ma96}, {\\it `` The smallness of the cosmological constant in natural Planck units is a result of an almost perfect thermodynamical limit. This is to say that the smallness of the cosmological constant is an effect due to an enormous number $N$ of hypothetical \\textsf{gr...
Exact two-component relativistic energy band theory and application
Zhao, Rundong; Zhang, Yong; Xiao, Yunlong; Liu, Wenjian, E-mail: liuwj@pku.edu.cn [Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871 (China)
2016-01-28
An exact two-component (X2C) relativistic density functional theory in terms of atom-centered basis functions is proposed for relativistic calculations of band structures and structural properties of periodic systems containing heavy elements. Due to finite radial extensions of the local basis functions, the periodic calculation is very much the same as a molecular calculation, except only for an Ewald summation for the Coulomb potential of fluctuating periodic monopoles. For comparison, the nonrelativistic and spin-free X2C counterparts are also implemented in parallel. As a first and pilot application, the band gaps, lattice constants, cohesive energies, and bulk moduli of AgX (X = Cl, Br, I) are calculated to compare with other theoretical results.
Exact two-component relativistic energy band theory and application.
Zhao, Rundong; Zhang, Yong; Xiao, Yunlong; Liu, Wenjian
2016-01-28
An exact two-component (X2C) relativistic density functional theory in terms of atom-centered basis functions is proposed for relativistic calculations of band structures and structural properties of periodic systems containing heavy elements. Due to finite radial extensions of the local basis functions, the periodic calculation is very much the same as a molecular calculation, except only for an Ewald summation for the Coulomb potential of fluctuating periodic monopoles. For comparison, the nonrelativistic and spin-free X2C counterparts are also implemented in parallel. As a first and pilot application, the band gaps, lattice constants, cohesive energies, and bulk moduli of AgX (X = Cl, Br, I) are calculated to compare with other theoretical results.
Troxel, M A; Ishak, Mustapha
2013-01-01
We study the effects and implications of anisotropies at the scale of galaxy clusters by building an exact general relativistic model of a cluster using the inhomogeneous and anisotropic Szekeres metric. The model is built from a modified Navarro-Frenk-White (NFW) density profile. We compare this to a corresponding spherically symmetric structure in the Lemaitre-Tolman (LT) model and quantify the impact of introducing varying levels of anisotropy. We examine two physical measures of gravitational infall -- the growth rate of density and the velocity of the source dust in the model. We introduce a generalization of the LT dust velocity profile for the Szekeres metric and demonstrate its consistency with the growth rate of density. We find that the growth rate of density in one substructure increases by 0.5%, 1.5%, and 3.75% for 5%, 10%, and 15% levels of introduced anisotropy, which is measured as the fractional displaced mass relative to the spherically symmetric case. The infall velocity of the dust is found...
Boson star in a gravitation theory with dilaton.
Zhijian, Tao; Xue, Xun
1992-03-01
The authors study the possible static spherically symmetric configuration of stellar objects comprised of bosons in a gravitation theory differing from Einstein's theory in the sense that the dilaton field appears in the theory as a nonlinear realization of dilatation invariance. Different scales of the dilaton interacting with a complex scalar field and different scales of the mass of the complex scalar field are considered.
Renk, Janina; Montanari, Francesco
2016-01-01
Observations of cosmological large scale structures (LSS) offer a unique opportunity to test the nature of gravity. We address the impact of consistent modifications of gravity on the largest observable scales, focusing on relativistic effects in galaxy number counts and the cross-correlation between the matter distribution and the cosmic microwave background temperature anisotropies. Our analysis applies to a very broad class of general scalar-tensor theories encoded in the Horndeski Lagrangian and is fully consistent on linear scales, retaining the full dynamics of the scalar field and not assuming quasi-static evolution. As particular examples we consider both, self-accelerating covariant Galileons and parameterizations of the properties that fully describe the linear theory. We investigate the impact of these models on relativistic corrections to galaxy clustering using the hi_class code. We find that especially effects which involve integrals along the line of sight (gravitational lensing, time delay and...
LIGO GW150914 and GW151226 gravitational wave detection and generalized gravitation theory (MOG
J.W. Moffat
2016-12-01
Full Text Available The nature of gravitational waves in a generalized gravitation theory is investigated. The linearized field equations and the metric tensor quadrupole moment power and the decrease in radius of an inspiralling binary system of two compact objects are derived. The generalized Kerr metric describing a spinning black hole is determined by its mass M and the spin parameter a=cS/GM2. The LIGO-Virgo collaboration data is fitted with smaller binary black hole masses in agreement with the current electromagnetic, observed X-ray binary upper bound for a black hole mass, M≲10M⊙.
A New Parameter Set for the Relativistic Mean Field Theory
Nerlo-Pomorska, B; Nerlo-Pomorska, Bozena; Sykut, Joanna
2004-01-01
Subtracting the Strutinsky shell corrections from the selfconsistent energies obtained within the Relativistic Mean Field Theory (RMFT) we have got estimates for the macroscopic part of the binding energies of 142 spherical even-even nuclei. By minimizing their root mean square deviations from the values obtained with the Lublin-Srasbourg Drop (LSD) model with respect to the nine RMFT parameters we have found the optimal set (NL4). The new parameters reproduce also the radii of these nuclei with an accuracy comparable with that obtained with the NL1 and NL3 sets.
Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills Theory
Caron-Huot, Simon; Henn, Johannes M.
2014-01-01
he classical Kepler problem, as well as its quantum mechanical version, the hydrogen atom, enjoys a well-known hidden symmetry, the conservation of the Laplace-Runge-Lenz vector, which makes these problems superintegrable. Is there a relativistic quantum field theory extension that preserves...... this symmetry? In this Letter we show that the answer is positive: in the nonrelativistic limit, we identify the dual conformal symmetry of planar N=4 super Yang-Mills theory with the well-known symmetries of the hydrogen atom. We point out that the dual conformal symmetry offers a novel way to compute...... the spectrum of bound states of massive W bosons in the theory. We perform nontrivial tests of this setup at weak and strong coupling and comment on the possible extension to arbitrary values of the coupling....
Nyambuya, G G
2010-01-01
This paper is part of a series on the Azimuthally Symmetric Theory of Gravitation (ASTG) which is built on Laplace-Poisson's well known equation. We show herein that the emergent equations from the ASTG, under some critical conditions determined by the spin, do possess repulsive gravitational fields in the polar regions of the gravitating body in question. This places the ASTG on an interesting pedestal to infer the origins of outflows as a repulsive gravitational phenomenon. Outflows are a ubiquitous phenomenon found in star forming systems and their true origin is a question yet to be settled. Given the current thinking on their origin, the direction that the present paper takes is nothing short of an asymptotic break from conventional wisdom; at the very least, it is a complete paradigm shift because gravitation is not at all associated with this process, but rather it is thought to be an all-attractive force that only tries to squash matter together onto a single point. Additionally, we show that the emer...
Ordinary matter in nonlinear affine gauge theories of gravitation
Tiemblo, A; Tiemblo, A; Tresguerres, R
1994-01-01
We present a general framework to include ordinary fermionic matter in the metric--affine gauge theories of gravity. It is based on a nonlinear gauge realization of the affine group, with the Lorentz group as the classification subgroup of the matter and gravitational fields.
Super-renormalizable and finite gravitational theories
Modesto, Leonardo, E-mail: lmodesto@fudan.edu.cn; Rachwał, Lesław, E-mail: rachwal@fudan.edu.cn
2014-12-15
We hereby introduce and extensively study a class of non-polynomial higher derivative theories of gravity that realize a ultraviolet (UV) completion of Einstein general relativity. These theories are unitary (ghost free) and at most only one-loop divergences survive. The outcome is a class of theories super-renormalizable in even dimension and finite in odd dimension. Moreover, we explicitly prove in D=4 that there exists an extension of the theory that is completely finite and all the beta functions vanish even at one-loop. These results can be easily extended in extra dimensions and it is likely that the higher dimensional theory can be made finite, too. Therefore we have the possibility for “finite quantum gravity” in any dimension.
Lou, Yu-Qing; Xia, Yu-Kai
2017-05-01
We study magnetohydrodynamic (MHD) self-similar collapses and void evolution, with or without shocks, of a general polytropic quasi-spherical magnetofluid permeated by random transverse magnetic fields under the Paczynski-Wiita gravity that captures essential general relativistic effects of a Schwarzschild black hole (BH) with a growing mass. Based on the derived set of non-linear MHD ordinary differential equations, we obtain various asymptotic MHD solutions, the geometric and analytical properties of the magnetosonic critical curve (MSCC) and MHD shock jump conditions. Novel asymptotic MHD solution behaviours near the rim of central expanding voids are derived analytically. By exploring numerical global MHD solutions, we identify allowable boundary conditions at large radii that accommodate a smooth solution and show that a reasonable amount of magnetization significantly increases the mass accretion rate in the expansion-wave-collapse solution scenario. We also construct the counterparts of envelope-expansion-core-collapse solutions that cross the MSCC twice, which are found to be closely paired with a sequence of global smooth solutions satisfying a novel type of central MHD behaviours. MHD shocks with static outer and various inner flow profiles are also examined. Astrophysical applications include dynamic core collapses of magnetized massive stars and compact objects as well as formation of supermassive, hypermassive, dark matter and mixed matter BHs in the Universe, including the early Universe. Such gigantic BHs can be detected in X-ray/gamma-ray sources, quasars, ultraluminous infrared galaxies or extremely luminous infrared galaxies and dark matter overwhelmingly dominated elliptical galaxies as well as massive dark matter halos, etc. Gravitational waves and electromagnetic wave emissions in broad band (including e.g., gamma-ray bursts and fast radio bursts) can result from this type of dynamic collapses of forming BHs involving magnetized media.
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...
Noncommutative Field Theory on Homogeneous Gravitational Waves
Halliday, S; Halliday, Sam; Szabo, Richard J.
2006-01-01
We describe an algebraic approach to the time-dependent noncommutative geometry of a six-dimensional Cahen-Wallach pp-wave string background supported by a constant Neveu-Schwarz flux, and develop a general formalism to construct and analyse quantum field theories defined thereon. Various star-products are derived in closed explicit form and the Hopf algebra of twisted isometries of the plane wave is constructed. Scalar field theories are defined using explicit forms of derivative operators, traces and noncommutative frame fields for the geometry, and various physical features are described. Noncommutative worldvolume field theories of D-branes in the pp-wave background are also constructed.
Gravitational Decoherence, Alternative Quantum Theories and Semiclassical Gravity
Hu, B L
2014-01-01
In this report we discuss three aspects: 1) Semiclassical gravity theory (SCG): 4 levels of theories describing the interaction of quantum matter with classical gravity; 2) Alternative Quantum Theories: Discerning those which are derivable from general relativity (GR) plus quantum field theory (QFT) from those which are not; 3) Gravitational Decoherence: Derivation of a master equation and examination of the assumptions which led to the claims of observational possibilities. We list three sets of corresponding problems worthy of pursuit: a) Newton-Schr\\"odinger Equations in relation to SCG; b) Master equation of gravity-induced effects serving as discriminator of 2); and c) Role of gravity in macroscopic quantum phenomena.
Slice Energy and Conformal Frames in Theories of Gravitation
Cotsakis, S
2004-01-01
We examine and compare the behaviour of the scalar field slice energy in different classes of theories of gravity, in particular higher-order and scalar-tensor theories. We find a universal formula for the energy and compare the resulting conservation laws with those known in general relativity. This leads to a comparison between the inflaton, the dilaton and other forms of scalar fields present in these generalized theories. It also shows that all such conformally-related, generalized theories of gravitation allow for the energy on a slice to be invariably defined and its fundamental properties be insensitive to conformal transformations.
Relativistic cosmology; Cosmologia Relativista
Bastero-Gil, M.
2015-07-01
Relativistic cosmology is nothing but the study of the evolution of our universe expanding from the General Theory of Relativity, which describes the gravitational interaction at any scale and given its character far-reaching is the force that dominate the evolution of the universe. (Author)
Relativistic density functional theory for finite nuclei and neutron stars
Piekarewicz, J
2015-01-01
The main goal of the present contribution is a pedagogical introduction to the fascinating world of neutron stars by relying on relativistic density functional theory. Density functional theory provides a powerful--and perhaps unique--framework for the calculation of both the properties of finite nuclei and neutron stars. Given the enormous densities that may be reached in the core of neutron stars, it is essential that such theoretical framework incorporates from the outset the basic principles of Lorentz covariance and special relativity. After a brief historical perspective, we present the necessary details required to compute the equation of state of dense, neutron-rich matter. As the equation of state is all that is needed to compute the structure of neutron stars, we discuss how nuclear physics--particularly certain kind of laboratory experiments--can provide significant constrains on the behavior of neutron-rich matter.
BIRKHOFF'S EQUATIONS AND GEOMETRICAL THEORY OF ROTATIONAL RELATIVISTIC SYSTEM
LUO SHAO-KAI; CHEN XIANG-WEI; FU JING-LI
2001-01-01
The Birkhoffian and Birkhoff's functions of a rotational relativistic system are constructed, the Pfaff action of rotational relativistic system is defined, the Pfaff-Birkhoff principle of a rotational relativistic system is given, and the Pfaff-Birkhoff-D'Alembert principles and Birkhoff's equations of rotational relativistic system are constructed. The geometrical description of a rotational relativistic system is studied, and the exact properties of Birkhoff's equations and their forms onR × T*M for a rotational relativistic system are obtained. The global analysis of Birkhoff's equations for a rotational relativistic system is studied, the global properties of autonomous, semi-autonomous and non-autonomous rotational relativistic Birkhoff's equations, and the geometrical properties of energy change for rotational relativistic Birkhoff's equations are given.
Hamiltonian Poincaré gauge theory of gravitation
Tiemblo, A
1996-01-01
We develop a Hamiltonian formalism suitable to be applied to gauge theories in the presence of Gravitation, and to Gravity itself when considered as a gauge theory. It is based on a nonlinear realization of the Poincar\\'e group, taken as the local spacetime group of the gravitational gauge theory, with SO(3) as the classification subgroup. The Wigner--like rotation induced by the nonlinear approach singularizes out the role of time and allows to deal with ordinary SO(3) vectors. We apply the general results to the Einstein--Cartan action. We study the constraints and we obtain Einstein's classical equations in the extremely simple form of time evolution equations of the coframe. As a consequence of our approach, we identify the gauge--theoretical origin of the Ashtekar variables.
Fokker's type action at a distance theory of gravitation
Turygin, A. Iu.
1986-04-01
An attempt is made to develop a theory of direct gravitational interaction of an arbitrary order, i.e., a many-particle interaction. The situation considered is that of a moving particle in a fixed Riemannian space-time which interacts with a system characterized by a definite energy momentum tensor. A linear formulation of the Fokker type action is used to define particle equations of motion in a geodesic form in a metric of arbitrary order. A proof is developed to show that the resulting metric satisfies the Einstein equations and is commensurate with the Lorentz gauge in Wheeler-Feynman electrodynamics. When applied to many-particle interactions, the absorber theory of gravitational radiation that has been defined is effective only for a linear approximation solution to the Einstein equation, and will require further work to serve as a general absorber theory.
An overview of gravitational waves theory, sources and detection
Auger, Gerard
2017-01-01
This book describes detection techniques used to search for and analyze gravitational waves (GW). It covers the whole domain of GW science, starting from the theory and ending with the experimental techniques (both present and future) used to detect them. The theoretical sections of the book address the theory of general relativity and of GW, followed by the theory of GW detection. The various sources of GW are described as well as the methods used to analyse them and to extract their physical parameters. It includes an analysis of the consequences of GW observations in terms of astrophysics as well as a description of the different detectors that exist and that are planned for the future. With the recent announcement of GW detection and the first results from LISA Pathfinder, this book will allow non-specialists to understand the present status of the field and the future of gravitational wave science
Corrected Born-Infeld theory of electroweak and gravitational fields
Palatnik, D
1996-01-01
This paper suggests a correction to the theory presented in quant-ph/9511021. The theory is a direct generalization of the Born--Infeld theory of electromagnetism (1932) on the case of electroweak and gravitational interactions. The main notions of the model are the Dirac matrices and connections, given in a spinorial multiplet's representation. The action is symmetric with respect to linear transformations imposed on pairs of corresponding Dirac matrices, $\\gamma_{a}$, and dimensionless `momentum' operators, $\\pi_{a} = - iL(\\partial_{a} - \\Gamma_{a})$, where $\\Gamma_{a}$ are connections and $L$ is a characteristic length of order $10^{-32}$ cm. Claiming this symmetry as fundamental, one arrives at the most natural co-existance between gravitational and electroweak action terms.
Equilibrium thermodynamics in modified gravitational theories
Bamba, Kazuharu; Tsujikawa, Shinji
2009-01-01
We show that it is possible to obtain a picture of equilibrium thermodynamics on the apparent horizon in the expanding cosmological background for a wide class of modified gravity theories with the Lagrangian density $f(R, \\phi, X)$, where $R$ is the Ricci scalar and $X=-(\
Thermodynamics and Kinetic Theory of Relativistic Gases in 2-D Cosmological Models
Kremer, G M
2002-01-01
A kinetic theory of relativistic gases in a two-dimensional space is developed in order to obtain the equilibrium distribution function and the expressions for the fields of energy per particle, pressure, entropy per particle and heat capacities in equilibrium. Furthermore, by using the method of Chapman and Enskog for a kinetic model of the Boltzmann equation the non-equilibrium energy-momentum tensor and the entropy production rate are determined for a universe described by a two-dimensional Robertson-Walker metric. The solutions of the gravitational field equations that consider the non-equilibrium energy-momentum tensor - associated with the coefficient of bulk viscosity - show that opposed to the four-dimensional case, the cosmic scale factor attains a maximum value at a finite time decreasing to a "big crunch" and that there exists a solution of the gravitational field equations corresponding to a "false vacuum". The evolution of the fields of pressure, energy density and entropy production rate with th...
Golden Gadzirayi Nyambuya
2010-01-01
This paper is part of a series on the Azimuthally Symmetric Theory of Gravitation(ASTG).This theory is built on Laplace-Poisson's well known equation and it has been shown that the ASTG is capable of explaining,from a purely classical physics standpoint,the precession of the perihelion of solar planets as a consequence of the azimuthal symmetry emerging from the spin of the Sun.This symmetry has and must have an influence on the emergent gravitational field.We show herein that the emergent equations from the ASTG,under some critical conditions determined by the spin,do possess repulsive gravitational fields in the polar regions of the gravitating body in question.This places the ASTG on an interesting pedestal to infer the origins of outflows as a repulsive gravitational phenomenon.Outflows are a ubiquitous phenomenon found in star forming systems and their true origin is a question yet to be settled.Given the current thinking on their origin,the direction that the present paper takes is nothing short of an asymptotic break from conventional wisdom; at the very least,it is a complete paradigm shift because gravitation is not at all associated with this process,but rather it is thought to be an all-attractive force that only tries to squash matter together onto a single point.Additionally,we show that the emergent Azimuthally Symmetric Gravitational Field from the ASTG strongly suggests a solution to the supposed Radiation Problem that is thought to be faced by massive stars in their process of formation.That is,at～8-10 M⊙,radiation from the nascent star is expected to halt the accretion of matter.We show that in-falling material will fall onto the equatorial disk and from there,this material will be channeled onto the forming star via the equatorial plane,thus accretion of mass continues well past the value of～8-10 M⊙,albeit via the disk.Along the equatorial plane,the net force(with the radiation force included)on any material there-on right up to the
Massless and Massive Gauge-Invariant Fields in the Theory of Relativistic Wave Equations
Pletyukhov, V A
2010-01-01
In this work consideration is given to massless and massive gauge-invariant spin 0 and spin 1 fields (particles) within the scope of a theory of the generalized relativistic wave equations with an extended set of the Lorentz group representations. The results obtained may be useful as regards the application of a relativistic wave-equation theory in modern field models.
Objective realism and freedom of choice in relativistic quantum field theory
Bednorz, Adam
2016-01-01
An attempt to incorporate freedom of choice into relativistic quantum field theory is proposed. It is shown that it leads to breakdown of relativistic invariant properly defined objective realism. The argument does not rely on Bell theorem but direct analysis of invariance and positivity of objective correlations in quantum field theory.
Quantum Measurement Theory in Gravitational-Wave Detectors
Stefan L. Danilishin
2012-04-01
Full Text Available The fast progress in improving the sensitivity of the gravitational-wave detectors, we all have witnessed in the recent years, has propelled the scientific community to the point at which quantum behavior of such immense measurement devices as kilometer-long interferometers starts to matter. The time when their sensitivity will be mainly limited by the quantum noise of light is around the corner, and finding ways to reduce it will become a necessity. Therefore, the primary goal we pursued in this review was to familiarize a broad spectrum of readers with the theory of quantum measurements in the very form it finds application in the area of gravitational-wave detection. We focus on how quantum noise arises in gravitational-wave interferometers and what limitations it imposes on the achievable sensitivity. We start from the very basic concepts and gradually advance to the general linear quantum measurement theory and its application to the calculation of quantum noise in the contemporary and planned interferometric detectors of gravitational radiation of the first and second generation. Special attention is paid to the concept of the Standard Quantum Limit and the methods of its surmounting.
Quantum Measurement Theory in Gravitational-Wave Detectors.
Danilishin, Stefan L; Khalili, Farid Ya
2012-01-01
The fast progress in improving the sensitivity of the gravitational-wave detectors, we all have witnessed in the recent years, has propelled the scientific community to the point at which quantum behavior of such immense measurement devices as kilometer-long interferometers starts to matter. The time when their sensitivity will be mainly limited by the quantum noise of light is around the corner, and finding ways to reduce it will become a necessity. Therefore, the primary goal we pursued in this review was to familiarize a broad spectrum of readers with the theory of quantum measurements in the very form it finds application in the area of gravitational-wave detection. We focus on how quantum noise arises in gravitational-wave interferometers and what limitations it imposes on the achievable sensitivity. We start from the very basic concepts and gradually advance to the general linear quantum measurement theory and its application to the calculation of quantum noise in the contemporary and planned interferometric detectors of gravitational radiation of the first and second generation. Special attention is paid to the concept of the Standard Quantum Limit and the methods of its surmounting.
Gravitation experiments at Stanford. [using general relativity theory
Lipa, J. A.
1980-01-01
The experimental situation in post-Newtonian gravitation is briefly reviewed in order to reexamine the extent to which experiment supports or refutes general relativity. A description is given of the equivalence principle project, the gyroscope experiment, and the search for gravity waves. It is noted that even though some doubt has been cast on the value of the perihelion advance and the gravitational redshift as precise tests of general relativity in the past few years, many competing theories have been ruled out; in particular, the results from the Viking mission significantly reduce the credibility of the Brans-Dicke theory (Brans and Dicke, 1961). The dimensionless constant omega in this theory is now forced to exceed 50, while the value originally proposed was 6 (omega being infinity in general relativity). It is noted that the gyro experiment described is capable of putting much tighter limits on this parameter, and together with the other experiments in progress will help place gravitational theory on a firmer experimental footing.
Metric-affine gravitation theory and superpotentials
Giachetta, G.; Mangiarotti, L.; Saltarelli, A. [Camerino, Univ. (Italy). Dipt. di Matematica e Fisica
1997-05-01
They consider a metric-affine theory of gravity in which the dynamical fields are the Lorentzian metrics and the non-symmetric linear connections on the worked manifold X. Working with a Lagrangian density which is invariant under general covariant transformations and using standard tools of the calculus of variations, they study the corresponding currents. They find that the superpotential takes a nice form involving the torsion of the linear connection in a simple way and generalizing the well-known Komar superpotential. A feature of our approach is the use of the Poincare`-Cartan form in relation to the first variational formula of the calculus of variations.
What prevents gravitational collapse in string theory?
Mathur, Samir D
2016-01-01
It is conventionally believed that if a ball of matter of mass $M$ has a radius close to $2GM$ then it must collapse to a black hole. But string theory microstates (fuzzballs) have no horizon or singularity, and they do {\\it not} collapse. We consider two simple examples from classical gravity to illustrate how this violation of our intuition happens. In each case the `matter' arises from an extra compact dimension, but the topology of this extra dimension is not trivial. The pressure and density of this matter diverge at various points, but this is only an artifact of dimensional reduction; thus we bypass results like Buchadahl's theorem. Such microstates give the entropy of black holes, so these topologically nontrivial constructions dominate the state space of quantum gravity.
Scalar Gravitational Waves in the Effective Theory of Gravity
Mottola, Emil
2016-01-01
As a low energy effective field theory, classical General Relativity receives an infrared relevant modification from the conformal trace anomaly of the energy-momentum tensor of massless, or nearly massless, quantum fields. The local form of the effective action associated with the trace anomaly is expressed in terms of a dynamical scalar field that couples to the conformal factor of the spacetime metric, allowing it to propagate over macroscopic distances. Linearized around flat spacetime, this semi-classical EFT admits scalar gravitational wave solutions in addition to the transversely polarized tensor waves of the classical Einstein theory. The amplitude, Hamiltonian, energy flux, and quantization of the scalar wave modes are discussed. Astrophysical sources for scalar gravitational waves are considered, with the excited gluonic condensates in the interiors of neutron stars in merger events with other compact objects likely to provide the strongest burst signals.
A gravitational memory effect in "boosted" black hole perturbation theory
Gleiser, R J; Dominguez, Alfredo E.; Gleiser, Reinaldo J.
2003-01-01
Black hole perturbation theory, or more generally, perturbation theory on a Schwarzschild bockground, has been applied in several contexts, but usually under the simplifying assumption that the ADM momentum vanishes, namely, that the evolution is carried out and observed in the ``center of momentum frame''. In this paper we consider some consequences of the inclusion of a non vanishing ADM momentum in the initial data. We first provide a justification for the validity of the transformation of the initial data to the ``center of momentum frame'', and then analyze the effect of this transformation on the gravitational wave amplitude. The most significant result is the possibility of a type of gravitational memory effect that appears to have no simple relation with the well known Christodoulou effect.
\\pi N scattering in relativistic baryon chiral perturbation theory revisited
Alarcon, J M; Oller, J A; Alvarez-Ruso, L
2011-01-01
We have analyzed pion-nucleon scattering using the manifestly relativistic covariant framework of Infrared Regularization up to {\\cal O}(q^3) in the chiral expansion, where q is a generic small momentum. We describe the low-energy phase shifts with a similar quality as previously achieved with Heavy Baryon Chiral Perturbation Theory, \\sqrt{s}\\lesssim1.14 GeV. New values are provided for the {\\cal O}(q^2) and {\\cal O}(q^3) low-energy constants, which are compared with previous determinations. This is also the case for the scattering lengths and volumes. Finally, we have unitarized the previous amplitudes and as a result the energy range where data are reproduced increases significantly.
A New Theory for Unification of Electromagnetic and Gravitational Interactions
Li, Li-Xin
2015-01-01
In this paper we present a new theory for unification of electromagnetic and gravitational interactions. By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime, we derive the complete set of field equations on the four-dimensional spacetime from the five-dimensional Einstein field equation. We show that, besides the Einstein field equation on the four-dimensional spacetime, a new electromagnetic field equation is also derived: $\
III - Conservation of Gravitational Energy Momentum and Renormalizable Quantum Theory of Gravitation
Wisendanger, C
2011-01-01
Viewing gravitational energy-momentum $p_G^\\mu$ as equal by observation, but different in essence from inertial energy-momentum $p_I^\\mu$ naturally leads to the gauge theory of volume-preserving diffeormorphisms of an inner Minkowski space ${\\bf M}^{\\sl 4}$ which can describe gravitation at the classical level. This theory is quantized in the path integral formalism starting with a non-covariant Hamiltonian formulation with unconstrained canonical field variables and a manifestly positive Hamiltonian. The relevant path integral measure and weight are then brought into a Lorentz- and gauge-covariant form allowing to express correlation functions - applying the De Witt-Faddeev-Popov approach - in any meaningful gauge. Next the Feynman rules are developed and the quantum effective action at one loop in a background field approach is renormalized which results in an asymptotically free theory without presence of other fields and in a theory without asymptotic freedom including the Standard Model (SM) fields. Fina...
Dimensionally compactified Chern-Simon theory in 5D as a gravitation theory in 4D
Morales, Ivan; Oporto, Zui; Piguet, Olivier
2016-01-01
We propose a gravitation theory in 4 dimensional space-time obtained by compacting to 4 dimensions the five dimensional topological Chern-Simons theory with the gauge group SO(1,5) or SO(2,4) -- the de Sitter or anti-de Sitter group of 5-dimensional space-time. In the resulting theory, torsion, which is solution of the field equations as in any gravitation theory in the first order formalism, is not necessarily zero. However, a cosmological solution with zero torsion exists, which reproduces the Lambda-CDM cosmological solution of General Relativity. A realistic solution with spherical symmetry is also obtained.
Quantum Corrections on Relativistic Mean Field Theory for Nuclear Matter
ZHANG Qi-Ren; GAO Chun-Yuan
2011-01-01
We propose a quantization procedure for the nucleon-scalar meson system, in which an arbitrary mean scalar meson field Φ is introduced.The equivalence of this procedure with the usual one is proven for any given value of Φ.By use of this procedure, the scalar meson field in the Walecka's MFA and in Chin's RHA are quantized around the mean field.Its corrections on these theories are considered by perturbation up to the second order.The arbitrariness of Φ makes us free to fix it at any stage in the calculation.When we fix it in the way of Walecka's MFA, the quantum corrections are big, and the result does not converge.When we fix it in the way of Chin's RHA, the quantum correction is negligibly small, and the convergence is excellent.It shows that RHA covers the leading part of quantum field theory for nuclear systems and is an excellent zeroth order approximation for further quantum corrections, while the Walecka's MFA does not.We suggest to fix the parameter Φ at the end of the whole calculation by minimizing the total energy per-nucleon for the nuclear matter or the total energy for the finite nucleus, to make the quantized relativistic mean field theory (QRMFT) a variational method.
Gravitational radiation theory. M.A. Thesis - Rice Univ.; [survey of current research
Wilson, T. L.
1973-01-01
A survey is presented of current research in the theory of gravitational radiation. The mathematical structure of gravitational radiation is stressed. Furthermore, the radiation problem is treated independently from other problems in gravitation. The development proceeds candidly through three points of view - scalar, rector, and tensor radiation theory - and the corresponding results are stated.
Chavanis, Pierre-Henri
2014-01-01
Because of their superfluid properties, some compact astrophysical objects such as neutron stars may contain a significant part of their matter in the form of a Bose-Einstein condensate (BEC). We consider a partially-relativistic model of self-gravitating BECs where the relation between the pressure and the rest-mass density is assumed to be quadratic (as in the case of classical BECs) but pressure effects are taken into account in the relation between the energy density and the rest-mass density. At high densities, we get a stiff equation of state similar to the one considered by Zel'dovich (1961) in the context of baryon stars in which the baryons interact through a vector meson field. We determine the maximum mass of general relativistic BEC stars described by this equation of state by using the formalism of Tooper (1965). This maximum mass is slightly larger than the maximum mass obtained by Chavanis and Harko (2012) using a fully-relativistic model. We also consider the possibility that dark matter is ma...
Gravitational-wave emission in shift-symmetric Horndeski theories
Barausse, Enrico
2015-01-01
Gravity theories beyond General Relativity typically predict dipolar gravitational emission by compact-star binaries. This emission is sourced by "sensitivity" parameters depending on the stellar compactness. We introduce a general formalism to calculate these parameters, and show that in shift-symmetric Horndeski theories stellar sensitivities and dipolar radiation vanish, provided that the binary's dynamics is perturbative (i.e. the post-Newtonian formalism is applicable) and cosmological-expansion effects can be neglected. This allows reproducing the binary-pulsar observed orbital decay.
Effective Gravitational Wave Stress-energy Tensor in Alternative Theories of Gravity
Stein, Leo C; Hughes, Scott A
2010-01-01
The inspiral of binary systems in vacuum is controlled by the rate of change of the system's energy, angular momentum and Carter constant. In alternative theories, such a change is induced by the effective stress-energy carried away by gravitational radiation and any other propagating degrees of freedom. We employ perturbation theory and the short-wavelength approximation to compute this stress-energy tensor in a wide class of alternative theories. We find that this tensor is generally a modification of that first computed by Isaacson, where the corrections can dominate over the general relativistic term. In a wide class of theories, however, these corrections identically vanish at asymptotically flat, future, null infinity, reducing the stress-energy tensor to Isaacson's. We exemplify this phenomenon by first considering dynamical Chern-Simons modified gravity, which corrects the action via a scalar field and the contraction of the Riemann tensor and its dual. We then consider a wide class of theories with d...
Jones, Bernard J. T.; Markovic, Dragoljub
1997-06-01
Preface; Prologue: Conference overview Bernard Carr; Part I. The Universe At Large and Very Large Redshifts: 2. The size and age of the Universe Gustav A. Tammann; 3. Active galaxies at large redshifts Malcolm S. Longair; 4. Observational cosmology with the cosmic microwave background George F. Smoot; 5. Future prospects in measuring the CMB power spectrum Philip M. Lubin; 6. Inflationary cosmology Michael S. Turner; 7. The signature of the Universe Bernard J. T. Jones; 8. Theory of large-scale structure Sergei F. Shandarin; 9. The origin of matter in the universe Lev A. Kofman; 10. New guises for cold-dark matter suspects Edward W. Kolb; Part II. Physics and Astrophysics Of Relativistic Compact Objects: 11. On the unification of gravitational and inertial forces Donald Lynden-Bell; 12. Internal structure of astrophysical black holes Werner Israel; 13. Black hole entropy: external facade and internal reality Valery Frolov; 14. Accretion disks around black holes Marek A. Abramowicz; 15. Black hole X-ray transients J. Craig Wheeler; 16. X-rays and gamma rays from active galactic nuclei Roland Svensson; 17. Gamma-ray bursts: a challenge to relativistic astrophysics Martin Rees; 18. Probing black holes and other exotic objects with gravitational waves Kip Thorne; Epilogue: the past and future of relativistic astrophysics Igor D. Novikov; I. D. Novikov's scientific papers and books.
Quantum Measurement Theory in Gravitational-Wave Detectors
Danilishin, Stefan L
2012-01-01
The fast progress in improving the sensitivity of the gravitational-wave (GW) detectors, we all have witnessed in the recent years, has propelled the scientific community to the point, when quantum behaviour of such immense measurement devices as kilometer-long interferometers starts to matter. The time, when their sensitivity will be mainly limited by the quantum noise of light is round the corner, and finding the ways to reduce it will become a necessity. Therefore, the primary goal we pursued in this review was to familiarize a broad spectrum of readers with the theory of quantum measurements in the very form it finds application in the area of gravitational-wave detection. We focus on how quantum noise arises in gravitational-wave interferometers and what limitations it imposes on the achievable sensitivity. We start from the very basic concepts and gradually advance to the general linear quantum measurement theory and its application to the calculation of quantum noise in the contemporary and planned int...
Revisiting Conserved Charges in Higher Curvature Gravitational Theories
Ghodrati, M; Setare, M R
2016-01-01
Restricting the covariant gravitational phase spaces to the manifold of parametrized families of solutions, the mass, angular momenta, entropies, and electric charges can be calculated by a single and simple method. In this method, which has been called "solution phase space method", conserved charges are unambiguous and regular. Moreover, entropies and other conserved charges can be calculated on arbitrary surfaces, not necessarily horizons or asymptotics. Hence, the first law of thermodynamics would be simply an identity relating the exact symmetries to which the mass, angular momentum, electric charge and entropy are attributed. In this paper, we apply this powerful method to the $f(R)$ gravitational theories accompanied by the terms quadratic in the Riemann and Ricci tensors. Furthermore, conserved charges and the first law of thermodynamics for some of their black hole solutions are exemplified. The examples include Warped BTZ, charged static BTZ, and 3-dimensional $z=3$ Lifshitz black holes.
Theory and Numerics of Gravitational Waves from Preheating after Inflation
Dufaux, Jean Francois; Felder, Gary N; Kofman, Lev; Uzan, Jean-Philippe
2007-01-01
Preheating after inflation involves large, time-dependent field inhomogeneities, which act as a classical source of gravitational radiation. The resulting spectrum might be probed by direct detection experiments if inflation occurs at a low enough energy scale. In this paper, we develop a theory and algorithm to calculate, analytically and numerically, the spectrum of energy density in gravitational waves produced from an inhomogeneous background of stochastic scalar fields in an expanding universe. We derive some generic analytical results for the emission of gravity waves by stochastic media of random fields, which can test the validity/accuracy of numerical calculations. We contrast our method with other numerical methods in the literature, and then we apply it to preheating after chaotic inflation. In this case, we are able to check analytically our numerical results, which differ significantly from previous works. We discuss how the gravity wave spectrum builds up with time and find that the amplitude an...
Bethe ansatz matrix elements as non-relativistic limits of form factors of quantum field theory
Kormos, M.; Mussardo, G.; Pozsgay, B.
2010-01-01
We show that the matrix elements of integrable models computed by the algebraic Bethe ansatz (BA) can be put in direct correspondence with the form factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe ansatz model can be regarded as a suitable non-relativistic
Dohn, Asmus Ougaard; Møller, Klaus Braagaard; Sauer, Stephan P. A.
2013-01-01
The geometry of tetracyanoplatinate(II) (TCP) has been optimized with density functional theory (DFT) calculations in order to compare different computational strategies. Two approximate scalar relativistic methods, i.e. the scalar zeroth-order regular approximation (ZORA) and non-relativistic ca...
Gravitational Stokes parameters. [for electromagnetic and gravitational radiation in relativity
Anile, A. M.; Breuer, R. A.
1974-01-01
The electromagnetic and gravitational Stokes parameters are defined in the general theory of relativity. The general-relativistic equation of radiative transfer for polarized radiation is then derived in terms of the Stokes parameters for both high-frequency electromagnetic and gravitational waves. The concept of Stokes parameters is generalized for the most general class of metric theories of gravity, where six (instead of two) independent states of polarization are present.
Patil, Mandar; Mishra, Priti; Narasimha, D.
2017-01-01
Binary black holes have been in the limelight of late due to the detection of gravitational waves from coalescing compact binaries in the events GW150914 and GW151226. In this paper we study gravitational lensing by the binary black holes modeled as an equal mass Majumdar-Papapetrou dihole metric and show that this system displays features that are quite unprecedented and absent in any other lensing configuration investigated so far in the literature. We restrict our attention to the light rays which move on the plane midway between the two identical black holes, which allows us to employ various techniques developed for the equatorial lensing in the spherically symmetric spacetimes. If distance between the two black holes is below a certain threshold value, then the system admits two photon spheres. As in the case of a single black hole, infinitely many relativistic images are formed due to the light rays which turn back from the region outside the outer (unstable) photon sphere, all of which lie beyond a critical angular radius with respect to the lens. However, in the presence of the inner (stable) photon sphere, the effective potential after admitting minimum turns upwards and blows up for the smaller values of radii and the light rays that enter the outer photon sphere can turn back, leading to the formation of a new set of infinitely many relativistic images, all of which lie below the critical radius from the lens mentioned above. As the distance between the two black holes is increased, two photon spheres approach one another, merge and eventually disappear. In the absence of the photon sphere, apart from the formation of a finite number of discrete relativistic images, the system remarkably admits a radial caustic, which has never been observed in the context of relativistic lensing before. Thus the system of the binary black hole admits novel features both in the presence and absence of photon spheres. We discuss possible observational signatures and
Three findings to model a quantum-gravitational theory
Alfonso-Faus, Antonio
2008-01-01
In 1967 Zeldovich expressed the cosmological constant lambda in terms of G, m and h, the gravitational constant, the mass of a fundamental particle and Plancks constant. In 1972 Weinberg expressed m in terms of h, G, the speed of light c and the Hubble parameter H. We proved that both expressions are identical. We also found proportionality between c and H. The critical mass balancing the outward quantum mechanical spreading of the wave function, and its inward gravitational collapse, has been recently estimated. We identify this mass with Zeldovich and Weinberg mass. A semi classical gravity model is reinforced and provides an insight for the modelling of a quantum-gravitational theory. The time evolution of the peak probability density for a free particle, a wave function initially filling the whole Universe, explains the later geometrical properties of the fundamental particles. We prove that they end up acquiring a constant size given by their Compton wavelength. The size of the fundamental particles, as ...
Critical behavior in the Brans-Dicke theory of gravitation
Chiba, T; Chiba, Takeshi; Soda, Jiro
1996-01-01
The collapse of a massless scalar field in the Brans-Dicke theory of gravitation is studied in the analysis of both analytical solution and numerical one. By conformally transforming the Roberts's solution into the Brans-Dicke frame, we find for \\omega > -3/2 that a continuous self-similarity continues and that the critical exponent does depend on \\omega. By conformally transforming the Choptuik's solution into the Brans-Dicke frame, we find for \\omega > -3/2 that at the critical solution shows discrete self-similarity, however, the critical exponent depends strongly on \\omega while the echoing parameter weakly on it.
Stability of 2-body orbits in retarded gravitation theory (RGT)
Raju, C K
2015-01-01
The recently formulated retarded gravitation theory (RGT) explains the non-Newtonian velocities of stars in spiral galaxies, *without any new hypothesis*, and may hence be tested even in the laboratory. However, doubts have been expressed that those higher rotation velocities in RGT may be due to instabilities. We resolve these doubts by solving the full functional differential equations of RGT for a model 2-body planetary system. The solution is stable and closely agrees with the Newtonian solution for this planetary case. Thus, the big difference between RGT and Newtonian gravity for a spiral galaxy is not due to any instability in RGT.
New symbolic tools for differential geometry, gravitation, and field theory
Anderson, I. M.; Torre, C. G.
2012-01-01
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors, algebraic classification of solutions of the Einstein equations, and symmetry reduction of field equations.
Green's function relativistic mean field theory for Λ hypernuclei
Ren, S.-H.; Sun, T.-T.; Zhang, W.
2017-05-01
The relativistic mean field theory with the Green's function method is extended to study Λ hypernuclei. Taking the hypernucleus Ca61Λ as an example, the single-particle resonant states for Λ hyperons are investigated by analyzing the density of states, and the corresponding energies and widths are given. Different behaviors are observed for the resonant states, i.e., the distributions of the very narrow 1 f5 /2 and 1 f7 /2 states are very similar to bound states while those of the wide 1 g7 /2 and 1 g9 /2 states are like scattering states. Besides, the impurity effect of Λ hyperons on the single-neutron resonant states is investigated. For most of the resonant states, both the energies and widths decrease with adding more Λ hyperons due to the attractive Λ N interaction. Finally, the energy level structure of Λ hyperons in the Ca hypernucleus isotopes with mass number A =53 -73 are studied; obvious shell structure and small spin-orbit splitting are found for the single-Λ spectrum.
Spectral fine structure of the atomic ground states based on full relativistic theory
Zhenghe Zhu; Yongjian Tang
2011-01-01
@@ We focus on the full relativistic quantum mechanical calculations from boron to fluorine atoms with electronic configuration of 1s22s22pn (n = 1, 2, 3, 4, and 5), where 1s22s2 is the closed shell and 2pn is the open shell. Their active electrons in the open shell occupy all the six spinors as far as possible.Therefore, we suggest a new rule called "maximum probability" for the full symmetry group relativistic theory. Furthermore, the spectral fine structure of the atomic ground states based on the full relativistic theory and their intervals of L-S splitting are all reasonable. It is impossible to calculate the L-S splitting through non-relativistic quantum mechanics. The relativistic effect of atomic mass is increased significantly by about 12 folds from boron atom to fluorine atom.%We focus on the full relativistic quantum mechanical calculations from boron to fluorine atoms with electronic configuration of 1s22s22pn (n = 1, 2, 3, 4, and 5), where 1s22s2 is the closed shell and 2pn is the open shell. Their active electrons in the open shell occupy all the six spinors as far as possible.Therefore, we suggest a new rule called "maximum probability" for the full symmetry group relativistic theory. Furthermore, the spectral fine structure of the atomic ground states based on the full relativistic theory and their intervals of L-S splitting are all reasonable. It is impossible to calculate the L-S splitting through non-relativistic quantum mechanics. The relativistic effect of atomic mass is increased significantly by about 12 folds from boron atom to fluorine atom.
A new unified theory of electromagnetic and gravitational interactions
Li, Li-Xin
2016-12-01
In this paper we present a new unified theory of electromagnetic and gravitational interactions. By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime, we derive the complete set of field equations in the four-dimensional spacetime from the fivedimensional Einstein field equation. Besides the Einstein field equation in the four-dimensional spacetime, an electromagnetic field equation is obtained: ∇a F ab - ξ R b a A a = -4π J b with ξ = -2, where F ab is the antisymmetric electromagnetic field tensor defined by the potential vector A a , R ab is the Ricci curvature tensor of the hypersurface, and J a is the electric current density vector. The electromagnetic field equation differs from the Einstein-Maxwell equation by a curvature-coupled term ξ R b a A a , whose presence addresses the problem of incompatibility of the Einstein-Maxwell equation with a universe containing a uniformly distributed net charge, as discussed in a previous paper by the author [L.-X. Li, Gen. Relativ. Gravit. 48, 28 (2016)]. Hence, the new unified theory is physically different from Kaluza-Klein theory and its variants in which the Einstein-Maxwell equation is derived. In the four-dimensional Einstein field equation derived in the new theory, the source term includes the stress-energy tensor of electromagnetic fields as well as the stress-energy tensor of other unidentified matter. Under certain conditions the unidentified matter can be interpreted as a cosmological constant in the four-dimensional spacetime. We argue that, the electromagnetic field equation and hence the unified theory presented in this paper can be tested in an environment with a high mass density, e.g., inside a neutron star or a white dwarf, and in the early epoch of the universe.
Pitts, J Brian
2016-01-01
Classical and quantum field theory provide not only realistic examples of extant notions of empirical equivalence, but also new notions of empirical equivalence, both modal and occurrent. A simple but modern gravitational case goes back to the 1890s, but there has been apparently total neglect of the simplest relativistic analog, with the result that an erroneous claim has taken root that Special Relativity could not have accommodated gravity even if there were no bending of light. The fairly recent acceptance of nonzero neutrino masses shows that widely neglected possibilities for nonzero particle masses have sometimes been vindicated. In the electromagnetic case, there is permanent underdetermination at the classical and quantum levels between Maxwell's theory and the one-parameter family of Proca's electromagnetisms with massive photons, which approximate Maxwell's theory in the limit of zero photon mass. While Yang-Mills theories display similar approximate equivalence classically, quantization typically ...
Relativistic (SR-ZORA) quantum theory of atoms in molecules properties.
Anderson, James S M; Rodríguez, Juan I; Ayers, Paul W; Götz, Andreas W
2017-01-15
The Quantum Theory of Atoms in Molecules (QTAIM) is used to elucidate the effects of relativity on chemical systems. To do this, molecules are studied using density-functional theory at both the nonrelativistic level and using the scalar relativistic zeroth-order regular approximation. Relativistic effects on the QTAIM properties and topology of the electron density can be significant for chemical systems with heavy atoms. It is important, therefore, to use the appropriate relativistic treatment of QTAIM (Anderson and Ayers, J. Phys. Chem. 2009, 115, 13001) when treating systems with heavy atoms. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
Constraining gravitational interactions in the M theory effective action
Basu, Anirban
2013-01-01
We consider purely gravitational interactions of the type D^{2k} R^4 in the effective action of M theory in 11 dimensional flat spacetime, where k \\geq 0. The duality between M theory on S^1 and type IIA string theory, and the structure of the dilaton dependence of string amplitudes, show that the only non-vanishing interactions in the M theory effective action have k=3n. The coefficient of the D^{6n} R^4 interaction in M theory is determined by the genus (n+1) string amplitude of the D^{6n} R^4 interaction in the type IIA theory. Focussing on the even-even spin structure part of the type IIA string amplitude, this coefficient is given by the type IIB genus (n+1) amplitude, which we constrain using supersymmetry, S-duality and maximal supergravity. The source terms of the Poisson equations satisfied by the S-duality invariant IIB couplings play a central role in the analysis. This procedure yields partial contributions to several multi-loop type IIB string amplitudes, from which we extract the coefficients of...
Theory of superconductivity of gravitation and the dark matter enigma
Santiago-Germán, Wenceslao
2011-01-01
In this article, the question of the nature of cold dark matter is approached from a new angle. By invoking the Cauchy problem of relativity it is shown how, under very precise astrophysical conditions, the Einstein general theory of relativity is formally equivalent to the Ginzburg-Landau theory of superconductivity. This fact lead us to suspect that the superconductivity of gravitation ought to be a real physical process occurring in the outskirts of galaxies. It is found that quantum mechanically gravity can achieve a type-II superconductor state characterised by the Gizburg-Landau parameter $\\kappa=1.5$, and it is suggested that a probability flux of Cooper pairs (quantum gravitational geons charged with vacuum energy) are directly responsible for the flatness exhibited by the rotation curves in spiral galaxies, as well as the exotic behaviour observed in galactic cluster collisions. If this hypothesis proves correct, the whole phenomenon of dark matter may count, after all, as another triumph for Einstei...
5th International School on Field Theory and Gravitation
Following the philosophy that the International School on Field Theory and Gravitation must be held each three years in different Brazilian Universities and, if possible, in different brazilian states, the next meeting will take place at Physics Institute of Universidade Federal do Mato Grosso, UFMT, Cuiabá city on April, 20-24/2009 very close to the beautiful Pantanal and Chapada dos Guimarães area. The goal of the meeting is to promote a greater integration among many physicists from the local university, UFMT, Co-organizing institutions in Brasil and foreign countries such as Canada, USA, Italy, China, England, Swiss, Spain, Brazil and others; to stimulate the organization of scientific events in our physics Institute and thus contributing to local research activities; to exhibit different fields of physics and to stimulate new lines of theoretical research and technological developments in the Universidade Federal do Mato Grosso, UFMT. Finally, we make efforts to promote the development of advanced studies, taking it to the present core of research in a strong process of affirmation of new lines of theoretical studies in our Physics Institute. To this, we invite colleagues, collaborators, researchers, students, and friends to attend this fifth edition of International School on Field Theory and gravitation-2009.
Particle content and degrees of freedom of a gravitational field in 4th order theories of gravity
Moebius, K.
In gravitational theories of fourth order, the influence of certain properties of the field equations (tracelessness, conformal invariance, scale invariance, or their breaking) for the particle content (number of degrees of freedom, mass, and spin) is investigated. Using the Cauchy initial-value problem and a counting method first developed by Einstein, it is possible to get a useful definition of the concept of the degrees of freedom for the full nonlinear theory. This is due to the fact that this method incorporates the concrete structure of the field equations (and thus their nonlinearities). Analyzing different general-relativistic field theories via these approaches, the influence of the various structures of nonlinearities is discussed. It is, in particular, shown that those results obtained by the spin projection formalism can be reproduced by nonlinear methods.
Gravitational wave polarization modes in $f(R)$ theories
Rizwana, Kausar H; Philippe, Jetzer
2016-01-01
Many studies have been carried out in the literature to evaluate the number of polarization modes of gravitational waves in modified theories, in particular in $f(R)$ theories. In the latter ones, besides the usual two transverse-traceless tensor modes present in general relativity, there are two additional scalar ones: a massive longitudinal mode and a massless transverse mode (the so-called breathing mode). This last mode has often been overlooked in the literature, due to the assumption that the application of the Lorenz gauge implies transverse-traceless wave solutions. We however show that this is in general not possible and, in particular, that the traceless condition cannot be imposed due to the fact that we no longer have a Minkowski background metric. Our findings are in agreement with the results found using the Newman-Penrose formalism, and thus clarify the inconsistencies found so far in the literature.
The Affine Structure of Gravitational Theories: Symplectic Groups and Geometry
Capozziello, Salvatore; De Laurentis, Mariafelicia
2014-01-01
We give a geometrical description of gravitational theories from the viewpoint of symmetries and affine structure. We show how gravity, considered as a gauge theory, can be consistently achieved by the nonlinear realization of the conformal-affine group in an indirect manner: due the partial isomorphism between $CA\\left( 3,1\\right) $ and the centrally extended $Sp\\left( 8\\right) $, we perform a nonlinear realization of the centrally extended (CE)$Sp\\left( 8\\right) $ in its semi-simple version. In particular, starting from the bundle structure of gravity, we derive the conformal-affine Lie algebra and then, by the non-linear realization, we define the coset field transformations, the Cartan forms and the inverse Higgs constraints. Finally we discuss the geometrical Lagrangians where all the information on matter fields and their interactions can be contained.
Conservation laws in metric-affine gravitation theories: Superpotentials
Giachetta, G.; Giambo`, R.; Mangiarotti, L. [Camerino, Univ. (Italy). Dipt. di Matematica e Fisica
1997-08-01
By applying the machinery of the Lagrangian formalism in field theory, they study the conservation laws of a metric-affine gravitation theory in which the dynamical fields are the spin structures, the linear connections and the fermion fields on a 4-dimensional manifold. The system is assumed to be symmetric with respect to the group of all transformations of the spin bundle. The results obtained are the following. The currents associated with the infinitesimal vertical transformations of the symmetry group vanish identically. As a consequence, to every vector field on the world manifold there corresponds a well-defined current, namely the energy-momentum current. The superpotential term contained in this current is independent of the presence of fermion fields. The expression they get for the superpotential coincides with that found in the purely metric-affine context and generalized the well-known expression obtained by Komar.
Cosmology in new gravitational scalar-tensor theories
Saridakis, Emmanuel N
2016-01-01
We investigate the cosmological applications of new gravitational scalar-tensor theories, which are novel modifications of gravity possessing 2+2 propagating degrees of freedom, arising from a Lagrangian that includes the Ricci scalar and its first and second derivatives. Extracting the field equations we obtain an effective dark energy sector that consists of both extra scalar degrees of freedom, and we determine various observables. We analyze two specific models and we obtain a cosmological behavior in agreement with observations, i.e. transition from matter to dark energy era, with the onset of cosmic acceleration. Additionally, for a particular range of the model parameters, the equation-of-state parameter of the effective dark energy sector can exhibit the phantom-divide crossing. These features reveal the capabilities of these theories, since they arise solely from the novel, higher-derivative terms.
Gravitational collapse in Ho\\v{r}ava-Lifshitz theory
Greenwald, Jared; Satheeshkumar, V H; Wang, Anzhong
2013-01-01
We study gravitational collapse of a spherical fluid in Ho\\v{r}ava-Lifshitz theory with the projectability condition and an arbitrary coupling constant $\\lambda$, where $|\\lambda - 1|$ characterizes the deviation of the theory from general relativity in the infrared limit. The junction conditions across the surface of a collapsing star are derived under the (minimal) assumption that the junctions be mathematically meaningful in terms of generalized functions. When the collapsing star is made of a homogeneous and isotropic perfect fluid, {and} the external region is described by a stationary spacetime, the problem reduces to the matching of six independent conditions. When the perfect fluid is pressureless (a dust fluid), it is found that such matching is possible only in the case $\\lambda = 1$. In this case, the external spacetime is described by the Schwarzschild (anti-) de Sitter solution written in Painlev\\'e-Gullstrand coordinates. Our treatment can be easily generalized to other versions of Ho\\v{r}ava-Li...
Patil, Mandar; Narasimha, D
2016-01-01
Binary black holes have been in limelight off late due to the detection of gravitational waves from coalescing compact binaries in the events GW150914 and GW151226. In this paper we study gravitational lensing by the binary black holes modeled as equal mass Majumdar-Papapetrou dihole metric and show that this system displays features that are quite unprecedented and absent in any other lensing configuration investigated so far. We restrict our attention to the light rays which move on the plane midway between the two identical black holes, which allows us to employ techniques developed for the equatorial lensing in spherically symmetric spacetimes. If distance between the two black holes is below a certain threshold value, the system admits two photon spheres. As in the case of single black hole, infinitely many relativistic images are formed due to the light rays which turn back from the region outside the outer (unstable) photon sphere, all of which lie beyond a critical angular radius with respect to the l...
AlMuhammad, Anwar S
2002-01-01
Relying on the magnetic dipole model of the pulsar, we use the extension of the work of Haxton-Ruffini [31] for single charges by DePaolis-Ingrosso-Qadir [32] for an obliquely rotating magnetic dipole, to incorporate the effect of the gravitational mass. So, by using the numerical and analytical solutions of the differential equation for the radiation, we construct the energy spectra for different masses of the dipole-NS. These spectra show that, in relatively low angular momentum l, the effect of the gravitational mass is very significant in suppressing the relativistic enhancement factor, which had been found [27, 28, 32], by two to three orders of magnitude, as the mass changes from 0.5 solar mass to 3 solar masses. It is an indication that most of the angular momentum of the NS is retained as rotational kinetic energy instead of being radiated as an electromagnetic energy. Also, the suppressing in radiation energy is more or less independent of the angular momentum, and the high rotational velocity. We al...
Geometrical Unification of Gravitation and Dark Energy: The Universe as a Relativistic Particle
Hojman, Sergio A; Rubio, Carlos A
2014-01-01
The Lagrangian, the Hamilton--Jacobi equation and the Schr\\"{o}dinger, Dirac and Klein--Gordon equations for the Friedmann--Robertson--Walker--Quintessence (FRWQ) system are presented and solved exactly for different interesting scenarios. The classical Lagrangian reproduces the usual two (second order) dynamical equations for the radius of the Universe and for the scalar field as well as the (first order) constraint equation. The approach naturally unifies gravity and dark energy, which may be related to the tlaplon (scalar torsion potential). The Lagrangian and the equations of motion are those of a relativistic particle moving on a two dimensional spacetime where the conformal metric factor is related to the dark energy scalar field potential. This allows us to quantize the system, obtaining a Klein-Gordon equation when the Universe is considered as a spinless particle, and a Dirac equation when the Universe is thought as a relativistic spin particle.
B. Julia-Diaz, H. Kamano, T.-S. H. Lee, A. Matsuyama, T. Sato, N. Suzuki
2009-04-01
Within the relativistic quantum field theory, we analyze the differences between the $\\pi N$ reaction models constructed from using (1) three-dimensional reductions of Bethe-Salpeter Equation, (2) method of unitary transformation, and (3) time-ordered perturbation theory. Their relations with the approach based on the dispersion relations of S-matrix theory are dicusssed.
Unification of Non-Abelian SU(N) Gauge Theory and Gravitational Gauge Theory
WU Ning
2002-01-01
In this paper, a general theory on unification of non-Abelian SU(N) gauge interactions and gravitationalinteractions is discussed. SU(N) gauge interactions and gravitational interactions are formulated on the similar basisand are unified in a semi-direct product group GSU(N). Based on this model, we can discuss unification of fundamentalinteractions of Nature.
Ridgely, Charles T, E-mail: charles@ridgely.w [Thienes Engineering, Inc, La Mirada, CA 90638 (United States)
2011-03-15
When two gravitating bodies reside in a material medium, Newton's law of universal gravitation must be modified to account for the presence of the medium. A modified expression of Newton's law is known in the literature, but lacks a clear connection with existing gravitational theory. Newton's law in the presence of a homogeneous material medium is herein derived on the basis of classical, Newtonian gravitational theory and by a general relativistic use of Archimedes' principle. It is envisioned that the techniques presented herein will be most useful to graduate students and those undergraduate students having prior experience with vector analysis and potential theory.
Revisiting conserved charges in higher curvature gravitational theories
Ghodrati, M. [University of Michigan, Michigan Center for Theoretical Physics, Randall Laboratory of Physics, Ann Arbor, MI (United States); Hajian, K. [Institute for Research in Fundamental Sciences (IPM), School of Physics, P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Setare, M.R. [University of Kurdistan, Department of Science, Campus of Bijar, Bijar (Iran, Islamic Republic of)
2016-12-15
Restricting the covariant gravitational phase spaces to the manifold of parametrized families of solutions, the mass, angular momenta, entropies, and electric charges can be calculated by a single and simple method. In this method, which has been called the ''solution phase space method,'' conserved charges are unambiguous and regular. Moreover, assuming the generators of the charges to be exact symmetries, entropies and other conserved charges can be calculated on almost arbitrary surfaces, not necessarily horizons or asymptotics. Hence, the first law of thermodynamics would be a local identity relating the exact symmetries to which the mass, angular momentum, electric charge, and entropy are attributed. In this paper, we apply this powerful method to the f(R) gravitational theories accompanied by the terms quadratic in the Riemann and Ricci tensors. Furthermore, conserved charges and the first law of thermodynamics for some of their black hole solutions are exemplified. The examples include warped AdS{sub 3}, charged static BTZ, and 3-dimensional z = 3 Lifshitz black holes. (orig.)
Revisiting conserved charges in higher curvature gravitational theories
Ghodrati, M.; Hajian, K.; Setare, M. R.
2016-12-01
Restricting the covariant gravitational phase spaces to the manifold of parametrized families of solutions, the mass, angular momenta, entropies, and electric charges can be calculated by a single and simple method. In this method, which has been called the "solution phase space method," conserved charges are unambiguous and regular. Moreover, assuming the generators of the charges to be exact symmetries, entropies and other conserved charges can be calculated on almost arbitrary surfaces, not necessarily horizons or asymptotics. Hence, the first law of thermodynamics would be a local identity relating the exact symmetries to which the mass, angular momentum, electric charge, and entropy are attributed. In this paper, we apply this powerful method to the f( R) gravitational theories accompanied by the terms quadratic in the Riemann and Ricci tensors. Furthermore, conserved charges and the first law of thermodynamics for some of their black hole solutions are exemplified. The examples include warped AdS_3, charged static BTZ, and 3-dimensional z=3 Lifshitz black holes.
Smalley, L. L.
1983-01-01
The proper framework for testing Rastall's theory and its generalizations is in the case of non-negligible (i.e. discernible) gravitational effects such as gravity gradients. These theories have conserved integral four-momentum and angular momentum. The Nordtvedt effect then provides limits on the parameters which arise as the result of the non-zero divergence of the energy-momentum tensor.
Probing Gravitational Cat States in Canonical Quantum Theory vs Objective Collapse Theories
Derakhshani, Maaneli
2016-01-01
Using as a testbed the recently proposed "gravcat" experimental scheme in [1], we compare the properties of gravitational cat states in three descriptions: (1) canonical quantum theory (CQT) combined with the Newtonian limit of GR, (2) objective collapse theories (OCTs) extended to the regime of semiclassical Newtonian gravity, and (3) OCTs extended to incorporate quantized Newtonian gravity. For the CQT approach, we follow the treatment of Hu and Anastopoulos in [2]. For the OCTs, we conside...
Relativistic gravitational collapse in comoving coordinates: The post-quasistatic approximation
Herrera, L
2010-01-01
A general iterative method proposed some years ago for the description of relativistic collapse, is presented here in comoving coordinates. For doing that we redefine the basic concepts required for the implementation of the method for comoving coordinates. In particular the definition of the post-quasistatic approximation in comoving coordinates is given. We write the field equations, the boundary conditions and a set of ordinary differential equations (the surface equations) which play a fundamental role in the algorithm. As an illustration of the method, we show how to build up a model inspired in the well known Schwarzschild interior solution. Both, the adiabatic and non adiabatic, cases are considered.
Euclidean Complex Relativistic Mechanics: A New Special Relativity Theory
Vossos, Spyridon; Vossos, Elias
2015-09-01
Relativity Theory (RT) was fundamental for the development of Quantum Mechanics (QMs). Special Relativity (SR), as is applied until now, cancels the transitive attribute in parallelism, when three observers are related, because Lorentz Boost (LB) is not closed transformation. In this presentation, considering Linear Spacetime Transformation (LSTT), we demand the maintenance of Minkowski Spacetime Interval (S2). In addition, we demand this LSTT to be closed, so there is no need for axes rotation. The solution is the Vossos Matrix (ΛB) containing real and imaginary numbers. As a result, space becomes complex, but time remains real. Thus, the transitive attribute in parallelism, which is equivalent to the Euclidean Request (ER), is also valid for moving observers. Choosing real spacetime for the unmoved observer (O), all the natural sizes are real, too. Using Vossos Transformation (VT) for moving observers, the four-vectors’ zeroth component (such as energy) is real, in contrast with spatial components that are complex, but their norm is real. It is proved that moving (relative to O) human O' meter length, according to Lorentz Boost (LB). In addition, we find Rotation Matrix Vossos-Lorentz (RBL) that turns natural sizes’ complex components to real. We also prove that Speed of Light in Vacuum (c) is invariant, when complex components are used and VT is closed for three sequential observers. After, we find out the connection between two moving (relative to O) observers: X"= ΛLO"(o) ΛLO(O') X', using Lorentz Matrix (ΛL). We applied this theory, finding relations between natural sizes, that are the same as these extracted by Classic Relativity (CR), when two observers are related (i.e. relativistic Doppler shift is the same). But, the results are different, when more than two observers are related. VT of Electromagnetic Tensor (Fμv), leads to Complex Electromagnetic Fields (CEMFs) for a moving observer. When the unmoved observer O and a moving observer O' are
Towards an exact relativistic theory of Earth's geoid undulation
Kopeikin, Sergei M., E-mail: kopeikins@missouri.edu [Department of Physics & Astronomy, University of Missouri, Columbia, MO 65211 (United States); Siberian State Geodetic Academy, 10 Plakhotny St., Novosibirsk 630108 (Russian Federation); Mazurova, Elena M., E-mail: e_mazurova@mail.ru [Moscow State University of Geodesy and Cartography, 4 Gorokhovsky Alley, Moscow 105064 (Russian Federation); Siberian State Geodetic Academy, 10 Plakhotny St., Novosibirsk 630108 (Russian Federation); Karpik, Alexander P., E-mail: rector@ssga.ru [Siberian State Geodetic Academy, 10 Plakhotny St., Novosibirsk 630108 (Russian Federation)
2015-08-14
The present paper extends the Newtonian concept of the geoid in classic geodesy towards the realm of general relativity by utilizing the covariant geometric methods of the perturbation theory of curved manifolds. It yields a covariant definition of the anomalous (disturbing) gravity potential and formulates differential equation for it in the form of a covariant Laplace equation. The paper also derives the Bruns equation for calculation of geoid's height with full account for relativistic effects beyond the Newtonian approximation. A brief discussion of the relativistic Bruns formula is provided. - Highlights: • We apply general relativity to define the exact concept of relativistic geoid. • We derive relativistic equation of geoid and the reference level surface. • We employ the manifold perturbation theory to discuss geoid's undulation.
Theory of relativistic heat polynomials and one-sided Lévy distributions
Dattoli, G.; Górska, K.; Horzela, A.; Penson, K. A.; Sabia, E.
2017-06-01
The theory of pseudo-differential operators is a powerful tool to deal with differential equations involving differential operators under the square root sign. These types of equations are pivotal elements to treat problems in anomalous diffusion and in relativistic quantum mechanics. In this paper, we report on new links between fractional diffusion, quantum relativistic equations, and particular families of polynomials, linked to the Bessel polynomials in Carlitz form and playing the role of relativistic heat polynomials. We introduce generalizations of these polynomial families and point out their specific use for the solutions of problems of practical importance.
Ten-no, Seiichiro; Yamaki, Daisuke
2012-10-07
We propose explicitly correlated Ansatz for four-component relativistic methods within the framework of the no-pair approximation. Kinetically balanced geminal basis is derived to satisfy the cusp conditions in the non-relativistic limit based on the Lévy-Leblend-like equation. Relativistic variants of strong-orthogonality projection operator (Ansätze 2α and 2β) suitable for practical calculations are introduced by exploiting the orthogonal complement of the large-component basis. A pilot implementation is performed for the second order Møller-Plesset perturbation theory.
Effective gravitational couplings for cosmological perturbations in generalized Proca theories
De Felice, Antonio; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li
2016-01-01
We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lema\\^{i}tre-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to non-trivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling $G_{\\rm eff}$ with matter density perturbations under a quasi-static approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility ...
Relativistic Brueckner-Hartree-Fock theory for finite nuclei
Shen, Shihang; Liang, Haozhao; Meng, Jie; Ring, Peter; Zhang, Shuangquan
2016-01-01
Starting with a bare nucleon-nucleon interaction, for the first time the full relativistic Brueckner-Hartree-Fock equations are solved for finite nuclei in a Dirac-Woods-Saxon basis. No free parameters are introduced to calculate the ground-state properties of finite nuclei. The nucleus $^{16}$O is investigated as an example. The resulting ground-state properties, such as binding energy and charge radius, are considerably improved as compared with the non-relativistic Brueckner-Hartree-Fock results and much closer to the experimental data. This opens the door for \\emph{ab initio} covariant investigations of heavy nuclei.
Effective gravitational couplings for cosmological perturbations in generalized Proca theories
De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li
2016-08-01
We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to nontrivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling Geff with matter density perturbations under a quasistatic approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility for reducing Geff. In fact, within the parameter space, Geff can be even smaller than the Newton gravitational constant G at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter η and the evolution of the growth rate f σ8 are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the Λ CDM model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry.
Gravitational Cherenkov losses in theories based on modified Newtonian dynamics.
Milgrom, Mordehai
2011-03-18
Survival of high-energy cosmic rays (HECRs) against gravitational Cherenkov losses is shown not to cast strong constraints on modified Newtonian dynamics (MOND) theories that are compatible with general relativity (GR): theories that coincide with GR for accelerations ≫a(0) (a(0) is the MOND constant). The energy-loss rate, E, is many orders smaller than those derived in the literature for theories with no extra scale. Modification to GR, which underlies E, enters only beyond the MOND radius of the particle: r(M)=(Gp/ca(0))(1/2). The spectral cutoff, entering E quadratically, is thus r(M)(-1), not k(dB)=p/ℏ. Thus, E is smaller than published rates, which use k(dB), by a factor ∼(r(M)k(dB))(2)≈10(39)(cp/3×10(11) Gev)(3). Losses are important only beyond D(loss)≈qℓ(M), where q is a dimensionless factor, and ℓ(M)=c(2)/a(0) is the MOND length, which is ≈2π times the Hubble distance.
Some classes of gravitational shock waves from higher order theories of gravity
Oikonomou, V. K.
2017-02-01
We study the gravitational shock wave generated by a massless high energy particle in the context of higher order gravities of the form F(R,R_{μν}R^{μν},R_{μναβ}R^{μν αβ}). In the case of F(R) gravity, we investigate the gravitational shock wave solutions corresponding to various cosmologically viable gravities, and as we demonstrate the solutions are rescaled versions of the Einstein-Hilbert gravity solution. Interestingly enough, other higher order gravities result to the general relativistic solution, except for some specific gravities of the form F(R_{μν}R^{μν}) and F(R,R_{μν}R^{μν}), which we study in detail. In addition, when realistic Gauss-Bonnet gravities of the form R+F(G) are considered, the gravitational shock wave solutions are identical to the general relativistic solution. Finally, the singularity structure of the gravitational shock waves solutions is studied, and it is shown that the effect of higher order gravities makes the singularities milder in comparison to the general relativistic solutions, and in some particular cases the singularities seem to be absent.
COMPRESSIBILITY OF NUCLEI IN RELATIVISTIC MEAN FIELD-THEORY
BOERSMA, HF; MALFLIET, R; SCHOLTEN, O
1991-01-01
Using the relativistic Hartree approximation in the sigma-omega model we study the isoscalar giant monopole resonance. It is shown that the ISGMR of lighter nuclei has non-negligible anharmonic terms. The compressibility of nuclear matter is determined using a leptodermous expansion.
Theory of non-relativistic three-particle scattering
Malfliet, R.; Ruijgrok, Th.
1967-01-01
A new method, using asymptotically stationary states, is developed to calculate the S-matrix for the scattering of a non-relativistic particle by the bound state of two other particles. For the scattering with breakup of this bound state, we obtain a simplified form of the Faddeev integral
Classical field theory on electrodynamics, non-Abelian gauge theories and gravitation
Scheck, Florian
2012-01-01
The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes wit...
Tensor Fields in Relativistic Quantum Mechanics
Dvoeglazov, Valeriy V
2015-01-01
We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We discuss corresponding massless limits. We analize the quantum field theory taking into account the mass dimensions of the notoph and the photon. Next, we deduced the gravitational field equations from relativistic quantum mechanics.
Dynamics of perturbations in Double Field Theory & non-relativistic string theory
Ko, Sung Moon [Department of Physics, Sogang University,Seoul 121-742 (Korea, Republic of); Melby-Thompson, Charles M. [Kavli Institute for the Physics and Mathematics of the Universe (WPI),The University of Tokyo Institutes for Advanced Study (UTIAS), The University of Tokyo,Kashiwanoha, Kashiwa, 277-8583 (Japan); Department of Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Meyer, René [Kavli Institute for the Physics and Mathematics of the Universe (WPI),The University of Tokyo Institutes for Advanced Study (UTIAS), The University of Tokyo,Kashiwanoha, Kashiwa, 277-8583 (Japan); Park, Jeong-Hyuck [Department of Physics, Sogang University,Seoul 121-742 (Korea, Republic of)
2015-12-22
Double Field Theory provides a geometric framework capable of describing string theory backgrounds that cannot be understood purely in terms of Riemannian geometry — not only globally (‘non-geometry’), but even locally (‘non-Riemannian’). In this work, we show that the non-relativistic closed string theory of Gomis and Ooguri http://dx.doi.org/10.1063/1.1372697 arises precisely as such a non-Riemannian string background, and that the Gomis-Ooguri sigma model is equivalent to the Double Field Theory sigma model of http://dx.doi.org/10.1016/j.nuclphysb.2014.01.003 on this background. We further show that the target-space formulation of Double Field Theory on this non-Riemannian background correctly reproduces the appropriate sector of the Gomis-Ooguri string spectrum. To do this, we develop a general semi-covariant formalism describing perturbations in Double Field Theory. We derive compact expressions for the linearized equations of motion around a generic on-shell background, and construct the corresponding fluctuation Lagrangian in terms of novel completely covariant second order differential operators. We also present a new non-Riemannian solution featuring Schrödinger conformal symmetry.
More about a successful vector-tensor theory of gravitation
Dale, Roberto
2016-01-01
The vector-tensor (VT) theory of gravitation revisited in this article was studied in previous papers, where it was proved that VT works and deserves attention. New observational data and numerical codes have motivated further development which is presented here. New research has been planed with the essential aim of proving that current cosmological observations, including Planck data, baryon acoustic oscillations (BAO), and so on, may be explained with VT, a theory which accounts for a kind of dark energy which has the same equation of state as vacuum. New versions of the codes CAMB and COSMOMC have been designed for applications to VT, and the resulting versions have been used to get the cosmological parameters of the VT model at suitable confidence levels. The parameters to be estimated are the same as ingeneral relativity (GR), plus a new parameter $D$. For $D=0$, VT linear cosmological perturbations reduces to those of GR, but the VT background may explain dark energy. The fits between observations and ...
More about a successful vector-tensor theory of gravitation
Dale, R.; Sáez, D.
2017-01-01
The vector-tensor (VT) theory of gravitation revisited in this article was studied in previous papers, where it was proved that VT works and deserves attention. New observational data and numerical codes have motivated further development which is presented here. New research has been planed with the essential aim of proving that current cosmological observations, including Planck data, baryon acoustic oscillations (BAO), and so on, may be explained with VT, a theory which accounts for a kind of dark energy which has the same equation of state as vacuum. New versions of the codes CAMB and COSMOMC have been designed for applications to VT, and the resulting versions have been used to get the cosmological parameters of the VT model at suitable confidence levels. The parameters to be estimated are the same as in general relativity (GR), plus a new parameter D. For D = 0, VT linear cosmological perturbations reduces to those of GR, but the VT background may explain dark energy. The fits between observations and VT predictions lead to non vanishing |D| upper limits at the 1σ confidence level. The value D = 0 is admissible at this level, but this value is not that of the best fit in any case. Results strongly suggest that VT may explain current observations, at least, as well as GR; with the advantage that, as it is proved in this paper, VT has an additional parameter which facilitates adjustments to current observational data.
Relativistic n-body wave equations in scalar quantum field theory
Emami-Razavi, Mohsen [Centre for Research in Earth and Space Science, York University, Toronto, Ontario, M3J 1P3 (Canada)]. E-mail: mohsen@yorku.ca
2006-09-21
The variational method in a reformulated Hamiltonian formalism of Quantum Field Theory (QFT) is used to derive relativistic n-body wave equations for scalar particles (bosons) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic n-body wave equations. The equations are shown to have the Schroedinger non-relativistic limits, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Some examples of approximate ground state solutions of the n-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields.
Excess Charge for Pseudo-relativistic Atoms in Hartree-Fock Theory
Dall'Acqua, Anna; Solovej, Jan Philip
2010-01-01
We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge $Z$ and the fine structure constant $\\alpha$ as long as $Z\\alpha$ is bounded.......We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge $Z$ and the fine structure constant $\\alpha$ as long as $Z\\alpha$ is bounded....
Excess Charge for Pseudo-relativistic Atoms in Hartree-Fock Theory
Dall'Acqua, Anna; Solovej, Jan Philip
2010-01-01
We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge $Z$ and the fine structure constant $\\alpha$ as long as $Z\\alpha$ is bounded.......We prove within the Hartree-Fock theory of pseudo-relativistic atoms that the maximal negative ionization charge and the ionization energy of an atom remain bounded independently of the nuclear charge $Z$ and the fine structure constant $\\alpha$ as long as $Z\\alpha$ is bounded....
Non-relativistic Schroedinger theory on q-deformed quantum spaces III, Scattering theory
Wachter, H
2007-01-01
This is the third part of a paper about non-relativistic Schroedinger theory on q-deformed quantum spaces like the braided line or the three-dimensional q-deformed Euclidean space. Propagators for the free q-deformed particle are derived and their basic properties are discussed. A time-dependent formulation of scattering is proposed. In this respect, q-analogs of the Lippmann-Schwinger equation are given. Expressions for their iterative solutions are written down. It is shown how to calculate S-matrices and transition probabilities. Furthermore, attention is focused on the question what becomes of unitarity of S-matrices in a q-deformed setting. The examinations are concluded by a discussion of the interaction picture and its relation to scattering processes.
Towards a Gravitational Analog to S-duality in Non-abelian Gauge Theories
García-Compéan, H; Plebanski, J F; Ramírez, C
1998-01-01
It is well known that Yang-Mills theories do possess a phase of non-Abelian strong-weak duality invariance. Moreover, dual theories, with inverted couplings, to non-Abelian, non-supersymmetric gauge theories have been constructed. Following a similar procedure we propose a non-dynamical gravitational analog to this kind of theories.
A probability theory for non-equilibrium gravitational systems
Peñarrubia, Jorge
2015-08-01
This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed as a special type of diffusion process in the integral-of-motion space. In time-varying potentials with a fixed spatial symmetry the diffusion coefficients are closely related to virial quantities, such as the specific moment of inertia, the virial factor and the mean kinetic and potential energy of microcanonical particle ensembles. The non-equilibrium distribution function is found by convolving the initial distribution function with the Green function that solves Einstein's equation for freely diffusing particles. Such a convolution also yields a natural solution to the Fokker-Planck equations in the energy space. Our mathematical formalism can be generalized to potentials with a time-varying symmetry, where diffusion extends over multiple dimensions of the integral-of-motion space. The new probability theory is in many ways analogous to stochastic calculus, with two significant differences: (i) the equations of motion that govern the trajectories of particles are fully deterministic, and (ii) the diffusion coefficients can be derived self-consistently from microcanonical phase-space averages without relying on ergodicity assumptions. For illustration we follow the cold collapse of N-body models in a time-dependent logarithmic potential. Comparison between the analytical and numerical results shows excellent agreement in regions where the potential evolution does not depart too strongly from the adiabatic regime.
grim: A Flexible, Conservative Scheme for Relativistic Fluid Theories
Chandra, Mani; Foucart, Francois; Gammie, Charles F.
2017-03-01
Hot, diffuse, relativistic plasmas such as sub-Eddington black-hole accretion flows are expected to be collisionless, yet are commonly modeled as a fluid using ideal general relativistic magnetohydrodynamics (GRMHD). Dissipative effects such as heat conduction and viscosity can be important in a collisionless plasma and will potentially alter the dynamics and radiative properties of the flow from that in ideal fluid models; we refer to models that include these processes as Extended GRMHD. Here we describe a new conservative code, grim, that enables all of the above and additional physics to be efficiently incorporated. grim combines time evolution and primitive variable inversion needed for conservative schemes into a single step using an algorithm that only requires the residuals of the governing equations as inputs. This algorithm enables the code to be physics agnostic as well as flexibility regarding time-stepping schemes. grim runs on CPUs, as well as on GPUs, using the same code. We formulate a performance model and use it to show that our implementation runs optimally on both architectures. grim correctly captures classical GRMHD test problems as well as a new suite of linear and nonlinear test problems with anisotropic conduction and viscosity in special and general relativity. As tests and example applications, we resolve the shock substructure due to the presence of dissipation, and report on relativistic versions of the magneto-thermal instability and heat flux driven buoyancy instability, which arise due to anisotropic heat conduction, and of the firehose instability, which occurs due to anisotropic pressure (i.e., viscosity). Finally, we show an example integration of an accretion flow around a Kerr black hole, using Extended GRMHD.
Symmetries in tetrad theories. [of gravitational fields and general relativity
Chinea, F. J.
1988-01-01
The isometry conditions for gravitational fields are given directly at the tetrad level, rather than in terms of the metric. As an illustration, an analysis of the curvature collineations and Killing fields for a twisting type-N vacuum gravitational field is made.
Gravitomagnetic corrections on gravitational waves
Capozziello, S; Forte, L; Garufi, F; Milano, L
2009-01-01
Gravitational waveforms and production could be considerably affected by gravitomagnetic corrections considered in relativistic theory of orbits. Beside the standard periastron effect of General Relativity, new nutation effects come out when c^{-3} corrections are taken into account. Such corrections emerge as soon as matter-current densities and vector gravitational potentials cannot be discarded into dynamics. We study the gravitational waves emitted through the capture, in the gravitational field of massive binary systems (e.g. a very massive black hole on which a stellar object is inspiralling) via the quadrupole approximation, considering precession and nutation effects. We present a numerical study to obtain the gravitational wave luminosity, the total energy output and the gravitational radiation amplitude. From a crude estimate of the expected number of events towards peculiar targets (e.g. globular clusters) and in particular, the rate of events per year for dense stellar clusters at the Galactic Cen...
Harder, T Mark
2016-01-01
It is shown how Fermionic material particles can emerge from a covariant formulation of the de Broglie-Bohm theory. Material particles are continuous fields, formed as the eigenvalue of the Schrodinger field operator, evaluated along a Bohmian trajectory. The motivation for this work is due to a theorem proved by Malament that states there cannot be a relativistic quantum mechanics of localizable particles.
Shape Coexistence for 179Hg in Relativistic Mean-Field Theory
WANG Nan; MENG Jie; ZHAO En-Guang
2005-01-01
The potential energy surface of179 Hg is traced and the multi-shape coexistence phenomenon in that nucleus is studied within the relativistic mean-field theory with quadrupole moment constraint. The calculation results of binding energies and charge radii of mercury isotopes are in good agreement with the experimental data.
On the Theory of Resonances in Non-Relativistic QED and Related Models
Abou Salem, Walid K.; Faupin, Jeremy; Froehlich, Juerg;
We study the mathematical theory of quantum resonances in the standard model of non-relativistic QED and in Nelson's model. In particular, we estimate the survival probability of metastable states corresponding to quantum resonances and relate the resonances to poles of an analytic continuation...
Amplification of Gravitational Waves During Inflation in Brans-Dicke Theory
Berman, M S; Berman, Marcelo S.; Trevisan, Luis A.
2001-01-01
We show that Gravitational Waves are exponetially amplified in the inflationary phase in Brans-Dicke theory, so that it would be possible to detect them and in this way verify several features of physical reality.
Spacetime Dependence of Local Temperature in Relativistic Quantum Field Theory
Gransee, Michael
2016-01-01
The spacetime dependence of the inverse temperature four-vector $\\boldsymbol{\\beta}$ for certain states of the quantized Klein-Gordon field on (parts of) Minkowski spacetime is discussed. These states fulfill a recently proposed version of the Kubo-Martin-Schwinger (KMS) boundary value condition, the so-called "local KMS (LKMS) condition". It turns out that, depending on the mass parameter $m\\geq 0$, any such state can be extended either (i) to a LKMS state on some forward or backward lightcone, with $\\boldsymbol{\\beta}$ depending linearily on spacetime, or (ii) to a thermal equilibrium (KMS) state on all of Minkowski space with constant $\\boldsymbol{\\beta}$. This parallels previously known results for local thermal equilibrium (LTE) states of the quantized Klein-Gordon field. Furthermore, in the case of a massless field our results point to a discrepancy with some classic results in general approaches to (non-quantum) relativistic thermodynamics.
Theoretical frameworks for testing relativistic gravity. 5: Post-Newtonian limit of Rosen's theory
Lee, D. L.; Caves, C. M.
1974-01-01
The post-Newtonian limit of Rosen's theory of gravity is evaluated and is shown to be identical to that of general relativity, except for the PPN parameter alpha sub 2, which is related to the difference in propagation speeds for gravitational and electromagnetic waves. Both the value of alpha sub 2 and the value of the Newtonian gravitational constant depend on the present cosmological structure of the Universe. If the cosmological structure has a specific but presumably special form, the Newtonian gravitational constant assumes its current value, alpha sub 2 is zero, the post-Newtonian limit of Rosen's theory is identical to that of general relativity--and standard solar system experiments cannot distinguish between the two theories.
Theoretical frameworks for testing relativistic gravity. V - Post-Newtonian limit of Rosen's theory
Lee, D. L.; Ni, W.-T.; Caves, C. M.; Will, C. M.
1976-01-01
The post-Newtonian limit of Rosen's theory of gravity is evaluated and is shown to be identical to that of general relativity, except for the post-Newtonian parameter alpha sub 2 (which is related to the difference in propagation speeds for gravitational and electromagnetic waves). Both the value of alpha sub 2 and the value of the Newtonian gravitational constant depend on the present cosmological structure of the Universe. If the cosmological structure has a specific (but presumably special) form, the Newtonian gravitational constant assumes its current value, alpha sub 2 is zero, the post-Newtonian limit of Rosen's theory is identical to that of general relativity - and standard solar system experiments cannot distinguish between the two theories.
Classical Electron Model with Negative Energy Density in Einstein-Cartan Theory of Gravitation
Ray, S; Ray, Saibal; Bhadra, Sumana
2002-01-01
Experimental result regarding the maximum limit of the radius of the electron \\sim 10^{-16} cm and a few of the theoretical works suggest that the gravitational mass which is a priori a positive quantity in Newtonian mechanics may become negative in general theory of relativity. It is argued that such a negative gravitational mass and hence negative energy density also can be obtained with a better physical interpretation in the framework of Einstein-Cartan theory.
QIAN Shang-Wu
2006-01-01
This paper briefly discusses some interesting features for the external region of the spherical symmetric mass in the new theory of gravitation VGM, Le. The theory of gravitation by considering the vector graviton field and the metric field, such as pseudo-singularity, curvature tensor, static limit, event horizon, and the radial motion of a particle. All these features are different from the corresponding features obtained from general relativity.
Poles in the $S$-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics
Dandekar, Yogesh; Minwalla, Shiraz
2014-01-01
An all orders formula for the $S$-matrix for 2 $\\rightarrow$ 2 scattering in large N Chern-Simons theory coupled to a fundamental scalar has recently been conjectured. We find a scaling limit of the theory in which the pole in this $S$-matrix is near threshold. We argue that the theory must be well described by non-relativistic quantum mechanics in this limit, and determine the relevant Schroedinger equation. We demonstrate that the $S$-matrix obtained from this Schroedinger equation agrees perfectly with this scaling limit of the relativistic $S$-matrix; in particular the pole structures match exactly. We view this matching as a nontrivial consistency check of the conjectured field theory $S$-matrix.
Operator Product Expansion and Conservation Laws in Non-Relativistic Conformal Field Theories
Golkar, Siavash
2014-01-01
We explore the consequences of conformal symmetry for the operator product expansions in nonrelativistic field theories. Similar to the relativistic case, the OPE coefficients of descendants are related to that of the primary. However, unlike relativistic CFTs the 3-point function of primaries is not completely specified by conformal symmetry. Here, we show that the 3-point function between operators with nonzero particle number, where (at least) one operator has the lowest dimension allowed by unitarity, is determined up to a numerical coefficient. We also look at the structure of the family tree of primaries with zero particle number and discuss the presence of conservation laws in this sector.
On the microscopic nature of dissipative effects in special relativistic kinetic theory
Garcia-Perciante, A L; Garcia-Colin, L S
2010-01-01
A microscopic formulation of the definition of both the heat flux and the viscous stress tensor is proposed in the framework of kinetic theory for relativistic gases emphasizing on the physical nature of such fluxes. A Lorentz transformation is introduced as the link between the laboratory and local comoving frames and thus between molecular and chaotic velocities. With such transformation, the dissipative effects can be identified as the averages of the chaotic kinetic energy and the momentum flux out of equilibrium, respectively. Within this framework, a kinetic foundation of the ensuing transport equations for the relativistic gas is achieved. To our knowledge, this result is completely novel.
Relativistic transport theory for simple fluids at first order in the gradients: a stable picture
Sandoval-Villalbazo, A; García-Colin, L S
2008-01-01
In this paper we show how using a relativistic kinetic equation. The ensuing expression for the heat flux can be casted in the form required by Classical Irreversible Thermodynamics. Indeed, it is linearly related to the temperature and number density gradients and not to the acceleration as the so called first order in the gradients theories contend. Since the specific expressions for the transport coefficients are irrelevant for our purposes, the BGK form of the kinetic equation is used. Moreover, from the resulting hydrodynamic equations it is readily seen that no instabilities are present in the transverse hydrodynamic velocity mode of the simple relativistic fluid.
One-Proton Halo in 31Cl with Relativistic Mean-Field Theory
蔡翔舟; 沈文庆; 任中洲; 蒋维洲; 方德清; 张虎勇; 钟晨; 魏义彬; 郭威; 马余刚; 朱志远
2002-01-01
We investigate proton-rich isotopes s1,32Cl using the nonlinear relativistic mean-field model. It is shown that this model can reproduce the properties of these nuclei well. A long tail appears in the calculated proton density distribution of 31 Cl. The results of relativistic density-dependent Hartree theory show a similar trend of tail density distribution. It is strongly suggested that there is a proton halo in 31Cl and it is indicated that there may be a proton skin in 32 Cl. The relation between the proton halo in 31Cl and the new proton magic number is discussed.
Breit-Pauli and direct perturbation theory calculations of relativistic helium polarizability.
Cencek, W; Szalewicz, K; Jeziorski, B
2001-06-18
Large Gaussian-type geminal wave function expansions and direct perturbation theory (DPT) of relativistic effects have been applied to calculate the relativistic contribution to the static dipole polarizability of the helium atom. It has been demonstrated that DPT is superior for this purpose to traditional Breit-Pauli calculations. The resulting value of the molar polarizability of 4He is 0.517254(1) cm3 x mol(-1), including a literature estimate of QED effects. As a by-product, a very accurate value of the nonrelativistic helium second hyperpolarizability, gamma = 43.104227(1) atomic units (without the mass-polarization correction), has been obtained.
Effective Gravitational Theories in String Theory and the AdS/CFT Correspondence
Pedersen, Andreas Vigand
We consider various aspects of effective gravitational theories, including supergravity, within the framework of the blackfold approach. The thesis is naturally split into three parts. In the first part of the thesis, we explore the blackfold approach and explain how it is possible to write down...... an effective theory for higher dimensional extended black holes in a uid/elastic perturbative derivative expansion. Moreover, we show that the approach is quite universal and can be extended to various supergravities. Finally, we consider a new generalization of the method, which allows us to treat (SUGRA......) probe branes in uxed dilatonic backgrounds. In the second part, we construct and analyze thermal spinning giant gravitons in IIB/M-theory. The analysis employs the thermal brane probe method based on the blackfold approach. In addition to heating up the solution, and examining the effects from having...
Towards a Gravitational Analog to S-duality in Non-abelian Gauge Theories
Garcia-Compean, H.; Obregon, O.; Plebanski, J. F.; Ramirez, C.
1997-01-01
For non-abelian non-supersymmetric gauge theories, generic dual theories have been constructed. In these theories the couplings appear inverted. However, they do not possess a Yang-Mills structure but rather are a kind of non-linear sigma model. It is shown that for a topological gravitational model an analog to this duality exists.
Nesterov, Dmitry, E-mail: nesterov@lpi.r [Laboratoire de Mathematiques et Physique Theorique, Universite Francois-Rabelais Tours, Federation Denis Poisson - CNRS, Parc de Grandmont, 37200 Tours (France)] [Theory Department, Lebedev Physical Institute, Leninsky Prospect 53, Moscow, Russia, 119991 (Russian Federation); Solodukhin, Sergey N., E-mail: Sergey.Solodukhin@lmpt.univ-tours.f [Laboratoire de Mathematiques et Physique Theorique, Universite Francois-Rabelais Tours, Federation Denis Poisson - CNRS, Parc de Grandmont, 37200 Tours (France)
2011-01-11
We calculate parameters in the low energy gravitational effective action and the entanglement entropy in a wide class of theories characterized by improved ultraviolet (UV) behavior. These include (i) local and non-local Lorentz invariant theories in which inverse propagator is modified by higher-derivative terms and (ii) theories described by non-Lorentz invariant Lifshitz type field operators. We demonstrate that the induced cosmological constant, gravitational couplings and the entropy are sensitive to the way the theory is modified in UV. For non-Lorentz invariant theories the induced gravitational effective action is of the Horava-Lifshitz type. We show that under certain conditions imposed on the dimension of the Lifshitz operator the couplings of the extrinsic curvature terms in the effective action are UV finite. Throughout the paper we systematically exploit the heat kernel method appropriately generalized for the class of theories under consideration.
Robin, Caroline
2016-01-01
A new theoretical approach to spin-isospin excitations in open-shell nuclei is presented. The developed method is based on the relativistic meson-exchange nuclear Lagrangian of Quantum Hadrodynamics and extends the response theory for superfluid nuclear systems beyond relativistic quasiparticle random phase approximation in the proton-neutron channel (pn-RQRPA). The coupling between quasiparticle degrees of freedom and collective vibrations (phonons) introduces a time-dependent effective interaction, in addition to the exchange of pion and $\\rho$-meson taken into account without retardation. The time-dependent contributions are treated in the resonant time-blocking approximation, in analogy to previously developed relativistic quasiparticle time blocking approximation (RQTBA) in the neutral (non-isospin-flip) channel. The new method is called proton-neutron RQTBA (pn-RQTBA) and applied to Gamow-Teller resonance in a chain of neutron-rich Nickel isotopes $^{68-78}$Ni. A strong fragmentation of the resonance al...
Suleymanov, Michael; Horwitz, Lawrence; Yahalom, Asher
2017-06-01
A relativistic 4D string is described in the framework of the covariant quantum theory first introduced by Stueckelberg [ Helv. Phys. Acta 14, 588 (1941)], and further developed by Horwitz and Piron [ Helv. Phys. Acta 46, 316 (1973)], and discussed at length in the book of Horwitz [Relativistic Quantum Mechanics, Springer (2015)]. We describe the space-time string using the solutions of relativistic harmonic oscillator [ J. Math. Phys. 30, 66 (1989)]. We first study the problem of the discrete string, both classically and quantum mechanically, and then turn to a study of the continuum limit, which contains a basically new formalism for the quantization of an extended system. The mass and energy spectrum are derived. Some comparison is made with known string models.
Dynamical Relativistic Systems and the Generalized Gauge Fields of Manifestly Covariant Theories
Horwitz, L P
1998-01-01
The problem of the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on phase space. The original work of Zaslovskii et al showed that the resulting evolution contains a stochastic flow in phase space to unbounded energy. Subsequent studies have formulated the problem in terms of a relativistically charged particle in interaction with the electromagnetic field. We review the standard derivation of the covariant Lorentz force, and review the structure of the relativistic equations used to study this problem. We show that the Lorentz force equation can be derived as well from the manifestly covariant mechanics of Stueckelberg in the presence of a standard Maxwell field. We show how this agreement is achieved, and criticize some of the fundamental assumptions underlying these derivations. We argue that a more complete theory, involving ``off-shell'' electromagnetic fields should be utilized. We then discuss the formulation of the off-shell electromagne...
Mueller, Bernhard; Marek, Andreas
2012-01-01
We present a detailed theoretical analysis of the gravitational-wave (GW) signal of the post-bounce evolution of core-collapse supernovae (SNe), employing for the first time relativistic, two-dimensional (2D) explosion models with multi-group, three-flavor neutrino transport based on the ray-by-ray-plus approximation. The waveforms reflect the accelerated mass motions associated with the characteristic evolutionary stages that were also identified in previous works: A quasi-periodic modulation by prompt postshock convection is followed by a phase of relative quiescence before growing amplitudes signal violent hydrodynamical activity due to convection and the standing accretion shock instability during the accretion period of the stalled shock. Finally, a high-frequency, low-amplitude variation from proto-neutron star (PNS) convection below the neutrinosphere appears superimposed on the low-frequency trend associated with the aspherical expansion of the SN shock after the onset of the explosion. Relativistic e...
Without gravity, you would float into space. Gravity pulls matter together: it holds us onto the Earth, it holds the Earth in orbit around the sun and it holds our solar system in orbit about the centre of the galaxy. Everything with mass feels the attraction of gravity. The strength of the attraction between 2 objects depends on their masses. Despite its omnipresence, gravity is the weakest of the 4 forces. It is insignificant at the scale of human beings: when a group of visitors walks past, gravity doesn't pull you towards them! At even smaller scales, the gravitational pull between the electron and the proton is about 1040 times weaker than the electromagnetic attraction between them. Text for the interactive: Why does the same mass weigh more on the Earth than on the moon ?
Theory of Relativistic Reference Frames for High-Precision Astrometric Space Missions
Kopeikin, S M
2000-01-01
Recent modern space missions deliver invaluable information about origin of our universe, physical processes in the vicinity of black holes and other exotic astrophysical objects, stellar dynamics of our galaxy, etc. On the other hand, space astrometric missions make it possible to determine with unparalleled precision distances to stars and cosmological objects as well as their physical characteristics and positions on the celestial sphere. Permanently growing accuracy of space astronomical observations and the urgent need for adequate data processing algorithms require corresponding development of an adequate theory of reference frames along with unambiguous description of propagation of light rays from a source of light to observer. Such a theory must be based on the Einstein's general relativity and account for numerous relativistic effects both in the solar system and outside of its boundary. The main features of the relativistic theory of reference frames are presented in this work. A hierarchy of the f...
Stephan, Karl D
2016-01-01
After centuries, the long-standing problem of the nature of ball lightning may be closer to a solution. The relativistic-microwave theory of ball lightning recently proposed by Wu accounts for many of the leading characteristics of ball lightning, which most previous theories have failed to do. It involves the impact of a lightning-caused relativistic electron bunch to soil, producing an EM pulse that forms a plasma bubble. While the theory presents a plausible account of ball-lightning formation, storing electromagnetic energy long enough to account for the observed lifetime of such objects was not demonstrated. Here we show how such a structure can develop the high Q factor (~10^10) needed for the observed lifetimes of ~seconds for ball lightning, and show that the structure is radially stable, given certain assumptions.
Frontiers in relativistic celestial mechanics
2014-01-01
Relativistic celestial mechanics – investigating the motion celestial bodies under the influence of general relativity – is a major tool of modern experimental gravitational physics. With a wide range of prominent authors from the field, this two-volume series consists of reviews on a multitude of advanced topics in the area of relativistic celestial mechanics – starting from more classical topics such as the regime of asymptotically-flat spacetime, light propagation and celestial ephemerides, but also including its role in cosmology and alternative theories of gravity as well as modern experiments in this area.
Exact Theory to a Gravitational Wave Detector. New Experiments Proposed
Rabounski D.
2006-04-01
Full Text Available We deduce exact solutions to the deviation equation in the cases of both free and spring-connected particles. The solutions show that gravitational waves may displace particles in a two-particle system only if they are in motion with respect to each other or the local space (there is no effect if they are at rest. We therefore propose a new experimental statement for the detection of gravitational waves: use a suspended solid-body detector self-vibrating so that there are relative oscillations of its butt-ends. Or, in another way: use a free-mass detector fitted with suspended, vibrating mirrors. Such systems may have a relative displacement of the butt-ends and a time shift in the butt-ends, produced by a falling gravitational wave.
Quantum corrections to the Relativistic mean-field theory
Maydanyuk, Sergei P; Bakry, Ahmed
2016-01-01
In this paper, we compare the RMF theory and the model of deformed oscillator shells (DOS) in description of the quantum properties of the bound states of the spherically symmetric light nuclei. We obtain an explicit analytical relation between differential equations for the RMF theory and DOS model, which determine wave functions for nucleons. On such a basis we perform analysis of correspondence of quantum properties of nuclei. We find: (1) Potential $V_{RMF}$ of the RMF theory for nucleons has the wave functions $f$ and $g$ with joint part $h$ coincident exactly with the nucleon wave function of DOS model with potential $V_{\\rm shell}$. But, a difference between $V_{RMF}$ and $V_{\\rm shell}$ is essential for any nucleus. (2) The nucleon wave functions and densities obtained by the DOS and RMF theories are essentially different. The nucleon densities of the RMF theory contradict to knowledge about distribution of the proton and neutron densities inside the nuclei obtained from experimental data. This indica...
Local Thermal Equilibrium States in Relativistic Quantum Field Theory
Gransee, Michael
2016-01-01
It is well-known that thermal equilibrium states in quantum statistical mechanics and quantum field theory can be described in a mathematically rigorous manner by means of the so-called Kubo-Martin-Schwinger (KMS) condition, which is based on certain analyticity and periodicity properties of correlation functions. On the other hand, the characterization of non-equilibrium states which only locally have thermal properties still constitutes a challenge in quantum field theory. We discuss a recent proposal for characterization of such states by a generalized KMS condition. The connection of this proposal to a proposal by D. Buchholz, I. Ojima and H.-J. Roos for characterizing local thermal equilibrium states in quantum field theory is discussed.
On a basic conceptual confusion in gravitational radiation theory
Ashtekar, Abhay; Bonga, Béatrice
2017-10-01
In much of the literature on linearized gravitational waves two completely different notions are called transverse traceless modes and labelled habTT , often in different sections of the same reference, without realizing the underlying inconsistency. We compare and contrast the two notions and find that the difference persists even at leading asymptotic order near future null infinity \
Using Gravitational Analogies to Introduce Elementary Electrical Field Theory Concepts
Saeli, Susan; MacIsaac, Dan
2007-01-01
Since electrical field concepts are usually unfamiliar, abstract, and difficult to visualize, conceptual analogies from familiar gravitational phenomena are valuable for teaching. Such analogies emphasize the underlying continuity of field concepts in physics and support the spiral development of student understanding. We find the following four…
An empirical theory for gravitationally unstable flow in porous media
Farajzadeh, R.; Meulenbroek, B.J.; Daniel, D.; Riaz, A.; Bruining, J.
2013-01-01
In this paper, we follow a similar procedure as proposed by Koval (SPE J 3(2):145–154, 1963) to analytically model CO2 transfer between the overriding carbon dioxide layer and the brine layer below it. We show that a very thin diffusive layer on top separates the interface from a gravitationally
The general theory of secondary weak gravitational lensing
Clarkson, Chris
2015-01-01
Weak gravitational lensing is normally assumed to have only two principle effects: a magnification of a source and a distortion of the sources shape in the form of a shear. However, further distortions are actually present owing to changes in the gravitational field across the scale of the ray bundle of light propagating to us, resulting in the familiar arcs in lensed images. This is normally called the flexion, and is approximated by Taylor expanding the shear and magnification across the image plane. However, the physical origin of this effect arises from higher-order corrections in the geodesic deviation equation governing the gravitational force between neighbouring geodesics - so involves derivatives of the Riemann tensor. We show that integrating the second-order geodesic deviation equation results in a 'Hessian map' for gravitational lensing, which is a higher-order addition to the Jacobi map. We derive the general form of the Hessian map in an arbitrary spacetime paying particular attention to the sep...
Gravitational Wave Spectrums from Pole-like Inflations based on Generalized Gravity Theories
Hwang, J
1998-01-01
We present a general and unified formulation which can handle the classical evolution and quantum generation processes of the cosmological gravitational wave in a broad class of generalized gravity theories. Applications are made in several inflation models based on the scalar-tensor theory, the induced gravity, and the low energy effective action of string theory. The gravitational wave power spectrums based on the vacuum expectation value of the quantized fluctuating metric during the pole-like inflation stages are derived in analytic forms. Assuming that the gravity theory transits to Einstein one while the relevant scales remain in the superhorizon scale, we derive the consequent power spectrums and the directional fluctuations of the relic radiation produced by the gravitational wave. The spectrums seeded by the vacuum fluctuations in the pole-like inflation models based on the generalized gravity show a distinguished common feature which differs from the scale invariant spectrum generated in an exponent...
Massive gravitational waves from f(R) theories of gravity: Potential detection with LISA
Capozziello, Salvatore [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , INFN Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Edificio G, via Cintia, I-80126 Napoli (Italy)], E-mail: capozzie@na.infn.it; Corda, Christian [Associazione Galileo Galilei, via Pier Cironi 16, 59100 Prato (Italy); Centro di Scienze Naturali, via di Galceti 74, 59100 Prato (Italy)], E-mail: christian.corda@ego-gw.it; De Laurentis, Maria Felicia [Relativity and Gravitation Group, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino (Italy)], E-mail: mariafelicia.delaurentist@polito.it
2008-11-27
This Letter is a generalization of previous results on gravitational waves (GWs) from f(R) theories of gravity. In some previous papers, particular f(R) theories have been linearized for the first time in the literature. Now, the process is further generalized, showing that every f(R) theory can be linearized producting a third massive mode of gravitational radiation. In this framework, previous results are particular cases of the more general problem that is discussed in this Letter. The potential detectability of such massive GWs with LISA is also discussed with the auxilium of longitudinal response functions.
Massive gravitational waves from f(R) theories of gravity: Potential detection with LISA
Capozziello, Salvatore; De Laurentis, Maria Felicia
2008-01-01
This letter is a generalization of previous results on gravitational waves (GWs) from f(R) theories of gravity. In some previous papers, particular f(R) theories have been linearized for the first time in the literature. Now, the process is further generalized, showing that every f(R) theory can be linearized producting a third massive mode of gravitational radiation. In this framework, previous results are particular cases of the more general problem that is discussed in this letter. The potential detectability of such massive GWs with LISA is also discussed with the auxilium of longitudinal response functions.
Gravitational Higgs Mechanism in Neutron Star Interiors
Coates, Andrew; Sotiriou, Thomas P
2016-01-01
We suggest that nonminimally coupled scalar fields can lead to modifications of the microphysics in the interiors of relativistic stars. As a concrete example, we consider the generation of a non-zero photon mass in such high-density environments. This is achieved by means of a light gravitational scalar, and the scalarization phase transition in scalar-tensor theories of gravitation. Two distinct models are presented, and phenomenological implications are briefly discussed.
On the role of the chaotic velocity in relativistic kinetic theory
Moratto, Valdemar [Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340 México D.F. (Mexico); García-Perciante, A. L. [Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana-Cuajimalpa, Prol. Vasco de Quiroga 4871, México D. F. 05348 (Mexico)
2014-01-14
In this paper we revisit the concept of chaotic velocity within the context of relativistic kinetic theory. Its importance as the key ingredient which allows to clearly distinguish convective and dissipative effects is discussed to some detail. Also, by addressing the case of the two component mixture, the relevance of the barycentric comoving frame is established and thus the convenience for the introduction of peculiar velocities for each species. The fact that the decomposition of molecular velocity in systematic and peculiar components does not alter the covariance of the theory is emphasized. Moreover, we show that within an equivalent decomposition into space-like and time-like tensors, based on a generalization of the relative velocity concept, the Lorentz factor for the chaotic velocity can be expressed explicitly as an invariant quantity. This idea, based on Ellis' theorem, allows to foresee a natural generalization to the general relativistic case.
Time-dependent Relativistic Mean-field Theory and Random Phase Approximation
P.Ring; D.Vretenar; A.Wandelt; NguyenVanGiai; MAZhong-yu; CAOLi-gang
2001-01-01
The relativistic random phase approximation (RRPA) is derived from the time-dependent relativistic mean field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the usual particle-hole ph-states, but also ah configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116Sn. It is shown that
Estimates on Functional Integrals of Quantum Mechanics and Non-relativistic Quantum Field Theory
Bley, Gonzalo A.; Thomas, Lawrence E.
2017-01-01
We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantum mechanics and non-relativistic quantum field theory, functionals of the form {E[{exp}(A_T)]} , the (effective) action {A_T} being a function of particle trajectories up to time T. The estimates in turn yield rigorous lower bounds for ground state energies, via the Feynman-Kac formula. The upper bounds are obtained by writing the action for these functional integrals in terms of stochastic integrals. The method is illustrated in familiar quantum mechanical settings: for the hydrogen atom, for a Schrödinger operator with {1/|x|^2} potential with small coupling, and, with a modest adaptation of the method, for the harmonic oscillator. We then present our principal applications of the method, in the settings of non-relativistic quantum field theories for particles moving in a quantized Bose field, including the optical polaron and Nelson models.
Construction of relativistic quantum theory: a progress report
Noyes, H.P.
1986-06-01
We construct the particulate states of quantum physics using a recursive computer program that incorporates non-determinism by means of locally arbitrary choices. Quantum numbers and coupling constants arise from the construction via the unique 4-level combinatorial hierarchy. The construction defines indivisible quantum events with the requisite supraluminal correlations, yet does not allow supraluminal communication. Measurement criteria incorporate c, h-bar and m/sub p/ or (not ''and'') G, connected to laboratory events via finite particle number scattering theory and the counter paradigm. The resulting theory is discrete throughout, contains no infinities, and, as far as we have developed it, is in agreement with quantum mechanical and cosmological fact.
Babourova, O V; Kudlaev, P E
2016-01-01
On the basis of the Poincare-Weyl gauge theory of gravitation, a new conformal Weyl-Dirac theory of gravitation is proposed, which is a gravitational theory in Cartan-Weyl spacetime with the Dirac scalar field representing the dark matter model. A static approximate axially symmetric solution of the field equations in vacuum is obtained. On the base of this solution in the Newtonian approximation one considers the problem of rotation velocities in spiral components of galaxies.
Restoration of rotational symmetry in deformed relativistic mean-field theory
YAO Jiang-Ming; MENG Jie; Pena Arteaga Daniel; Ring Peter
2009-01-01
We report on a very recently developed three-dimensional angular momentum projected relativistic mean-field theory with point-coupling interaction (3DAMP+RMF-PC). Using this approach the same effective nucleon-nucleon interaction is adopted to describe both the single-particle and collective motions in nuclei.Collective states with good quantum angular momentum are built projecting out the intrinsic deformed meanfield states. Results for 24Mg are shown as an illustrative application.
Nucleon-to-Delta axial transition form factors in relativistic baryon chiral perturbation theory
Geng, L S; Alvarez-Ruso, L; Vacas, M J Vicente
2008-01-01
We report a theoretical study of the axial Nucleon to Delta(1232) ($N\\to\\Delta$) transition form factors up to one-loop order in relativistic baryon chiral perturbation theory. We adopt a formalism in which the $\\Delta$ couplings obey the spin-3/2 gauge symmetry and, therefore, decouple the unphysical spin-1/2 fields. We compare the results with phenomenological form factors obtained from neutrino bubble chamber data and in quark models.
Komorovsky, Stanislav; Repisky, Michal; Malkin, Elena; Demissie, Taye B; Ruud, Kenneth
2015-08-11
We present an implementation of the nuclear spin-rotation (SR) constants based on the relativistic four-component Dirac-Coulomb Hamiltonian. This formalism has been implemented in the framework of the Hartree-Fock and Kohn-Sham theory, allowing assessment of both pure and hybrid exchange-correlation functionals. In the density-functional theory (DFT) implementation of the response equations, a noncollinear generalized gradient approximation (GGA) has been used. The present approach enforces a restricted kinetic balance condition for the small-component basis at the integral level, leading to very efficient calculations of the property. We apply the methodology to study relativistic effects on the spin-rotation constants by performing calculations on XHn (n = 1-4) for all elements X in the p-block of the periodic table and comparing the effects of relativity on the nuclear SR tensors to that observed for the nuclear magnetic shielding tensors. Correlation effects as described by the density-functional theory are shown to be significant for the spin-rotation constants, whereas the differences between the use of GGA and hybrid density functionals are much smaller. Our calculated relativistic spin-rotation constants at the DFT level of theory are only in fair agreement with available experimental data. It is shown that the scaling of the relativistic effects for the spin-rotation constants (varying between Z(3.8) and Z(4.5)) is as strong as for the chemical shieldings but with a much smaller prefactor.
PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY
Tsai, Shang-Hsi; Yang, Jaw-Yen, E-mail: shanghsi@gmail.com [Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan (China)
2015-07-20
A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.
Constraining Gravitational Theories by Observing Magnetic White Dwarfs
Preuss, O; Haugan, Mark P; Solanki, S K; Preuss, Oliver; Jordan, Stefan; Haugan, Mark P.; Solanki, Sami K.
2004-01-01
Under the assumption of a specific nonminimal coupling of torsion to Under the assumption of a specific nonminimal coupling of torsion to electromagnetism, spacetime is birefringent in the presence of a gravitational field leading to depolarization of light emitted from extended astrophysical sources. We use polarimetric data of the magnetic white dwarf RE J0317-853 to set for the very first time constraints on the essential coupling constant for this effect, giving k^2 <22 m^2. electromagnetism, spacetime is birefringent in the presence of a gravitational field leading to depolarization of light emitted from extended astrophysical sources. We use polarimetric data of the magnetic white dwarf RE J0317-853 to set for the very first time constraints on the essential coupling constant for this effect, giving k^2 <22 m^2.
Phase transition for black holes in dilatonic Einstein-Gauss-Bonnet theory of gravitation
Khimphun, Sunly; Lee, Bum-Hoon; Lee, Wonwoo
2016-11-01
We study the thermodynamic properties of a black hole and the Hawking-Page phase transition in the asymptotically anti-de Sitter spacetime in the dilatonic Einstein-Gauss-Bonnet theory of gravitation. We show how the higher-order curvature terms can influence both the thermodynamic properties and the phase transition. We evaluate both heat capacity and free energy difference to determine the local and global thermodynamic stabilities, respectively. We find that the phase transition occurs from the thermal anti-de Sitter to a small spherical black hole geometry and occurs to a hyperbolic black hole geometry in the (dilatonic) Einstein-Gauss-Bonnet theory of gravitation unlike those in Einstein's theory of gravitation.
Phase transition for black holes in Dilatonic Einstein-Gauss-Bonnet theory of gravitation
Khimphun, Sunly; Lee, Wonwoo
2016-01-01
We study the thermodynamic properties of a black hole and the Hawking-Page phase transition in the asymptotically anti-de Sitter spacetime in the Dilatonic Einstein-Gauss-Bonnet theory of gravitation. We show how the higher-order curvature terms can influence both the thermodynamic properties and the phase transition. We evaluate both heat capacity and free energy difference to determine the local and global thermodynamic stabilities, respectively. We show that the phase transition occurs from the thermal anti-de Sitter to a small spherical black hole geometry and occurs to a large hyperbolic black hole geometry in the (Dilatonic) Einstein-Gauss-Bonnet theory of gravitation unlike those in Einstein's theory of gravitation.
Prasanna, A R
2017-01-01
This book suitable for post graduates in Physics and Astrophysics aims at introducing the theory of general relativity as an important background for doing astrophysics. Starting from a detailed discussion of the various mathematical concepts for doing general relativity, the book introduces the geometric description of gravity. It gives a brief historical perspective to classical mechanics and electrodynamics making an attempt to establish the necessity of special relativity as propounded by Einstein extending to General Relativity. This book is a good starting point for post graduates wanting to pursue the modern topics of Cosmology, High energy astrophysics and related areas.
Faller, Sven
2007-01-01
In the last years a lot of papers were published treating general relativity as an effective field theory. We are dealing with general relativity and the combination of general relativity and scalar QED as effective field theories. For effective field theories the quantization is well known therefore we are able to quantize general relativity and the combination of general relativity and scalar QED. The vertex rules can be extracted from the action and the non-analytical contributions to the 1-loop scattering matrix of scalars and charged scalars are calculated in the non-relativistic limit. The non-analytical parts of the scattering amplitudes yield the long range, low energy, leading quantum corrections. From the general relativity as an effective field theory the leading quantum corrections to the Newtonian gravity is constructed. General relativity combined with scalar QED yield the post-Newtonian and quantum corrections to the two-particle non-relativistic scattering matrix potential for charged scalar p...
Rica, Sergio
2016-01-01
The recent observation of gravitational waves, stimulates the question of the longtime evolution of the space-time fluctuations. Gravitational waves interact themselves through the nonlinear character of Einstein's equations of general relativity. This nonlinear wave interaction allows the spectral energy transfer from mode to mode. According to the wave turbulence theory, the weakly nonlinear interaction of gravitational waves leads to the existence of an irreversible kinetic regime that dominates the longtime evolution. The resulting kinetic equation suggests the existence of an equilibrium wave spectrum and the existence of a non-equilibrium Kolmogorov-Zakharov spectrum for spatio-temporal fluctuations. Evidence of these solutions extracted in the fluctuating signal of the recent observations will be discussed in the paper. Probably, the present results would be pertinent in the new age of development of gravitational astronomy, as well as, in new tests of General Relativity.
Hot and dense matter beyond relativistic mean field theory
Zhang, Xilin
2016-01-01
Properties of hot and dense matter are calculated in the framework of quantum hadro-dynamics by including contributions from two-loop (TL) diagrams arising from the exchange of iso-scalar and iso-vector mesons between nucleons. Our extension of mean-field theory (MFT) employs the same five density-independent coupling strengths which are calibrated using the empirical properties at the equilibrium density of iso-spin symmetric matter. Results of calculations from the MFT and TL approximations are compared for conditions of density, temperature, and proton fraction encountered in astrophysics applications involving compact objects. The TL results for the equation of state (EOS) of cold pure neutron matter at sub- and near-nuclear densities agree well with those of modern quantum Monte Carlo and effective field-theoretical approaches. Although the high-density EOS in the TL approximation for neutron-star matter is substantially softer than its MFT counterpart, it is able to support a $2M_\\odot$ neutron star req...
Planetary and Lunar Ephemerides: Testing Alternate Gravitational Theories
Myles Standish, E.
2009-05-01
Planetary and lunar ephemerides have been improved over the past century by many orders of magnitude. It is expected that they will continue to improve in the future. The improvements come from more accurate observational data, from increased and refined modeling of the gravitational equations of motion, and from the ability to numerically integrate the equations of motion. Present-day ephemerides have the accuracy to be able to test a number of proposed possible modifications to the presently accepted laws of gravitation. In the future, with further improved accuracies, the ephemerides will be able to test increasingly subtle modifications. Experiments show that the Voyager range residuals at Uranus and Neptune, reported by Anderson et al. (1995), are fully consistent with other observational data and with present-day ephemerides; they do not require a modification to the ephemerides. The modification to the laws of gravitation which is usually quoted to explain the Pioneer Anomaly, that of a constant acceleration of 8.74 x 10**(-10) m/sec**2 directed toward the sun, added to each planet's acceleration, has been shown to be completely inconsistent with the planetary ephemerides. A suggested alternative form, where the acceleration is proportional to the planet's radial velocity, is marginally acceptable, but only when applied to just the planets past Saturn. A further form, where the acceleration is proportional to the planet's radial velocity squared, is acceptable to the planets from Saturn outward. In none of the cases that were tested, can the force modifications be applied to Jupiter: the changes in the solution parameters used to adjust the ephemerides become totally unacceptable.
Hu, Jinniu; Shen, Hong
2016-01-01
We study the properties of nuclear matter with lattice nucleon-nucleon ($NN$) potential in the relativistic Brueckner-Hartree-Fock (RBHF) theory. To use this potential in such a microscopic many-body theory, we firstly have to construct a one-boson-exchange potential (OBEP) based on the latest lattice $NN$ potential. Three mesons, pion, $\\sigma$ meson, and $\\omega$ meson, are considered. Their coupling constants and cut-off momenta are determined by fitting the on-shell behaviors and phase shifts of the lattice force, respectively. Therefore, we obtain two parameter sets of the OBEP potential (named as LOBEP1 and LOBEP2) with these two fitting ways. We calculate the properties of symmetric and pure neutron matter with LOBEP1 and LOBEP2. In non-relativistic Brueckner-Hartree-Fock case, the binding energies of symmetric nuclear matter are around $-3$ and $-5$ MeV at saturation densities, while it becomes $-8$ and $-12$ MeV in relativistic framework with $^1S_0,~^3S_1,$ and $^3D_1$ channels using our two paramet...
Gravitational Duality in MacDowell-Mansouri Gauge Theory
García-Compéan, H; Ramírez, C
1998-01-01
Strong-weak duality invariance can only be defined for particular sectors of supersymmetric Yang-Mills theories. Nevertheless, for full non-Abelian non-supersymmetric theories, dual theories with inverted couplings, have been found. We show that an analogous procedure allows to find the dual action to the gauge theory of gravity constructed by the MacDowell-Mansouri model plus the superposition of a $\\Theta$ term.
The nucleon and Delta-resonance masses in relativistic chiral effective-field theory
V. Pascalutsa; M. Vanderhaeghen
2005-11-28
We study the chiral behavior of the nucleon and De-isobar masses within a manifestly covariant chiral effective-field theory, consistent with the analyticity principle. We compute the {pi} N and {pi}{Delta} one-loop contributions to the mass and field-normalization constant, and find that they can be described in terms of universal relativistic loop functions, multiplied by appropriate spin, isospin and coupling constants. We show that these relativistic one-loop corrections, when properly renormalized, obey the chiral power-counting and vanish in the chiral limit. The results including only the {pi} N-loop corrections compare favorably with the lattice QCD data for the pion-mass dependence of the nucleon and De masses, while inclusion of the {pi}/De loops tends to spoil this agreement.
Proton rich nuclei at and beyond the proton drip line in the Relativistic Mean Field theory
Geng, L S; Meng, J
2003-01-01
The Relativistic Mean Field theory is applied to the analysis of ground-state properties of deformed proton-rich odd-Z nuclei in the region $55\\le Z \\le 73$ >. The model uses the TMA and NL3 effective interactions in the mean-field Lagrangian, and describes pairing correlations by the density-independent delta-function interaction. The model predicts the location of the proton drip line, the ground-state quadrupole deformation, one-proton separation energy at and beyond the proton drip line, the deformed single-particle orbital occupied by the odd valence proton and the corresponding spectroscopic factor. The results are in good agreement with the available experimental data except for some odd-odd nuclei in which the proton-neutron pairing may become important and are close to those of Relativistic Hartree-Bogoliubov model.
Relativistic theory of inverse beta-decay of polarized neutron in strong magnetic field
S Shinkevich; A Studenikin
2005-08-01
The relativistic theory of the inverse beta-decay of polarized neutron, + → + -, in strong magnetic field is developed. For the proton wave function we use the exact solution of the Dirac equation in the magnetic filed that enables us to account exactly for effects of the proton momentum quantization in the magnetic field and also for the proton recoil motion. The effect of nucleons anomalous magnetic moments in strong magnetic fields is also discussed. We examine the cross-section for different energies and directions of propagation of the initial neutrino accounting for neutron polarization. It is shown that in the super-strong magnetic field the totally polarized neutron matter is transparent for neutrinos propagating antiparallel to the direction of polarization. The developed relativistic approach can be used for calculations of cross-sections of the other URCA processes in strong magnetic fields.
Goenner, Hubert F M
2016-01-01
We will follow the growth of gravitational theory in Germany from 1915 to the 1990s, i.e., relativistic theories of gravitation, mainly Einstein's, as a branch of physics in the sense of social, more precisely institutional history. As criteria for a continued professionalizing of the field, we use the numbers of published research papers, reviews, monographs, courses at universities, appointments of lecturers or professors as well as the status of those involved (members of academies). The foundation of special institutes for gravitational research and of particular divisions of physical societies forms the final stage of this process of institutionalization. At present, an institutionalization of research in relativistic gravitation has been achieved in Germany through a thriving topical section "Relativity and Gravitation" of the German Physical Society and a Max-Planck-Institute for Gravitational Physics. While an institutionalization of the field became achieved, the situation for young German relativist...
Strauss, Y
1999-01-01
We apply the quantum Lax-Phillips scattering theory to a relativistically covariant quantum field theoretical form of the (soluble) Lee model. We construct the translation representations with the help of the wave operators, and show that the resulting Lax-Phillips $S$-matrix is an inner function (the Lax-Phillips theory is essentially a theory of translation invariant subspaces). We then discuss the non-relativistic limit of this theory, and show that the resulting kinematic relations coincide with the conditions required for the Galilean description of a decaying system.
The 5D Fully-Covariant Theory of Gravitation and Its Astrophysical Applications
Tianxi Zhang
2014-12-01
Full Text Available In this paper, we comprehensively review the five-dimensional (5D fully-covariant theory of gravitation developed by Zhang two decades ago and its recent applications in astrophysics and cosmology. This 5D gravity describes not only the fields, but also the matter and its motion in a 5D spacetime. The greatest advantage of this theory is that there does not exist any unknown parameter, so that we can apply it to explain astrophysical and cosmological issues by quantitatively comparing the results obtained from it with observations and to predict new effects that could not be derived from any other gravitational theories. First, the 5D covariant description of matter and its motion enabled Zhang to analytically derive the fifteenth component of the 5D energy-momentum tensor of matter ( T - 44 , which significantly distinguishes this 5D gravity from other 5D gravitational theories that usually assumed a T - 44 with an unknown parameter, called the scalar charge s, and, thus, to split the 5D covariant field equation into (4 + 1 splitting form as the gravitational, electromagnetic, and scalar field equations. The gravitational field equation turns into the 4D Einstein’s field equation of general relativity if the scalar field is equal to unity. Then, Zhang solved the field equations and obtained an exact static spherically-symmetric external solution of the gravitational, electromagnetic and scalar fields, in which all integral constants were completely determined with a perfect set of simple numbers and parameters that only depend on the mass and electric charge of the matter, by comparing with the obtained weak internal solution of the fields at a large radial distance. In the Einstein frame, the exact field solution obtained from the 5D fully-covariant theory of gravitation reduces to the Schwarzschild solution when the matter is electrically neutral and the fields are weak in strength. This guarantees that the four fundamental tests (light
Relativistic many-body theory a new field-theoretical approach
Lindgren, Ingvar
2016-01-01
This revised second edition of the author’s classic text offers readers a comprehensively updated review of relativistic atomic many-body theory, covering the many developments in the field since the publication of the original title. In particular, a new final section extends the scope to cover the evaluation of QED effects for dynamical processes. The treatment of the book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insufficient to explain the accurate experimental data recently obtained, particularly for highly charged ions. The main text is divided into...
A probability theory for non-equilibrium gravitational systems
Peñarrubia, Jorge
2015-01-01
This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed as a special type of diffusion process in the integral-of-motion space. In time-varying potentials with a fixed spatial symmetry the diffusion coefficients are closely related to virial quantities, such as the specific moment of inertia, the virial factor and the mean kinetic and potential energy of microcanonical particle ensembles. The non-equilibrium distribution function (DF) is found by convolving the initial DF with the Green function that solves Einstein's equation for freely diffusing particles. Such a convolution also yields a natural solution to the Fokker-Planck equations in the energy space. Our mathematical formalism can be generalized to potentials with a time-varying symmetry, where diffusion extends over multiple dimensions of the integral-of-motion space. Th...
吴亚波; 李磊
2002-01-01
We establish the double complex Ashtekar gravitational theory with the cosmological term. In particular, by performing the 3+1 decomposition of the double Ashtekar action containing the cosmological term to pass on the Hamiltonian framework, the double Ashtekar constraint equations are derived, which respectively correspond to Lorentzian and Euclidean gravity.
First test of Verlinde's theory of emergent gravity using weak gravitational lensing measurements
Brouwer, Margot M.; Visser, Manus R.; Dvornik, Andrej; Hoekstra, Henk; Kuijken, Konrad; Valentijn, Edwin A.; Bilicki, Maciej; Blake, Chris; Brough, Sarah; Buddelmeijer, Hugo; Erben, Thomas; Heymans, Catherine; Hildebrandt, Hendrik; Holwerda, Benne W.; Hopkins, Andrew M.; Klaes, Dominik; Liske, Jochen; Loveday, Jon; McFarland, John; Nakajima, Reiko; Sifón, Cristóbal; Taylor, Edward N.
2017-01-01
Verlinde proposed that the observed excess gravity in galaxies and clusters is the consequence of emergent gravity (EG). In this theory, the standard gravitational laws are modified on galactic and larger scales due to the displacement of dark energy by baryonic matter. EG gives an estimate of the e
Energy and Momentum Localization: An Important Problem in the Theory of Gravitation
Korunur, M; Salti, M; Aydogdu, O
2005-01-01
Using the Einstein, Bergmann-Thomson and Landau-Lifshitz's energy and momentum complexes and theirs teleparallel gravity versions, we compute the energy and momentum of the universe in inhomogeneous cosmological models and show that energy-momentum complexes give same results in both of gravitation theories in inhomogeneous spacetime.
Some Plane Symmetric Inhomogeneous Cosmological Models in the Scalar-Tensor Theory of Gravitation
Ali, Ahmad T; Mahmoud, S R
2014-01-01
The present study deals with the inhomogeneous plane symmetric models in scalar - tensor theory of gravitation. We used symmetry group analysis method to solve the field equations analytically. A new class of similarity solutions have been obtained by considering the inhomogeneous nature of metric potential. The physical behavior and geometrical aspects of the derived models are also discussed.
Robin, Caroline; Litvinova, Elena
2016-07-01
A new theoretical approach to spin-isospin excitations in open-shell nuclei is presented. The developed method is based on the relativistic meson-exchange nuclear Lagrangian of Quantum Hadrodynamics and extends the response theory for superfluid nuclear systems beyond relativistic quasiparticle random phase approximation in the proton-neutron channel (pn-RQRPA). The coupling between quasiparticle degrees of freedom and collective vibrations (phonons) introduces a time-dependent effective interaction, in addition to the exchange of pion and ρ -meson taken into account without retardation. The time-dependent contributions are treated in the resonant time-blocking approximation, in analogy to the previously developed relativistic quasiparticle time-blocking approximation (RQTBA) in the neutral (non-isospin-flip) channel. The new method is called proton-neutron RQTBA (pn-RQTBA) and is applied to the Gamow-Teller resonance in a chain of neutron-rich nickel isotopes 68-78Ni . A strong fragmentation of the resonance along with quenching of the strength, as compared to pn-RQRPA, is obtained. Based on the calculated strength distribution, beta-decay half-lives of the considered isotopes are computed and compared to pn-RQRPA half-lives and to experimental data. It is shown that a considerable improvement of the half-life description is obtained in pn-RQTBA because of the spreading effects, which bring the lifetimes to a very good quantitative agreement with data.
Relativistic warm plasma theory of nonlinear laser-driven electron plasma waves.
Schroeder, C B; Esarey, E
2010-05-01
A relativistic, warm fluid model of a nonequilibrium, collisionless plasma is developed and applied to examine nonlinear Langmuir waves excited by relativistically intense, short-pulse lasers. Closure of the covariant fluid theory is obtained via an asymptotic expansion assuming a nonrelativistic plasma temperature. The momentum spread is calculated in the presence of an intense laser field and shown to be intrinsically anisotropic. Coupling between the transverse and longitudinal momentum variances is enabled by the laser field. A generalized dispersion relation is derived for Langmuir waves in a thermal plasma in the presence of an intense laser field. Including thermal fluctuations in three-velocity-space dimensions, the properties of the nonlinear electron plasma wave, such as the plasma temperature evolution and nonlinear wavelength, are examined and the maximum amplitude of the nonlinear oscillation is derived. The presence of a relativistically intense laser pulse is shown to strongly influence the maximum plasma wave amplitude for nonrelativistic phase velocities owing to the coupling between the longitudinal and transverse momentum variances.
A fundamental special-relativistic theory valid for all real-valued speeds
Vedprakash Sewjathan
1984-01-01
Full Text Available This paper constitutes a fundamental rederivation of special relativity based on the c-invariance postulate but independent of the assumption ds′2=±ds2 (Einstein [1], Kittel et al [2], Recami [3], the equivalence principle, homogeneity of space-time, isotropy of space, group properties and linearity of space-time transformations or the coincidence of the origins of inertial space-time frames. The mathematical formalism is simpler than Einstein's [4] and Recami's [3]. Whilst Einstein's subluminal and Recami's superluminal theories are rederived in this paper by further assuming the equivalence principle and mathematical inverses [4,3], this paper derives (independent of these assumptions with physico-mathematical motivation an alternate singularity-free special-relativistic theory which replaces Einstein's factor [1/(1−V2/c2]12 and Recami's extended-relativistic factor [1/(V2/c2−1]12 by [(1−(V2/c2n/(1−V2/c2]12, where n equals the value of (m(V/m02 as |V|→c. In this theory both Newton's and Einstein's subluminal theories are experimentally valid on account of negligible terms. This theory implies that non-zero rest mass luxons will not be detected as ordinary non-zero rest mass bradyons because of spatial collapse, and non-zero rest mass tachyons are undetectable because they exist in another cosmos, resulting in a supercosmos of matter, with the possibility of infinitely many such supercosmoses, all moving forward in time. Furthermore this theory is not based on any assumption giving rise to the twin paradox controversy. The paper concludes with a discussion of the implications of this theory for general relativity.
Kutzelnigg, W.
1990-03-01
Methods for perturbation theory of relativistic corrections for an electron in a Coulomb field are divided into three categories: (1) in terms of 4-component spinors; (2) in terms of the ‘large components’ of the Dirac spinor; (3) involving a Foldy-Wouthuysen type transformation, where one attempts to obtain a two-component spinor different from the ‘large component’. In methods of category 1 (the ‘direct perturbation theory’ of paper I of this series, the related approaches by Rutkowski as well as by Gesteszy, Grosse, and Thaller and a somewhat different one by Moore) the wave function, the energy and the Hamiltonian are analytic in c -2. No divergent terms arise. In methods of category 2 (that of the elemination of the small component as well as a similarity transformation in intermediate normalization) wave function and energy are still analytic in c -2, but the effective Hamiltonian no longer is. Regularized results can be obtained by controlled cancellation of divergent terms. In category 3 both the effective Hamiltonian and the wave function are highly singular and non-analytic in c -1. A controlled cancellation of divergent terms is at least very difficult. These pathologic feature survive in the non-relativistic limit and have hence little to do with relativistic effects. They are related to the fact that for r → 0 the sign of the quantum number κ rather than that of the energy determines which component of the Dirac spinor is large and which is small. In the limit r → 0 and c → ∞ the Foldy-Wouthuysen wave function of a 2 p 1/2 state is a 1 p wave function. Hierarchies of transformations of the Dirac equation and its non-relativistic limit are presented and discussed. Finally the problem of the regularization of effective Hamiltonians on 2-component level ‘for electrons only’ is addressed.
Analysis of JET LCHD/ICRH synergy experiments in terms of relativistic current drive theory
Start, D.F.H.; Baranov, Y.; Brusati, M.; Ekedahl, A.; Froissard, P.; Gormezano, C.; Jacquinot, J.; Paquin, L.; Rimini, F.G. [Commission of the European Communities, Abingdon (United Kingdom). JET Joint Undertaking; Cox, M.; Gardner, C.; O`Brien, M.R. [UKAEA Culham Lab., Abingdon (United Kingdom); Di Vita, A. [Ansaldo SpA, Genoa (Italy)
1994-07-01
The present analysis shows that the observed efficiency of current drive with synergy between LHCD and ICRH is in good agreement with the relativistic theory of Karney and Fisch for Landau damped waves. The predicted power absorption from the fast wave by the electron tail is within 30% of the measured value. In the presence of significant fast electron diffusion within a slowing down time it would be possible to produce central current drive using multiple ICRF resonances even when the LHCD deposition is at half radius, as in an ITER type device. (authors). 4 refs., 6 figs.
Hayata, Tomoya; Hongo, Masaru; Noumi, Toshifumi
2015-01-01
We derive relativistic hydrodynamics from quantum field theories by assuming that the density operator is given by a local Gibbs distribution at initial time. We decompose the energy-momentum tensor and particle current into nondissipative and dissipative parts, and analyze their time-evolution in detail. Performing the path-integral formulation of the local Gibbs distribution, we microscopically derive the generating functional for the nondissipative hydrodynamics. We also construct a basis to study dissipative corrections. In particular, we derive the first-order dissipative hydrodynamic equations without choice of frame such as the Landau-Lifshitz or Eckart frame.
On the question of symmetries in non-relativistic diffeomorphism invariant theories
Banerjee, Rabin; Mukherjee, Pradip
2016-01-01
Nonrelativistic diffeomorphism invariance has recently emerged as a powerful tool for investigating various phenomena. The flat limit of such an invariance which should yield the Galilean invariance is, surprisingly, riddled with ambiguities and anomalies. We show that our approach, based on Galilean gauge theory, resolves these shortcomings. As a spin-off, we provide a systematic and unique way of interpreting nonrelativistic diffeomorphism invariance and Galilean invariance as appropriate nonrelativistic limits of relativistic invariances in curved and flat backgrounds, respectively. The complementary role of flat and nonrelativistic limits is highlighted.
Extreme Exotic Calcium Lambda Hypernuclei in the Relativistic Continuum Hartree-Bogoliubov Theory
L(U) Hong-Feng
2008-01-01
Exotic calcium lambda hypernuclei properties with the neutron number of 20-400 by a step of 20 are discussed by employing the relativistic continuum Hartree-Bogoliubov theory with a zero range pairing interaction. The Bethe-Weizs(a)cker mass formula of a multi-strange system and the Woods-Saxon-type potential of larnbda need to be modified for exotic calcium hypernuclei with unusual number of neutrons and lambdas. The possible neutron and lambda limits of exotic Ca larnbda hypernuclei are also investigated.
Evolution of $N = 28$ shell closure in relativistic continuum Hartree-Bogoliubov theory
Xia, Xuewei
2015-01-01
The $N = 28$ shell gap in sulfur, argon, calcium and titanium isotopes is investigated in the framework of relativistic continuum Hartree-Bogoliubov (RCHB) theory. The evolutions of neutron shell gap, separation energy, single particle energy and pairing energy are analyzed, and it is found that $N = 28$ shell gap is quenched in sulfur isotopes but persists in argon, calcium and titanium isotopes. The evolution of $N = 28$ shell gap in $N = 28$ isotonic chain is discussed, and the erosion of $N = 28$ shell gap is understood with the evolution of potential with proton number.
Proton and neutron skins of light nuclei within the Relativistic Mean Field theory
Geng, L S; Ozawa, A; Meng, J
2004-01-01
The Relativistic Mean Field (RMF) theory is applied to the analysis of ground-state properties of Ne, Na, Cl and Ar isotopes. In particular, we study the recently established proton skin in Ar isotopes and neutron skin in Na isotopes as a function of the difference between the proton and the neutron separation energy. We take the TMA effective interaction in the RMF Lagrangian, and describe pairing correlation by the density-independent delta-function interaction. We calculate single neutron and proton separation energies, quadrupole deformations, nuclear matter radii, and differences in proton radii and neutron radii, and compare these results with the recent experimental data.
Shell-model-like Approach (SLAP) for the Nuclear Properties in Relativistic Mean field Theory
MENG Jie; GUO Jian-you; LIU Lang; ZHANG Shuang-quan
2006-01-01
A Shell-model-like approach suggested to treat the pairing correlations in relativistic mean field theory is introduced,in which the occupancies thus obtained have been iterated back into the densities.The formalism and numerical techniques are given in detail.As examples,the ground state properties and low-lying excited states for Ne isotopes are studied.The results thus obtained are compared with the data available.The binding energies,the odd-even staggering,as well as the tendency for the change of the shapes in Ne isotopes are correctly reproduced.
Equation of state of a relativistic theory from a moving frame.
Giusti, Leonardo; Pepe, Michele
2014-07-18
We propose a new strategy for determining the equation of state of a relativistic thermal quantum field theory by considering it in a moving reference system. In this frame, an observer can measure the entropy density of the system directly from its average total momentum. In the Euclidean path integral formalism, this amounts to computing the expectation value of the off-diagonal components T(0k) of the energy-momentum tensor in the presence of shifted boundary conditions. The entropy is, thus, easily measured from the expectation value of a local observable computed at the target temperature T only. At large T, the temperature itself is the only scale which drives the systematic errors, and the lattice spacing can be tuned to perform a reliable continuum limit extrapolation while keeping finite-size effects under control. We test this strategy for the four-dimensional SU(3) Yang-Mills theory. We present precise results for the entropy density and its step-scaling function in the temperature range 0.9T(c)-20T(c). At each temperature, we consider four lattice spacings in order to extrapolate the results to the continuum limit. As a by-product, we also determine the ultraviolet finite renormalization constant of T(0k) by imposing suitable Ward identities. These findings establish this strategy as a solid, simple, and efficient method for an accurate determination of the equation of state of a relativistic thermal field theory over several orders of magnitude in T.
Modified Theories of Gravitation behind the Spacetime Deformation
Gagik Ter-Kazarian
2015-01-01
Full Text Available In the framework of proposed theory of spacetime deformation/distortion, we have a way to deform the spacetime through a nontrivial choice of the distortion-complex, displaying different connections, which may reveal different post-Riemannian spacetime structures as corollary. We extend this theory to address, in particular, the gauge model of the most general metric-affine gravity carrying both nontrivial torsion and nonmetricity. This model is constructed in the framework of the first order Lagrangian expressed in terms of the gauge potentials and their first derivatives. The equations of the standard theory, which have no propagating modes for torsion, can be equivalently replaced in modified framework by the modified equations, which in the limit of reducing the affine group leads to the modified Einstein-Cartan theory with dynamical torsion and beyond. In testing the modified framework for various particular cases, we use the Lagrange multipliers for extinguishing nonmetricity and torsion.
Description of Unstable Systems in Relativistic Quantum Mechanics in the Lax-Phillips Theory
Horwitz, L P
1998-01-01
We discuss some of the experimental motivation for the need for semigroup decay laws, and the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips $S$-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonances (eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips Hilbert space, and therefore all physical properties of the resonant states can be computed. We show that the parametrized relativistic quantum theory is a natural setting for the realization of the Lax-Phillips theory.
Ground-State Properties of Z = 59 Nuclei in the Relativistic Mean-Field Theory
ZHOU Yong; MA Zhong-Yu; CHEN Bao-Qiu; LI Jun-Qing
2000-01-01
Ground-state properties of Pr isotopes are studied in a framework of the relativistic mean-field (RMF) theory using the recently proposed parameter set TM1. Bardeen-Cooper-Schrieffer (BCS) pproximation and blocking method is adopted to deal with pairing interaction and the odd nucleon, respectively. The pairing forces are taken to be isospin dependent. The domain of the validity of the BCS theory and the positions of neutron and proton drip lines are studied. It is shown that RMF theory has provided a good description of the binding energy,isotope shifts and deformation of nuclei over a large range of Pr isotopes, which are in good agreement with those obtained in the finite-range droplet model.
Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories
Bastianello, Alvise
2016-01-01
We study the quench dynamics in continuous relativistic quantum field theory, more specifically the locality properties of the large time stationary state. After a quantum quench in a one-dimensional integrable model, the expectation values of local observables are expected to relax to a Generalised Gibbs Ensemble (GGE), constructed out of the conserved charges of the model. Quenching to a free bosonic theory, it has been shown that the system indeed relaxes to a GGE described by the momentum mode occupation numbers. Here we address the question whether the latter can be equivalently described by a GGE constructed with only local charges. We show that, in marked contrast to the lattice case, this is always impossible in continuous field theories and instead the recently discovered quasilocal charges are necessary. In particular we show that the discrepancy between the exact steady state and the local GGE is clearly manifested as a difference in the large distance behaviour of the two point correlation functio...
Chattopadhyay, S; Angom, D
2014-01-01
The perturbed relativistic coupled-cluster (PRCC) theory is applied to calculate the electric dipole polarizabilities of alkaline Earth metal atoms. The Dirac-Coulomb-Breit atomic Hamiltonian is used and we include the triple excitations in the relativistic coupled-cluster (RCC) theory. The theoretical issues related to the triple excitation cluster operators are described in detail and we also provide details on the computational implementation. The PRCC theory results are in good agreement with the experimental and previous theoretical results. We, then, highlight the importance of considering the Breit interaction for alkaline Earth metal atoms.
Gravitational radiation reaction and second order perturbation theory
Detweiler, Steven
2011-01-01
A point particle of small mass m moves in free fall through a background vacuum spacetime metric g0_ab and creates a first-order metric perturbation h^1ret_ab that diverges at the particle. Elementary expressions are known for the singular m/r part of h^1ret_ab and its tidal distortion determined by the Riemann tensor in a neighborhood of m. Subtracting this singular part h^1S_ab from h^1ret_ab leaves a regular remainder h^1R_ab. The self-force on the particle from its own gravitational field adjusts the world line at O(m) to be a geodesic of g0_ab+h^1R_ab. The generalization of this description to second-order perturbations is developed and results in a wave equation governing the second-order h^2ret_ab with a source that that has an O(m^2) contribution from the stress-energy tensor of m added to a term nonlinear in h^1ret_ab. Second-order self-force effects are described as well.
Fabris, J C
2015-01-01
General Relativity is the modern theory of gravitation. It has replaced the newtonian theory in the description of the gravitational phenomena. In spite of the remarkable success of the General Relativity Theory, the newtonian gravitational theory is still largely employed, since General Relativity, in most of the cases, just makes very small corrections to the newtonian predictions. Moreover, the newtonian theory is much simpler, technically and conceptually, when compared to the relativistic theory. In this text, we discuss the possibility of extending the traditional newtonian theory in order to incorporate typical relativistic effects, but keeping the simplicity of the newtonian framework. We denominate these extensions neo-newtonian theories. These theories are discussed mainly in the contexts of cosmology and compact astrophysical objects.
Gravitational waves from perturbed stars
Ferrari, Valeria
2011-01-01
Non radial oscillations of neutron stars are associated with the emission of gravitational waves. The characteristic frequencies of these oscillations can be computed using the theory of stellar perturbations, and they are shown to carry detailed information on the internal structure of the emitting source. Moreover, they appear to be encoded in various radiative processes, as for instance in the tail of the giant flares of Soft Gamma Repeaters. Thus, their determination is central to the theory of stellar perturbation. A viable approach to the problem consists in formulating this theory as a problem of resonant scattering of gravitational waves incident on the potential barrier generated by the spacetime curvature. This approach discloses some unexpected correspondences between the theory of stellar perturbations and the theory of quantum mechanics, and allows us to predict new relativistic effects.
Gravitational waves in the $f(R,T)$ theory of gravity
Alves, M E S; de Araujo, J C N; Malheiro, M
2016-01-01
There is a host of alternative theories of gravitation in the literature, among them the $f(R,T)$ recently elaborated by Harko and collaborators. In these theories the $R$ and $T$ are respectively the Ricci scalar and the trace of the energy momentum tensor. There is already in literature a series of studies of different forms of the $f(R,T)$ functions as well as their cosmological consequences. However, there is not so far in the literature studies related to the gravitational waves in $f(R,T)$ gravity. Here we consider such an issue, in particular studying the putative extra polarization models that can well appear in such theories. To do that, we consider different functional forms for $f(R,T)$.
Quantum Exact Non-Abelian Vortices in Non-relativistic Theories
Nitta, Muneto; Vinci, Walter
2014-01-01
Non-Abelian vortices arise when a non-Abelian global symmetry is exact in the ground state but spontaneously broken in the vicinity of their cores. In this case, there appear (non-Abelian) Nambu-Goldstone (NG) modes confined and propagating along the vortex. In relativistic theories, the Coleman-Mermin-Wagner theorem forbids the existence of a spontaneous symmetry breaking, or a long-range order, in 1+1 dimensions: quantum corrections restore the symmetry along the vortex and the NG modes acquire a mass gap. We show that in non-relativistic theories NG modes with quadratic dispersion relation confined on a vortex can remain gapless at quantum level. We provide a concrete and experimentally realizable example of a three-component Bose-Einstein condensate with U(1) x U(2) symmetry. We first show, at the classical level, the existence of S^3 = S^1 |x S^2 (S^1 fibered over S^2) NG modes associated to the breaking U(2) -> U(1) on vortices, where S^1 and S^2 correspond to type I and II NG modes, respectively. We th...
Δ (1232 ) effects in density-dependent relativistic Hartree-Fock theory and neutron stars
Zhu, Zhen-Yu; Li, Ang; Hu, Jin-Niu; Sagawa, Hiroyuki
2016-10-01
The density-dependent relativistic Hartree-Fock (DDRHF) theory is extended to include Δ isobars for the study of dense nuclear matter and neutron stars. To this end, we solve the Rarita-Schwinger equation for spin-3/2 particle. Both the direct and exchange terms of the Δ isobars' self-energies are evaluated in detail. In comparison with the relativistic mean field theory (Hartree approximation), a weaker parameter dependence is found for DDRHF. An early appearance of Δ isobars is recognized at ρB˜0.28 fm-3, comparable with that of hyperons. Also, we find that the Δ isobars' softening of the equation of state is mainly due to the reduced Fock contributions from the coupling of the isoscalar mesons, while the pion contributions are negligibly small. We finally conclude that with typical parameter sets, neutron stars with Δ isobars in their interiors could be as heavy as the two massive pulsars whose masses are precisely measured, with slightly smaller radii than normal neutron stars.
$\\Delta$ (1232) effects in density-dependent relativistic Hartree-Fock theory and neutron stars
Zhu, Zhen-Yu; Hu, Jin-Niu; Sagawa, Hiroyuki
2016-01-01
The density-dependent relativistic Hartree-Fock (DDRHF) theory is extended to include $\\Delta$-isobars for the study of dense nuclear matter and neutron stars. To this end, we solve the Rarita-Schwinger equation for spin-3/2 particle. Both the direct and exchange terms of the $\\Delta$-isobars' self-energies are evaluated in details. In comparison with the relativistic mean field theory (Hartree approximation), a weaker parameter dependence is found for DDRHF. An early appearance of $\\Delta$-isobars is recognized at $\\rho_B\\sim0.27$fm$^{-3}$, comparable with that of hyperons. Also, we find that the $\\Delta$-isobars' softening of the equation of state is found to be mainly due to the reduced Fock contributions from the coupling of the isoscalar mesons, while the pion contributions are found negligibly small. We finally conclude that with typical parameter sets, neutron stars with $\\Delta$-isobars in their interiors could be as heavy as the two massive pulsars whose masses are precisely measured, with slightly s...
The gravitational sector of 2d (0, 2) F-theory vacua
Lawrie, Craig; Schäfer-Nameki, Sakura; Weigand, Timo
2017-05-01
F-theory compactifications on Calabi-Yau fivefolds give rise to two-dimensional N = (0, 2) supersymmetric field theories coupled to gravity. We explore the dilaton supergravity defined by the moduli sector of such compactifications. The massless moduli spectrum is found by uplifting Type IIB compactifications on Calabi-Yau fourfolds. This spectrum matches expectations from duality with M-theory on the same elliptic fibration. The latter defines an N = 2 Supersymmetric Quantum Mechanics related to the 2d (0, 2) F-theory supergravity via circle reduction. Using our recent results on the gravitational anomalies of duality twisted D3-branes wrapping curves in Calabi-Yau fivefolds we show that the F-theory spectrum is anomaly free. We match the classical Chern-Simons terms of the M-theory Super Quantum Mechanics to one-loop contributions to the effective action by S 1 reduction of the dual F-theory.
Invariant quantities in the scalar-tensor theories of gravitation
Jarv, Laur; Saal, Margus; Vilson, Ott
2014-01-01
We consider the general scalar-tensor gravity without derivative couplings. By rescaling of the metric and reparametrization of the scalar field, the theory can be presented in different conformal frames and parametrizations. In this work we argue, that while due to the freedom to transform the metric and the scalar field, the scalar field itself does not carry a physical meaning (in a generic parametrization), there are functions of the scalar field and its derivatives which remain invariant under the transformations. We put forward a scheme how to construct these invariants, discuss how to formulate the theory in terms of the invariants, and show how the observables like parametrized post-Newtonian parameters and characteristics of the cosmological solutions can be neatly expressed in terms of the invariants. In particular, we describe the scalar field solutions in Friedmann-Lema\\^itre-Robertson-Walker cosmology in Einstein and Jordan frames, and explain their correspondence despite the approximate equation...
Exact Relativistic 'Antigravity' Propulsion
Felber, F S
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3^-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Exact Relativistic `Antigravity' Propulsion
Felber, Franklin S.
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Deformed Relativistic Hartree Theory in Coordinate Space and in Harmonic Oscillator Basis
ZHOU Shan-Gui; MENG Jie; Shuhei YAMAJI; YANG Si-Chun
2000-01-01
The deformed relativistic Hartree theory (DRH) is solved both in coordinate space (DRH-c) and in harmonic oscillator basis (DRH-o). Results obtained from these two methods are compared in details. The DRH-c and DRH-o calculations give similar total binding energies, deformation, level structures and radii for nitrogen iso topes, while their descriptions on the density distributions for drip-line nuclei are very different. The large spatiai istributions of nucleon densities, which is crucial to understand a weakly bound system, can only be obtained by DRH-c calculations. This implies that the DRH theory should be solved in coordinate space in order to describe uclei close to the drip line.
Relativistic light-shift theory of few-electron systems: Heliumlike highly charged ions
Postavaru, O.; Scafes, A. C.
2017-09-01
The light-shift theory of many-electron systems in a laser field is described using the projection operators technique. In heavy ions, the electrons are tightly bound by the Coulomb potential of the nucleus, which prohibits ionization even by strong lasers. However, interaction with the monofrequent laser field leads to dynamic shifts of the electronic energy levels, and the process is treated by second-order time-dependent perturbation theory. In order to treat heliumlike systems, one decomposes the corresponding matrix elements into hydrogenlike matrix elements using the independent particle model. We are applying a fully relativistic description of the electronic states by means of the Dirac equation. Our formalism goes beyond the Stark long-wavelength dipole approximation and takes into account nondipole effects of retardation and interaction with the magnetic field components of the laser beam.
Ni, W.-T.
1972-01-01
Metric theories of gravity are compiled and classified according to the types of gravitational fields they contain, and the modes of interaction among those fields. The gravitation theories considered are classified as (1) general relativity, (2) scalar-tensor theories, (3) conformally flat theories, and (4) stratified theories with conformally flat space slices. The post-Newtonian limit of each theory is constructed and its Parametrized Post-Newtonian (PPN) values are obtained by comparing it with Will's version of the formalism. Results obtained here, when combined with experimental data and with recent work by Nordtvedt and Will and by Ni, show that, of all theories thus far examined by our group, the only currently viable ones are general relativity, the Bergmann-Wagoner scalar-tensor theory and its special cases (Nordtvedt; Brans-Dicke-Jordan), and a recent, new vector-tensor theory by Nordtvedt, Hellings, and Will.
Gravitational field self-limitation and its role in the Universe
Gershtein, Semen S; Logunov, Anatolii A; Mestvirishvili, Mirian A [State Research Center ' Institute of High Energy Physics' , Protvino, Moscow Region (Russian Federation)
2006-11-30
It is shown that according to the relativistic theory of gravity, the gravitational field slows down the rate of time flow but stops doing so when the field is strong, thus displaying its tendency toward self-limitation of the gravitational potential. This property of the gravitational field prevents massive bodies from collapsing and allows a homogeneous isotropic universe to evolve cyclically. (physics of our days)
General relativistic tidal heating for Moller pseudotensor
So, Lau Loi
2015-01-01
Thorne elucidated that the relativistic tidal heating is the same as the Newtonian theory. Moreover, Thorne also claimed that the tidal heating is independent of how one localizes gravitational energy and is unambiguously given by a certain formula. Purdue and Favata calculated the tidal heating for different classical pseudotensors including Moller and obtained the results all matched with the Newtonian perspective. After re-examined this Moller pseudotensor, we find that there does not exist any tidal heating value. Thus we claim that the relativistic tidal heating is pseudotensor independent under the condition that if the peusdotensor is a Freud typed superpotential.
Gauge theories of gravitation a reader with commentaries
Blagojevic, Milutin
2013-01-01
In the last five decades, the gauge approach to gravity has represented a research area of increasing importance for our understanding of the physics of fundamental interactions. A full clarification of the gauge dynamics of gravity is expected to be the last missing link to the hidden structure of a consistent unification of all the fundamental interactions, based on the gauge principle. The aim of the present reprint volume, with commentaries by Milutin Blagojevi & 263; and Friedrich W Hehl, is to introduce graduate and advanced undergraduate students of theoretical or mathematical physics, or any other interested researcher, to the field of classical gauge theories of gravity. This is not just an ordinary reprint volume; it is a guide to the literature on gauge theories of gravity. The reader is encouraged first to study the introductory commentaries and to become familiar with the basic content of the reprints and related ideas, then he/she can choose to read a specific reprint or reprints, and after ...
Relativistic thermodynamics, a Lagrangian field theory for general flows including rotation
Frønsdal, Christian
Any theory that is based on an action principle has a much greater predictive power than one that does not have such a formulation. The formulation of a dynamical theory of General Relativity, including matter, is here viewed as a problem of coupling Einstein’s theory of pure gravity to an independently chosen and well-defined field theory of matter. It is well known that this is accomplished in a most natural way when both theories are formulated as relativistic, Lagrangian field theories, as is the case with Einstein-Maxwell theory. Special matter models of this type have been available; here a more general thermodynamical model that allows for vortex flows is presented. In a wider context, the problem of subjecting hydrodynamics and thermodynamics to an action principle is one that has been pursued for at least 150 years. A solution to this problem has been known for some time, but only under the strong restriction to potential flows. A variational principle for general flows has become available. It represents a development of the Navier-Stokes-Fourier approach to fluid dynamics. The principal innovation is the recognition that two kinds of flow velocity fields are needed, one the gradient of a scalar field and the other the time derivative of a vector field, the latter closely associated with vorticity. In the relativistic theory that is presented here, the latter is the Hodge dual of an exact 3-form, well known as the notoph field of Ogievetskij and Palubarinov, the B-field of Kalb and Ramond and the vorticity field of Lund and Regge. The total number of degrees of freedom of a unary system, including the density and the two velocity fields is 4, as expected — as in classical hydrodynamics. In this paper, we do not reduce Einstein’s dynamical equation for the metric to phenomenology, which would have denied the relevance of any intrinsic dynamics for the matter sector, nor do we abandon the equation of continuity - the very soul of hydrodynamics.
Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity
Hartong, Jelle; Obers, Niels A
2016-01-01
We show that certain three-dimensional Horava-Lifshitz gravity theories can be written as Chern-Simons gauge theories on various non-relativistic algebras. The algebras are specific extensions of the Bargmann, Newton-Hooke and Schroedinger algebra each of which has the Galilean algebra as a subalgebra. To show this we employ the fact that Horava-Lifshitz gravity corresponds to dynamical Newton-Cartan geometry. In particular, the extended Bargmann (Newton-Hooke) Chern-Simons theory corresponds to projectable Horava-Lifshitz gravity with a local U(1) gauge symmetry without (with) a cosmological constant. Moreover we identify an extended Schroedinger algebra containing 3 extra generators that are central with respect to the subalgebra of Galilean boosts, momenta and rotations, for which the Chern-Simons theory gives rise to a novel version of non-projectable conformal Horava-Lifshitz gravity that we refer to as Schroedinger gravity. This theory has a z=2 Lifshitz geometry as a vacuum solution and thus provides a...
Kang, Teyoun; Kim, Young-Kuk; Hur, Min Sup
2016-10-01
Owing to the rapid development of laser technologies, relativistically-induced transmittance (RT) of ultra-intense laser pulses in overdense plasmas is now a practically important matter. RT could give either deleterious or positive effects depending on the kinds of laser-plasma interactions. In radiation-pressure-acceleration (RPA), enhanced transmittance lowers the momentum transfer from the pulse to the ions. Meanwhile, in collisionless-electrostatic-shock, the acceleration efficiency can be increased owing to the effective heating of upstream electrons by transmitted laser fields. Previous theories mostly have handled RT in ideal plasmas, such as an infinitely long uniform plasma or a delta-function-like slab. In the actual applications, however, RT is generally combined with other dynamics, such as plasma density compression, leading to RT under a plasma in other cases. We developed one-dimensional RT theories for circularly polarized laser pulses, which would be used for such realistic plasma profiles. According to our theory, optimal thickness condition should be modified in RPA. Furthermore we developed our theory so that RT in the common two-step density plasma can be modeled. In this poster, we present the derivation and the comparison of the improved theory with PIC simulation results. This work was supported by the Basic Science Research Program (Grant Number NRF-2013R1A1A2006353).
Schwarzschild-type solution in an effective gravitational theory with local Galilean invariance
Cuzinatto, R R; De Montigny, M; Khanna, F C
2009-01-01
We construct a Schwarzschild-type exact external solution for a theory of gravity admitting local Galilean invariance. In order to realize the Galilean invariance we need to adopt a five-dimensional manifold. The solution for the gravitational field equations obeys a Birkhoff-like theorem. Three classic tests of general relativity are analyzed in detail: the perihelion shift of the planet Mercury, the deflection of light by the Sun, and the gravitational redshift of atomic spectral lines. The Galilean version of these tests exhibits an additional parameter $b$ related to the fifth-coordinate. This constant $b$ can be estimated by a comparison with observational data. We observe that the Galilean theory is able to reproduce the results traditionally predicted by general relativity in the limit of negligible $b$. This shows that the tests are not specifically Lorentz invariant.
Constraining Modified Theories of Gravity with Gravitational-Wave Stochastic Backgrounds.
Maselli, Andrea; Marassi, Stefania; Ferrari, Valeria; Kokkotas, Kostas; Schneider, Raffaella
2016-08-26
The direct discovery of gravitational waves has finally opened a new observational window on our Universe, suggesting that the population of coalescing binary black holes is larger than previously expected. These sources produce an unresolved background of gravitational waves, potentially observable by ground-based interferometers. In this Letter we investigate how modified theories of gravity, modeled using the parametrized post-Einsteinian formalism, affect the expected signal, and analyze the detectability of the resulting stochastic background by current and future ground-based interferometers. We find the constraints that Advanced LIGO would be able to set on modified theories, showing that they may significantly improve the current bounds obtained from astrophysical observations of binary pulsars.
Variational principle for the P(4) affine theory of gravitation and electromagnetism
Chilton, J.H.; Norris, L.K. [North Carolina State Univ., Raleigh, NC (United States)
1992-07-01
We propose a Lagrangian for the P(4) theory of gravitation and electromagnetism which is a straightforward generalization of the Einstein Lagrangian. A constrained Palatini variation of this Lagrangian yields the geometrical Einstein-Maxwell affine field equations. We show that these results can be extended easily to include both electric and magnetic charges. Finally, we consider conservation laws arising from the invariance properties of the Lagrangian. 14 refs.
Reddy, D. R. K.; Anitha, S.; Umadevi, S.
2016-11-01
In this paper, we investigate five dimensional space-time filled with minimally interacting dark matter and holographic dark energy in Brans-Dicke (Phys. Rev. 124:925, 1961) scalar-tensor theory of gravitation. The exact solutions of the field equations are obtained using (i) special law of variation for Hubble's parameter that yields constant value of deceleration parameter and (ii) a relation between metric potentials. The physical and geometrical aspects of the model are also discussed.
Strange quark matter attached to string cloud in general scalar tensor theory of gravitation
V U M Rao
2014-12-01
Full Text Available Bianchi type-VI0 space time with strange quark matter attached to string cloud in Nordtvedt [1] general scalar tensor theory of gravitation with the help of a special case proposed by Schwinger [2] is obtained. The field equations have been solved by using the anisotropy feature of the universe in the Bianchi type-VI0 space time. Some important features of the model, thus obtained, have been discussed
Strong-field effects and time asymmetry in general relativity and in bimetric gravitation theory
Damour, Thibault
1984-10-01
The concepts underlying our present theoretical understanding of the radiative two-condensed-body problem in general relativity and in bimetric gravitation theory are critically reviewed. The relevance of the 1935 Einstein-Rosen “bridge” article is emphasized. The possibility (first suggested by N. Rosen, for the linearized approximation) of extending to gravity the Wheeler-Feynman time-symmetric approach is questioned.
Regular Charged Solutions in Mφller's Tetrad Theory of Gravitation
Gamal G. L. Nashed
2007-01-01
We find the most general tetrads which give a regular charged spacetime in tetrad theory of gravitation. The metric is a static one and it includes the Schwarzschild and Reissner Nordstr(o)m black holes. The energy content contained in a sphere of radius R is calculated using the superpotential given by Mφller in the context of Weitzenb(o)ck spacetime.
Strong-field effects and time asymmetry in general relativity and in bimetric gravitation theory
Damour, T.
1984-10-01
The concepts underlying our present theoretical understanding of the radiative two-condensed-body problem in general relatively and in bimetric gravitation theory are critically reviewed. The relevance of the 1935 Einstein-Rosen ''bridge'' article is emphasized. The possibility (first suggested by N. Rosen, for the linearized approximation) of extending to gravity the Wheeler-Reynman time-symmetric approach is questioned.
NEWTONIAN EQUATIONS OF MOTION AND HARMONIC CONDITIONS IN THE THEORY OF GRAVITATION,
The relation between Newtonian equations of motion and harmonic conditions in Einstein’s theory of gravitation is examined. Assuming that a metric...tensor can be represented in the form of a power series, it is proved that in order to obtain Newtonian equations of motion, it is necessary to use...harmonic coordinate conditions of zero order. It is also proved that in Infeld’s method for deriving Newtonian equations of motion from the equations
Bagayoko, Diola
In 2014, 50 years following the introduction of density functional theory (DFT), a rigorous understanding of it was published [AIP Advances, 4, 127104 (2014)]. This understanding included necessary steps ab initio electronic structure calculations have to take if their results are to possess the full physical content of DFT. These steps guarantee the fulfillment of conditions of validity of DFT; not surprisingly, they have led to accurate descriptions of several dozens of semiconductors, from first principle, without invoking derivative discontinuity or self-interaction correction. This presentation shows the mathematically and physically rigorous understanding of the relativistic extension of DFT by Rajagopal and Callaway {Phys. Rev. B 7, 1912 (1973)]. As in the non-relativistic case, the attainment of the absolute minima of the occupied energies is a necessary condition for the corresponding current density to be that of the ground state of the system and for computational results to agree with corresponding, experimental ones. Acknowledgments:This work was funded in part by the US National Science Foundation [NSF, Award Nos. EPS-1003897, NSF (2010-2015)-RII-SUBR, and HRD-1002541], the US Department of Energy, National Nuclear Security Administration (NNSA, Award No. DE-NA0002630), LaSPACE, and LONI-SUBR.
Cannoni, Mirco [Universidad de Huelva, Departamento de Fisica Aplicada, Facultad de Ciencias Experimentales, Huelva (Spain)
2016-03-15
We find an exact formula for the thermally averaged cross section times the relative velocity left angle σv{sub rel} right angle with relativistic Maxwell-Boltzmann statistics. The formula is valid in the effective field theory approach when the masses of the annihilation products can be neglected compared with the dark matter mass and cut-off scale. The expansion at x = m/T >> 1 directly gives the nonrelativistic limit of left angle σv{sub rel} right angle, which is usually used to compute the relic abundance for heavy particles that decouple when they are nonrelativistic. We compare this expansion with the one obtained by expanding the total cross section σ(s) in powers of the nonrelativistic relative velocity vr. We show the correct invariant procedure that gives the nonrelativistic average left angle σv{sub rel} right angle {sub nr} coinciding with the large x expansion of left angle σv{sub rel} right angle in the comoving frame. We explicitly formulate flux, cross section, thermal average, collision integral of the Boltzmann equation in an invariant way using the true relativistic relative v{sub rel}, showing the uselessness of the Moeller velocity and further elucidating the conceptual and numerical inconsistencies related with its use. (orig.)
Meier, D L
2003-01-01
I review recent progress in the theory of relativistic jet production, with special emphasis on unifying black hole sources of stellar and supermassive size. Observations of both classes of objects, as well as theoretical considerations, indicate that such jets may be launched with a spine/sheath flow structure, having a much higher Lorentz factor ($\\sim 50$) near the axis and a lower speed ($\\Gamma \\sim 10$ or so) away from the axis. It has become clear that one can no longer consider models of accretion flows without also considering the production of a jet by that flow. Furthermore, the rotation rate of the black hole also must be taken into account. It provides a third parameter that should break the mass/accretion rate degeneracy and perhaps explain why some sources are radio loud and some radio quiet. Slow jet acceleration and collimation is expected theoretically, and can explain some of the observed features of AGN jet sources. Finally, relativistic jets launched by MHD/ED processes are Poynting flux ...
Magnetic properties of f-electron systems in spin-polarized relativistic density functional theory
Yamagami, H.; Mavromaras, A.; Kübler, J.
1997-12-01
The magnetic ground state of the series of lanthanide and actinide trivalent ions is investigated by means of spin-polarized relativistic spin-density functional theory. In the local density functional approximation (LDA) an internal effective magnetic field due to exchange and correlation couples to the spin degrees of freedom. The resulting set of coupled Dirac equations yields ground-state multiplets that obey the well-known Hund's rules. This remarkable result comes about by the coupling of the j = l + 1/2 with the j = l - 1/2 states due to the exchange - correlation potential that is, as usual, the functional derivative of the exchange - correlation energy with respect to the spin magnetic moment. The effect of the coupling is shown to depend on the varying relative strengths of spin - orbit coupling and exchange splitting within the f series. Since in the f levels the internal exchange splitting dominates rather than the spin - orbit splitting, the energy level scheme is that of the Paschen - Back effect, and thus features of the Russell - Saunders coupling persist in spite of relativistic effects.
Low-energy effective field theory for finite-temperature relativistic superfluids
Nicolis, Alberto
2011-01-01
We derive the low-energy effective action governing the infrared dynamics of relativistic superfluids at finite temperature. We organize our derivation in an effective field theory fashion-purely in terms of infrared degrees of freedom and symmetries. Our degrees of freedom are the superfluid phase \\psi, and the comoving coordinates for the volume elements of the normal fluid component. The presence of two sound modes follows straightforwardly from Taylor-expanding the action at second order in small perturbations. We match our description to more conventional hydrodynamical ones, thus linking the functional form of our Lagrangian to the equation of state, which we assume as an input. We re-derive in our language some standard properties of relativistic superfluids in the high-temperature and low-temperature limits. As an illustration of the efficiency of our methods, we compute the cross-section for a sound wave (of either type) scattering off a superfluid vortex at temperatures right beneath the critical on...
Bast, Radovan; Thorvaldsen, Andreas J.; Ringholm, Magnus; Ruud, Kenneth
2009-02-01
We present the first analytic calculations of the second hyperpolarizability in a relativistic framework. The calculations are made possible by our recent developments of a response theory built on a quasienergy formalism, in which the basis set may be both time and perturbation dependent. The approach is formulated for an arbitrary self-consistent field state in the atomic orbital basis. The implementation consists of a stand-alone code that only requires the unperturbed density in the atomic orbital basis as input, as well as a linear response solver by which we can determine the perturbed density matrices to different orders, at each new order solving equations that have the same structure as the linear response equation. Using these features of our formalism, we extend in this paper our approach to the relativistic domain, utilizing both two- and four-component relativistic wave functions. We apply the formalism to the calculation of the electronic and pure vibrational contributions to the second hyperpolarizability tensor for the hydrogen halides. Our results demonstrate that relativistic effects can be substantial for frequency-dependent second hyperpolarizabilities. Due to changes in the pole structure when going to the relativistic domain, the relativistic corrections to the hyperpolarizabilities are not transferable between different optical processes, except for very low frequencies.
Bast, Radovan; Thorvaldsen, Andreas J.; Ringholm, Magnus [Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Tromso, N-9037 Tromso (Norway); Ruud, Kenneth [Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Tromso, N-9037 Tromso (Norway)], E-mail: kenneth.ruud@chem.uit.no
2009-02-17
We present the first analytic calculations of the second hyperpolarizability in a relativistic framework. The calculations are made possible by our recent developments of a response theory built on a quasienergy formalism, in which the basis set may be both time and perturbation dependent. The approach is formulated for an arbitrary self-consistent field state in the atomic orbital basis. The implementation consists of a stand-alone code that only requires the unperturbed density in the atomic orbital basis as input, as well as a linear response solver by which we can determine the perturbed density matrices to different orders, at each new order solving equations that have the same structure as the linear response equation. Using these features of our formalism, we extend in this paper our approach to the relativistic domain, utilizing both two- and four-component relativistic wave functions. We apply the formalism to the calculation of the electronic and pure vibrational contributions to the second hyperpolarizability tensor for the hydrogen halides. Our results demonstrate that relativistic effects can be substantial for frequency-dependent second hyperpolarizabilities. Due to changes in the pole structure when going to the relativistic domain, the relativistic corrections to the hyperpolarizabilities are not transferable between different optical processes, except for very low frequencies.
Gravitational theories with stable (anti-)de Sitter backgrounds
Biswas, Tirthabir; Mazumdar, Anupam
2016-01-01
In this article we will construct the most general torsion-free parity-invariant covariant theory of gravity that is free from ghost-like and tachyonic nstabilities around constant curvature space-times in four dimensions. Specifically, this includes the Minkowski, de Sitter and anti-de Sitter backgrounds. We will first argue in details how starting from a general covariant action for the metric one arrives at an "equivalent" action that at most contains terms that are quadratic in curvatures but nevertheless is sufficient for the purpose of studying stability of the original action. We will then briefly discuss how such a "quadratic curvature action" can be decomposed in a covariant formalism into separate sectors involving the tensor, vector and scalar modes of the metric tensor; most of the details of the analysis however, will be presented in an accompanying paper. We will find that only the transverse and trace-less spin-2 graviton with its two helicity states and possibly a spin-0 Brans-Dicke type scala...
Observational constraints of the gravitational waves in the Brans-Dicke theory
Freitas, Rodolfo Camargo de; Goncalves, Sergio Vitorino de Borba [Universidade Federal do Espirito Santo (UFES), ES (Brazil). Dept. de Fisica. Grupo de Gravitacao e Cosmologia
2011-07-01
Full text: The cosmic inflation, which is the hypotheses that the early Universe has passed by a period of exponential expansion, is currently the most accepted and studied theory to explain the early fluctuations which evolved to the large scales structures which we observe today. The gravitational waves, when detected, can give us important information about inflation. In this work we investigate the quantum origin of the primordial cosmological gravitational waves in the Brans-Dicke theory. We compute the number of gravitons N{sub k} produced during the extended inflation and the three observables: the power spectrum P{sub T}, the spectral index n{sub T} and the energy density of the gravitational waves {Omega}{sub k}. By comparison with general relativity we see that the results for both theories are the same for the case of the particles number N{sub k} and for the case of the power spectrum P{sub T} and the energy density {Omega}{sub k} only when the Brans-Dicke coupling parameter {omega} has a value less than 10. For the spectral index n{sub T} we found that when {omega} is bigger than unity the spectral index approximates the expression found in the General Relativity. This may awake us to the possibility that {omega} varies with the cosmological scale. (author)
Spherically Symmetric Solution of the Weyl-Dirac Theory of Gravitation and its Consequences
Babourova, O. V.; Frolov, B. N.; Kudlaev, P. E.; Romanova, E. V.
2016-12-01
The Poincaré and Poincaré-Weyl gauge theories of gravitation with Lagrangians quadratic on curvature and torsion in post-Riemannian spaces with the Dirac scalar field is discussed in a historical aspect. The various hypotheses concerning the models of a dark matter with the help of a scalar field are considered. The new conformal Weyl-Dirac theory of gravitation is proposed, which is a gravitational theory in Cartan-Weyl spacetime with the Dirac scalar field representing the dark matter model. A static spherically symmetric solution of the field equations in vacuum for a central compact mass is obtained as the metrics conformal to the Yilmaz-Rosen metrics. On the base of this solution one considers a radial movement of an interplanetary spacecraft starting from the Earth. Using the Newton approximation one obtains that the asymptotic line-of-sight velocity in this case depends on the parameters of the solution, and therefore one can obtain, on basis of the observable data, the values of these parameters and then the value of a rest mass of the Dirac scalar field.
Faller, Sven [Universitaet Siegen, Theoretische Physik 1 (Germany)
2008-07-01
In the last years a lot of papers were published treating general relativity as an effective field theory. We are dealing with general relativity and the combination of general relativity and scalar QED as effective field theories. For effective field theories the quantization is well known therefore we are able to quantize general relativity and the combination of general relativity and scalar QED. The vertex rules can be extracted from the action and the non-analytical contributions to the 1-loop scattering matrix of scalars and charged scalars are calculated in the non-relativistic limit. The non-analytical parts of the scattering amplitudes yield the long range, low energy, leading quantum corrections. From the general relativity as an effective field theory the leading quantum corrections to the Newtonian gravity is constructed. General relativity combined with scalar QED yield the post-Newtonian and quantum corrections to the two-particle non-relativistic scattering matrix potential for charged scalar particles. The difference to other publications is finally discussed.
On the Relativistic Formulation of Matter
Vishwakarma, Ram Gopal
2012-01-01
A critical analysis of the relativistic formulation of matter reveals some surprising inconsistencies and paradoxes. Corrections are discovered which lead to the long-sought-after equality of the gravitational and inertial masses, which are otherwise different in general relativity. Realizing the potentially great impact of the discovered corrections, an overview of the situation is provided resulting from the newly discovered crisis, amid the evidences defending the theory.
Herrera, L
2011-01-01
We identify the factors responsible for the appearance of energy-density inhomogeneities in a self-gravitating fluid, and describe the evolution of those factors from an initially homogeneous distribution. It is shown that a specific combination of the Weyl tensor and/or local anisotropy of pressure and/or dissipative fluxes entails the formation of energy-density inhomogeneities. Different cases are analyzed in detail and in the particular case of dissipative fluids, the role of relaxational processes as well as non-local effects are brought out.
New parameterization of the effective field theory motivated relativistic mean field model
Kumar, Bharat; Singh, S. K.; Agrawal, B. K.; Patra, S. K.
2017-10-01
A new parameter set is generated for finite and infinite nuclear system within the effective field theory motivated relativistic mean field (ERMF) formalism. The isovector part of the ERMF model employed in the present study includes the coupling of nucleons to the δ and ρ mesons and the cross-coupling of ρ mesons to the σ and ω mesons. The results for the finite and infinite nuclear systems obtained using our parameter set are in harmony with the available experimental data. We find the maximum mass of the neutron star to be 2.03M⊙ and yet a relatively smaller radius at the canonical mass, 12.69 km, as required by the available data.
Nuclear Matter in Relativistic Mean Field Theory with Isovector Scalar Meson
Kubis, S
1997-01-01
Relativistic mean field (RMF) theory of nuclear matter with the isovector scalar mean field corresponding to the delta-meson [a_0(980)] is studied. While the delta-meson mean field vanishes in symmetric nuclear matter, it can influence properties of asymmetric nuclear matter in neutron stars. The RMF contribution due to delta-field to the nuclear symmetry energy is negative. To fit the empirical value, E_s=30 MeV, a stronger rho-meson coupling is required than in the absence of the delta-field. The energy per particle of neutron matter is then larger at high densities than the one with no delta-field included. Also, the proton fraction of beta-stable matter increases. Splitting of proton and neutron effective masses due to the delta-field can affect transport properties of neutron star matter.
Neutron Stars in Relativistic Mean Field Theory with Isovector Scalar Meson
Kubis, S; Stachniewicz, S
1998-01-01
We study the equation of state of beta-stable dense matter and models of neutron stars in the relativistic mean field theory with the isovector scalar mean field corresponding to the delta-meson [a_0(980)]. A range of values of the delta-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E_s=30 MeV. We find that the quantity most sensitive to the delta-meson coupling is the proton fraction of neutron star matter. It increases significantly in the presence of the delta-field. The energy per baryon also increases but the effect is smaller. The equation of state becomes slightly stiffer and the maximum neutron star mass increases for stronger delta-meson coupling.
Three-dimensional angular momentum projection in relativistic mean-field theory
Yao, J M; Ring, P; Arteaga, D Pena
2009-01-01
Based on a relativistic mean-field theory with an effective point coupling between the nucleons, three-dimensional angular momentum projection is implemented for the first time to project out states with designed angular momentum from deformed intrinsic states generated by triaxial quadrupole constraints. The same effective parameter set PC-F1 of the effective interaction is used for deriving the mean field and the collective Hamiltonian. Pairing correlations are taken into account by the BCS method using both monopole forces and zero range d-forces with strength parameters adjusted to experimental even-odd mass differences. The method is applied successfully to the isotopes 24Mg, 30Mg, and 32Mg.
Space-Time Quantization and Nonlocal Field Theory -Relativistic Second Quantization of Matrix Model
Tanaka, S
2000-01-01
We propose relativistic second quantization of matrix model of D particles in a general framework of nonlocal field theory based on Snyder-Yang's quantized space-time. Second-quantized nonlocal field is in general noncommutative with quantized space-time, but conjectured to become commutative with light cone time $X^+$. This conjecture enables us to find second-quantized Hamiltonian of D particle system and Heisenberg's equation of motion of second-quantized {\\bf D} field in close contact with Hamiltonian given in matrix model. We propose Hamilton's principle of Lorentz-invariant action of {\\bf D} field and investigate what conditions or approximations are needed to reproduce the above Heisenberg's equation given in light cone time. Both noncommutativities appearing in position coordinates of D particles in matrix model and in quantized space-time will be eventually unified through second quantization of matrix model.
Ground State Properties of Ds Isotopes Within the Relativistic Mean Field Theory
张海飞; 张鸿飞; 李君清
2012-01-01
The ground state properties of Ds (Z=110) isotopes (N=151-195) are studied in the framework of the relativistic mean field (RMF) theory with the effective interaction NL-Z2.The pairing correlation is treated within the conventional BCS approximation.The calculated binding energies are consistent with the results from finite-range droplet model (FRDM) and Macroscopic-microscopic method (MMM).The quadrupole deformation,α-decay energy,α-decay half-live,charge radius,two-neutron separation energy and single-particle spectra are analyzed for Ds isotopes to find new characteristics of superheavy nuclei (SHN).Among the calculated results it is rather distinct that the isotopic shift appears evidently at neutron number N=184.
The neutron halo structure of 17B studied with the relativistic Hartree-Bogoliubov theory
JI Juan-Xia; LI Jia-Xing; HAN Rui; WANG Jian-Song; HU Qiang
2012-01-01
The properties of neutron-rich boron isotopes are studied in the relativistic continuum HartreeBogoliubov theory in coordinate space with NL-SH,PK1 and TM2 effective interactions.Pairing corrections are taken into account by a density dependent force of zero range.The binding energies calculated for these nuclei agree with the experimental data quite well.The neutron-rich nucleus 17B has been predicted to have a two-neutron halo structure in its ground state.The halo structure of 17B is reproduced in a self-consistent way,and this halo is shown to be formed by the valence neutron level 2s1/2.
Description of 178 Hfm2 in the Constrained Relativistic Mean Field Theory
ZHANG Wei; PENG Jing; ZHANG Shuang-Quan
2009-01-01
Properties of the ground state of 178 Hf and the isomeric state 178Hfn2 are studied within the adiabatic and diabatic constrained relativistic mean field (RMF) approaches. The RMF calculations reproduce well the binding energy and the deformation for the ground state of 178Hf. Using the ground state single-particle eigenvalues obtained in the present calculation, the lowest excitation configuration with Kπ = 16+ is found to be v(7/2- [514])-1 (9/2+ [624])1 π(7/2+ [404])-1 (9/2-[514])1. Its excitation energy calculated by the RMF theory with time-odd fields taken into account is equal to 2.801 MeV, i.e., close to the 178 Hfm2 experimental excitation energy 2.446 MeV. The self-consistent procedure accounting for the time-odd component of the meson fields is the most important aspect of the present calculation.
Haas, Fernando
2016-11-01
A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the invariance condition develops as a set of partial differential equations determining the symmetry transformation. The solution is provided in the case of real scalar, complex scalar, free electromagnetic, and charged electromagnetic fields. Besides the usual conservation laws, a less popular symmetry is analyzed: the symmetry associated with the linear superposition of solutions, whenever applicable. The role of gauge invariance is emphasized. The case of the charged scalar particle under external electromagnetic fields is considered, and the accompanying Noether point symmetries determined. Noether point symmetries for a dynamical system in extended gravity cosmology are also deduced.
Systematic Derivation of Noether Point Symmetries in Special Relativistic Field Theories
Haas, Fernando
2016-01-01
A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the invariance condition develops as a set of partial differential equations determining the symmetry transformation. The solution is provided in the case of real scalar, complex scalar, free electromagnetic, and charged electromagnetic fields. Besides the usual conservation laws, a less popular symmetry is analyzed: the symmetry associated with the linear superposition of solutions, whenever applicable. The role of gauge invariance is emphasized. The case of the charged scalar particle under external electromagnetic fields is considered, and the accompanying Noether point symmetries determined.
Gabriel, G. J.
1980-01-01
A new theorem on a class of four-dimensional skew-symmetric tensors is demonstrated. Coupled with the relativistic covariant form of Maxwell's equations, this theorem consolidates the classifications of guided waves by combining the three types - TE, TM, TEM - under a uniform condition applied to the generating four-potential which is Lorentz invariant. Each type corresponds to a potential of which a pair of the four components vanishes in a particular frame. Through appropriate normalization conditions, the resulting time-domain equations for the field amplitudes are readily reduced to modified telegraphist equations, which in turn lead to distributed network representations for each of the three types. The ambiguity of distributed network formalisms in general is elucidated and the concept of network parameter densities such as traditionally employed in TEM transmission line theory is questioned.
Bast, Radovan; Jensen, Hans Jørgen Aagaard; Saue, Trond
2009-01-01
We report an implementation of adiabatic time-dependent density functional theory based on the 4-component relativistic Dirac-Coulomb Hamiltonian and a closed-shell reference. The implementation includes noncollinear spin magnetization and full derivatives of functionals, including hybrid...... and time reversal symmetry on trial vectors to obtain even better reductions in terms of memory and run time, and without invoking approximations. Further reductions are obtained by exploiting point group symmetries for D2h and subgroups in a symmetry scheme where symmetry reductions translate...... into reduction of algebra from quaternion to complex or real. For hybrid GGAs with noncollinear spin magnetization we derive a new computationally advantageous equation for the full second variational derivatives of such exchange-correlation functionals. We apply our implementation to calculations on the ns2...
Barausse, Enrico; Yunes, Nicolás; Chamberlain, Katie
2016-06-17
The aLIGO detection of the black-hole binary GW150914 opens a new era for probing extreme gravity. Many gravity theories predict the emission of dipole gravitational radiation by binaries. This is excluded to high accuracy in binary pulsars, but entire classes of theories predict this effect predominantly (or only) in binaries involving black holes. Joint observations of GW150914-like systems by aLIGO and eLISA will improve bounds on dipole emission from black-hole binaries by 6 orders of magnitude relative to current constraints, provided that eLISA is not dramatically descoped.
Tuning the stochastic background of gravitational waves with theory and observations
Corda, Christian; De Laurentis, Mariafelicia
2007-01-01
In this this paper the stochastic background of gravitational waves (SBGWs) is analyzed with the auxilium of the WMAP data. We emphasize that, in general, in previous works in the literature about the SBGWs, old COBE data were used. After this, we want to face the problem of how the SBGWs and f(R) gravity can be related, showing, vice versa, that a revealed SBGWs could be a powerly probe for a given theory of gravity. In this way, it will also be shown that the conformal treatment of SBGWs can be used to parametrize in a natural way f(R) theories.
Quantum Cosmology in Bergmann-Wagoner Scalar-tensor Gravitational Theory
Pimentel, L O; Pimentel, Luis O.; Mora, Cesar
2000-01-01
The Wheeler-DeWitt equation is solved for the Bergmann-Wagoner scalar-tensor gravitational theory in the case of Friedmann-Robertson- Walker cosmological model. We present solutions for several cosmological functions: i) \\lambda(\\phi)=0, ii) \\lambda(\\phi)=3\\Lambda_0\\phi and iii) a more complex \\lambda(\\phi), that depends on the choice of the coupling function, considering closed, flat and hyperbolic Friedmann universes (k=1, 0, -1). In the first two cases we show particular quantum wormhole solutions. Also, classical solutions are considered for some scalar-tensor theories, and we study the third quantization of some minisuperspace models.
PPN parameters in gravitational theory with non-minimally derivative coupling
Zhu, Yi
2015-01-01
The non-minimal coupling of the kinetic term to Einstein's tensor helps the implementation of inflationary models due to the gravitationally enhanced friction. We calculate the parameterized post-Newtonian parameters for the scalar-tensor theory of gravity with non-minimally derivative coupling. We find that under experiment constraint from the orbits of millisecond pulsars in our galaxy, the theory deviates from Einstein's general relativity in the order of $10^{-20}$, and the effect of the non-minimal coupling is negligible if we take the scalar field as dynamical dark energy. Under the assumed conditions, the scalar field is required to be massless.
Gravitational self-force in nonvacuum spacetimes: An effective field theory derivation
Zimmerman, Peter
2015-09-01
In this paper we investigate the motion of small compact objects in nonvacuum spacetimes using methods from effective field theory in curved spacetime. Although a vacuum formulation is sufficient in many astrophysical contexts, there are applications such as the role of the self-force in enforcing cosmic censorship in the context of the overcharging problem, which necessitate an extension into the nonvacuum regime. The defining feature of the self-force problem in nonvacuum spacetimes is the coupling between gravitational and nongravitational field perturbations. The formulation of the self-force problem for nonvacuum spacetimes was recently provided in simultaneous papers by Zimmerman and Poisson [Gravitational self-force in nonvacuum spacetimes, Phys. Rev. D 90, 084030 (2014)] and Linz, Friedmann, and Wiseman [Combined gravitational and electromagnetic self-force on charged particles in electrovac spacetimes, Phys. Rev. D 90, 084031 (2014)]. Here we distinguish ourselves by working with the effective action rather than the field equations. The formalism utilizes the multi-index notation developed by Zimmerman and Poisson [Gravitational self-force in nonvacuum spacetimes, Phys. Rev. D 90, 084030 (2014) to accommodate the coupling between the different fields. Using dimensional regularization, we arrive at a finite expression for the local self-force expressed in terms of multi-index quantities evaluated in the background spacetime. We then apply the formalism to compute the coupled gravitational self-force in two explicit cases. First, we calculate the self-force on a massive particle possessing scalar charge and moving in a scalarvac spacetime. We then derive an expression for the self-force on an electrically charged, massive particle moving in an electrovac spacetime. In both cases, the force is expressed as a sum of local terms involving tensors defined in the background spacetime and evaluated at the current position of the particle, as well as tail integrals
Krechet, V. G.; Oshurko, V. B.; Lodi, M. N.
2016-12-01
A gravitational interaction of a scalar field with conformal coupling nR/6{φ}^2 (n = const) is considered within the framework of the affine-metric theory of gravitation, with the interaction with torsion and nonmetricity taken into account. It is shown that for different values of the constant n different forms of nonlinearities are induced in the scalar field and, in particular, for n = -1 a nonlinearity corresponding to the potential of the axion field is induced. Possible astrophysical consequences of such an effect are considered.
Testing Relativistic Gravity with Radio Pulsars
Wex, Norbert
2014-01-01
Before the 1970s, precision tests for gravity theories were constrained to the weak gravitational fields of the Solar system. Hence, only the weak-field slow-motion aspects of relativistic celestial mechanics could be investigated. Testing gravity beyond the first post-Newtonian contributions was for a long time out of reach. The discovery of the first binary pulsar by Russell Hulse and Joseph Taylor in the summer of 1974 initiated a completely new field for testing the relativistic dynamics of gravitationally interacting bodies. For the first time the back reaction of gravitational wave emission on the binary motion could be studied. Furthermore, the Hulse-Taylor pulsar provided the first test bed for the orbital dynamics of strongly self-gravitating bodies. To date there are a number of pulsars known, which can be utilized for precision test of gravity. Depending on their orbital properties and their companion, these pulsars provide tests for various different aspects of relativistic dynamics. Besides tests...
Point-particle effective field theory III: relativistic fermions and the Dirac equation
Burgess, C. P.; Hayman, Peter; Rummel, Markus; Zalavári, László
2017-09-01
We formulate point-particle effective field theory (PPEFT) for relativistic spin-half fermions interacting with a massive, charged finite-sized source using a first-quantized effective field theory for the heavy compact object and a second-quantized language for the lighter fermion with which it interacts. This description shows how to determine the near-source boundary condition for the Dirac field in terms of the relevant physical properties of the source, and reduces to the standard choices in the limit of a point source. Using a first-quantized effective description is appropriate when the compact object is sufficiently heavy, and is simpler than (though equivalent to) the effective theory that treats the compact source in a second-quantized way. As an application we use the PPEFT to parameterize the leading energy shift for the bound energy levels due to finite-sized source effects in a model-independent way, allowing these effects to be fit in precision measurements. Besides capturing finite-source-size effects, the PPEFT treatment also efficiently captures how other short-distance source interactions can shift bound-state energy levels, such as due to vacuum polarization (through the Uehling potential) or strong interactions for Coulomb bound states of hadrons, or any hypothetical new short-range forces sourced by nuclei.
Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories
Bastianello, Alvise; Sotiriadis, Spyros
2017-02-01
We study the quench dynamics in continuous relativistic quantum field theory, more specifically the locality properties of the large time stationary state. After a quantum quench in a one-dimensional integrable model, the expectation values of local observables are expected to relax to a generalized Gibbs ensemble (GGE), constructed out of the conserved charges of the model. Quenching to a free bosonic theory, it has been shown that the system indeed relaxes to a GGE described by the momentum mode occupation numbers. We first address the question whether the latter can be written directly in terms of local charges and we find that, in contrast to the lattice case, this is not possible in continuous field theories. We then investigate the less stringent requirement of the existence of a sequence of truncated local GGEs that converges to the correct steady state, in the sense of the expectation values of the local observables. While we show that such a sequence indeed exists, in order to unequivocally determine the so-defined GGE, we find that information about the expectation value of the recently discovered quasi-local charges is in the end necessary, the latter being the suitable generalization of the local charges while passing from the lattice to the continuum. Lastly, we study the locality properties of the GGE and show that the latter is completely determined by the knowledge of the expectation value of a countable set of suitably defined quasi-local charges.
Biswas, Tirthabir; Koshelev, Alexey S.; Mazumdar, Anupam
2017-02-01
In this paper we provide the criteria for any generally covariant, parity preserving, and torsion-free theory of gravity to possess a stable de Sitter (dS) or anti-de Sitter (AdS) background. By stability we mean the absence of tachyonic or ghostlike states in the perturbative spectrum that can lead to classical instabilities and violation of quantum unitarity. While we find that the usual suspects, the F (R ) and F (G ) theories, can indeed possess consistent (A)dS backgrounds, G being the Gauss-Bonnet term, another interesting class of theories, string-inspired infinite derivative gravitational theories, can also be consistent around such curved vacuum solutions. Our study should not only be relevant for quantum gravity and early universe cosmology involving ultraviolet physics, but also for modifications of gravity in the infrared sector vying to replace dark energy.
Nonsymmetric unified theory of gravitation, electromagnetism and Yang-Mills field
Ragusa, S [Departamento de Fisica e Informatica, Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, CP 369, 13560-970 Sao Carlos, SP (Brazil)
2002-12-07
The recently studied new variation of Einstein's metric nonsymmetric unified field theory of gravitation and electromagnetism is enlarged to include the Yang-Mills field theory. It is shown that the antisymmetric part of the metric tensor, now a 2x2 matrix, can be made to describe both a field obeying Maxwell's equations and a field obeying Yang-Mills's field equations in the flat space linear approximation, thereby making its identification with the sum of a generalized electromagnetic and isotopic field strength tensors a possibly consistent procedure. The theory is shown to be free of unphysical ghost-negative energy radiative modes even when expanded on a curved Riemannian background. The Einstein-Maxwell-Yang-Mills theory is contained in the first approximation of the field equations on a curved general relativity background.
Conformal field theory of a space-filling string of gravitational ancestry
Bunster, Claudio
2016-01-01
We present a classical conformal field theory on an arbitrary two-dimensional spacetime background. The dynamical object is a space-filling string, and the evolution may be thought as occurring on the manifold of the conformal group. The theory is a "descendant" of the theory of gravitation in two-dimensional spacetime. The discussion is based on the relation of the deformations of the space-filling string with conformal transformations. The realization of the conformal algebra in terms of surface deformations possesses a classical central charge. The action principle, the conformal and Weyl invariances of the action, and the equations of motion are studied. The energy-momentum tensor, the coupling to Liouville matter, and the cancellation of anomalies are analyzed. The quantum theory is not discussed.
Gravitation and inertia; a rearrangement of vacuum in gravity
Ter-Kazarian, Gagik
2010-01-01
We address the gravitation and inertia in the framework of 'general gauge principle', which accounts for 'gravitation gauge group' generated by hidden local internal symmetry implemented on the flat space. We connect this group to nonlinear realization of the Lie group of 'distortion' of local internal properties of six-dimensional flat space, which is assumed as a toy model underlying four-dimensional Minkowski space. The agreement between proposed gravitational theory and available observational verifications is satisfactory. We construct relativistic field theory of inertia and derive the relativistic law of inertia. This theory furnishes justification for introduction of the Principle of Equivalence. We address the rearrangement of vacuum state in gravity resulting from these ideas.
Qui sera le nouvel Einstein ? Vers une nouvelle theorie de la gravitation
Bonnet-Bidaud, J. M.
1999-10-01
Un debat de plus d'un siecle a resurgi ces toutes dernieres annees avec une vigueur nouvelle. L'enjeu ? Mettre fin, ni plus ni moins, a l'une des contradictions les plus inouies de la physique fondamentale, en reconciliant mecanique quantique et relativite generale. En effet, a l'heure ou la gravitation semble enfin sur le point de fusionner avec les trois autres forces de la nature. il est certain que la relativite d'Einstein doit etre bientot remplacer par une autre theorie... Reste quye tous les physiciens sont loin de s'accorder sur la marche a suivree. Gravitation quantique, relativite d'echelle, supersymetrie, les candidates ne manquent pas.
Gravitational self-force in non-vacuum spacetimes: an effective field theory derivation
Zimmerman, Peter
2015-01-01
In this paper we investigate the motion of small compact objects in non-vacuum spacetimes using methods from effective field theory in curved spacetime. Although a vacuum formulation is sufficient in many astrophysical contexts, there are applications such as the role of the self-force in enforcing cosmic-censorship in the context of the overcharging problem, which necessitate an extension into the non-vacuum regime. The defining feature of the self-force problem in non-vacuum spacetimes is the coupling between gravitational and non-gravitational field perturbations. The formulation of the self-force problem for non-vacuum spacetimes was recently provided in simultaneous papers by Zimmerman and Poisson [1] and Linz, Friedmann, Wiseman [2]. Here we distinguish ourselves by working with the effective action rather than the field equations. The formalism utilizes the multi-index notation developed by Zimmerman and Poisson [1] to accommodate the coupling between the different fields. Using dimensional regularizat...
Stress-energy-momentum tensors in Lagrangian field theory; 2, gravitational superpotential
Giachetta, G
1995-01-01
Our investigation of differential conservation laws in Lagrangian field theory is based on the first variational formula which provides the canonical decomposition of the Lie derivative of a Lagrangian density by a projectable vector field on a bundle (Part 1: gr-qc/9510061). If a Lagrangian density is invariant under a certain class of bundle isomorphisms, its Lie derivative by the associated vector fields vanishes and the corresponding differential conservation laws take place. If these vector fields depend on derivatives of parameters of bundle transformations, the conserved current reduces to a superpotential. This Part of the work is devoted to gravitational superpotentials. The invariance of a gravitational Lagrangian density under general covariant transformations leads to the stress-energy-momentum conservation law where the energy-momentum flow of gravity reduces to the corresponding generalized Komar superpotential. The associated energy-momentum (pseudo) tensor can be defined and calculated on solu...
Theory-Agnostic Tests of GR with Multi-Band Gravitational Waves
Yunes, Nicolas; Barausse, Enrico; Chamberlain, Katherine
2017-01-01
The aLIGO detection of the black-hole binary GW150914 opened a new era for testing General Relativity in extreme gravity. One generic feature that can be constrained is the emission of dipole gravitational radiation by compact binaries. This is excluded to high accuracy in binary pulsars, but entire classes of gravitational theories predict this effect in binaries predominantly (or only) involving black holes. In this talk, I will describe how future, joint observations of GW150914-like systems by aLIGO and eLISA will dramatically improve bounds on dipole emission from black-hole binaries, probing extreme gravity with unprecedented accuracy. We acknowledge support from the NSF CAREER Grant PHY-1250636.
Post-Newtonian Approximation of a Scalar Theory of Gravitation and Application to Light Rays
Arminjon, M
1998-01-01
A scalar, preferred-frame theory of gravitation is summarized. Space-time is endowed with both a flat metric and a curved, "physical" metric. Motion is governed by a natural extension of Newton's second law, which implies geodesic motion only for a static field. The theory predicts Schwarzschild's exterior metric in the spherical static situation. It also predicts gravitation waves with the velocity of light. The equations of motion are recast into the "flat space - uniform time" form, and compared with the geodesic equations of motion. The principles of the post-Newtonian approximation of this theory are given, including the way to account for preferred-frame effects. This approximation is then developed more particularly for photons. It is found that the preferred-frame effects do not occur in this case, nor does the difference between Newton's second law and geodesic assumption. Thus, the post-Newtonian predictions of this theory for photons are indistinguishable from the standard post-Newtonian prediction...
Helmich-Paris, Benjamin; Repisky, Michal; Visscher, Lucas
2016-07-07
We present a formulation of Laplace-transformed atomic orbital-based second-order Møller-Plesset perturbation theory (MP2) energies for two-component Hamiltonians in the Kramers-restricted formalism. This low-order scaling technique can be used to enable correlated relativistic calculations for large molecular systems. We show that the working equations to compute the relativistic MP2 energy differ by merely a change of algebra (quaternion instead of real) from their non-relativistic counterparts. With a proof-of-principle implementation we study the effect of the nuclear charge on the magnitude of half-transformed integrals and show that for light elements spin-free and spin-orbit MP2 energies are almost identical. Furthermore, we investigate the effect of separation of charge distributions on the Coulomb and exchange energy contributions, which show the same long-range decay with the inter-electronic/atomic distance as for non-relativistic MP2. A linearly scaling implementation is possible if the proper distance behavior is introduced to the quaternion Schwarz-type estimates as for non-relativistic MP2.
Vargas, J.G.
1986-10-01
The kinematic aspects of the rocket-borne clock experiment by Vessot and Levine are analyzed with the revised Robertson's test theory of special relativity (Found. Phys. 14, 625 (1984)). Besides the expected time-dilation, it is found that the intermediate steps of this experiment yield in principle Michelson-Morley type information (a relation between longitudinal and transverse length contractions) in the third order of the velocities involved, but no relativity-of-simultaneity related effects. The flat space-time test theory induces a family of ''spherically symmetric'' line elements that become the Schwarzchild line element in the relativistic case and also in the abinito rest frame of the theory. These line elements represent the same space-time manifold, but pertain in a one-to-one correspondence to the different flat space-time coordinate transformations of the test theory. The conserved energy is related to the family of local energies in the tangent plane. No deviations from the orthodoxy appear at the pertinent levels of approximation. Hence the unexplained residuals of the Vessot-Levine experiment are not due in obvious ways to kinematic and gravitational frequency shifts caused by deviations of the ''real'' coordinate transformations from the Lorentz transformations.
Study of the Alpha-Decay Chain for7753 194Rn with Relativistic Mean-Field Theory
SHENG Zong-Qiang; GUO Jian-You
2008-01-01
The structures of the nuclei on the alpha-decay chain of 194Rn are investigated in the deformed relativistic mean-field theory with the effective interaction TMA. We put an emphasis on the ground state properties of 194Rn. The calculated alpha-decay energies and lifetimes are both very close to the experimental data for 186pb and 190po. For 194 Rn, the deviations are a little large on both the alpha-decay energy and the lifetime. We also calculate the alpha-decay energies for the isotopes 192～208Rn. The tendency for the change of the alpha-decay energies with neutron number is correctly reproduced in the relativistic mean-field theory (RMF). In general, the RMF theory can give a good description of the alpha decay chain of 194Rn.
In search of a primitive ontology for relativistic quantum field theory
Lam, Vincent [University of Lausanne, CH-1015 Lausanne (Switzerland)
2014-07-01
There is a recently much discussed approach to the ontology of quantum mechanics according to which the theory is ultimately about entities in 3-dimensional space and their temporal evolution. Such an ontology postulating from the start matter localized in usual physical space or spacetime, by contrast to an abstract high-dimensional space such as the configuration space of wave function realism, is called primitive ontology in the recent literature on the topic and finds its roots in Bell's notion of local beables. The main motivation for a primitive ontology lies in its explanatory power: the primitive ontology allows for a direct account of the behaviour and properties of familiar macroscopic objects. In this context, it is natural to look for a primitive ontology for relativistic quantum field theory (RQFT). The aim of this talk is to critically discuss this interpretative move within RQFT, in particular with respect to the foundational issue of the existence of unitarily inequivalent representations. Indeed the proposed primitive ontologies for RQFT rely either on a Fock space representation or a wave functional representation, which are strictly speaking only unambiguously available for free systems in flat spacetime. As a consequence, it is argued that these primitive ontologies constitute only effective ontologies and are hardly satisfying as a fundamental ontology for RQFT.
The Anomalous Nambu-Goldstone Theorem in Relativistic/Nonrelativistic Quantum Field Theory
Ohsaku, Tadafumi
2013-01-01
The anomalous Nambu-Goldstone (NG) theorem which is found as a violation of counting law of the number of NG bosons of the normal NG theorem in nonrelativistic and Lorentz-symmetry-violated relativistic theories is studied in detail, with emphasis on its mathematical aspect from Lie algebras, geometry to number theory. The basis of counting law of NG bosons in the anomalous NG theorem is examined by Lie algebras (local) and Lie groups (global). A quasi-Heisenberg algebra is found generically in various symmetry breaking schema of the anomalous NG theorem, and it indicates that it causes a violation/modification of the Heisenberg uncertainty relation in an NG sector which can be experimentally confirmed. The formalism of effective potential is presented for understanding the mechanism of anomalous NG theorem with the aid of our result of Lie algebras. After an investigation on a bosonic kaon condensation model with a finite chemical potential as an explicit Lorentz-symmetry-breaking parameter, a model Lagrangi...
Equation of state of a relativistic theory from a moving frame
Giusti, Leonardo
2014-01-01
We propose a new strategy for determining the equation of state of a relativistic thermal quantum field theory by considering it in a moving reference system. In this frame an observer can measure the entropy density of the system directly from its average total momentum. In the Euclidean path integral formalism, this amounts to compute the expectation value of the off-diagonal components T_{0k} of the energy-momentum tensor in presence of shifted boundary conditions. The entropy is thus easily measured from the expectation value of a local observable computed at the target temperature T only. At large T, the temperature itself is the only scale which drives the systematic errors, and the lattice spacing can be tuned to perform a reliable continuum limit extrapolation while keeping finite-size effects under control. We test this strategy for the four-dimensional SU(3) Yang-Mills theory. We present precise results for the entropy density and its step-scaling function in the temperature range 0.9 T_c - 20 T_c. ...
Cheng, Lan; Xiao, Yunlong; Liu, Wenjian
2009-12-28
It is recognized only recently that the incorporation of the magnetic balance condition is absolutely essential for four-component relativistic theories of magnetic properties. Another important issue to be handled is the so-called gauge problem in calculations of, e.g., molecular magnetic shielding tensors with finite bases. It is shown here that the magnetic balance can be adapted to distributed gauge origins, leading to, e.g., magnetically balanced gauge-including atomic orbitals (MB-GIAOs) in which each magnetically balanced atomic orbital has its own local gauge origin placed on its center. Such a MB-GIAO scheme can be combined with any level of theory for electron correlation. The first implementation is done here at the coupled-perturbed Dirac-Kohn-Sham level. The calculated molecular magnetic shielding tensors are not only independent of the choice of gauge origin but also converge rapidly to the basis set limit. Close inspections reveal that (zeroth order) negative energy states are only important for the expansion of first order electronic core orbitals. Their contributions to the paramagnetism are therefore transferable from atoms to molecule and are essentially canceled out for chemical shifts. This allows for simplifications of the coupled-perturbed equations.
Non-Hermitian ${\\cal PT}$-symmetric relativistic quantum theory in an intensive magnetic field
Rodionov, V N
2016-01-01
We develop relativistic non-Hermitian quantum theory and its application to neutrino physics in a strong magnetic field. It is well known, that one of the fundamental postulates of quantum theory is the requirement of Hermiticity of physical parameters. This condition not only guarantees the reality of the eigenvalues of Hamiltonian operators, but also implies the preservation of the probabilities of the considered quantum processes. However as it was shown relatively recently (Bender, Boettcher 1998), Hermiticity is a sufficient but it is not a necessary condition. It turned out that among non-Hermitian Hamiltonians it is possible to allocate a number of such which have real energy spectra and can ensure the development of systems over time with preserving unitarity. This type of Hamiltonians includes so-called parity-time (${\\cal PT}$) symmetric models which is already used in various fields of modern physics. The most developed in this respect are models, which used in the field of ${\\cal PT}$-symmetric op...
LRS Bianchi type-II string cosmological models in a modified theory of gravitation
Kanakavalli, T.; Ananda Rao, G.; Reddy, D. R. K.
2017-03-01
This paper is devoted to the investigation of spatially homogeneous anisotropic LRS Bianchi type-II cosmological models with string source in a modified theory of gravitation formulated by Harko et al. (Phys. Rev. D 84:024020, 2011) which is universally known as f( R, T) gravity. Here R is the Ricci scalar and T is the trace of the energy momentum tensor. By solving the field equation we have presented massive string and Takabyasi or p-string models in this theory. However it is interesting to note that geometric string in this space-time does not exist in this theory. Physical and geometrical properties of the strings obtained are also discussed.
Bianchi Type VI1 Viscous Fluid Cosmological Model in Wesson´s Theory of Gravitation
Khadekar, G. S.; Avachar, G. R.
2007-03-01
Field equations of a scale invariant theory of gravitation proposed by Wesson [1, 2] are obtained in the presence of viscous fluid with the aid of Bianchi type VIh space-time with the time dependent gauge function (Dirac gauge). It is found that Bianchi type VIh (h = 1) space-time with viscous fluid is feasible in this theory, whereas Bianchi type VIh (h = -1, 0) space-times are not feasible in this theory, even in the presence of viscosity. For the feasible case, by assuming a relation connecting viscosity and metric coefficient, we have obtained a nonsingular-radiating model. We have discussed some physical and kinematical properties of the models.
Beyond Einstein Gravity A Survey of Gravitational Theories for Cosmology and Astrophysics
Faraoni, Valerio
2011-01-01
Beyond Einstein’s Gravity is a graduate level introduction to extended theories of gravity and cosmology, including variational principles, the weak-field limit, gravitational waves, mathematical tools, exact solutions, as well as cosmological and astrophysical applications. The book provides a critical overview of the research in this area and unifies the existing literature using a consistent notation. Although the results apply in principle to all alternative gravities, a special emphasis is on scalar-tensor and f(R) theories. They were studied by theoretical physicists from early on, and in the 1980s they appeared in attempts to renormalize General Relativity and in models of the early universe. Recently, these theories have seen a new lease of life, in both their metric and metric-affine versions, as models of the present acceleration of the universe without introducing the mysterious and exotic dark energy. The dark matter problem can also be addressed in extended gravity. These applications are contr...
Equations of motion for the mass centers in a scalar theory of gravitation
Arminjon, M
2000-01-01
A scalar theory of gravitation with a preferred reference frame (PRF) is considered, that accounts for special relativity and reduces to it if the gravitational field cancels. The gravitating system consists of a finite number of perfect-fluid bodies. An " asymptotic " post-Newtonian (PN) approximation scheme is used, allowing an explicit weak-field limit with all fields expanded. Exact mass centers are defined and their exact equations of motion are derived. The PN expansion of these equations is obtained: the zero-order equations are those of Newtonian gravity (NG), and the equations for the first-order (PN) corrections depend linearly on the PN fields. For PN corrections to the motion of the mass centers, especially in the solar system, one may assume " very-well-separated " rigidly moving bodies with spherical self-fields of the zero-order approximation. The PN corrections reduce then to a time integration and include spin effects, which might be significant. It is shown that the Newtonian masses are not ...
Gravitational Energy for GR and Poincare Gauge Theories: a Covariant Hamiltonian Approach
Chen, Chiang-Mei; Tung, Roh-Suan
2015-01-01
Our topic concerns a long standing puzzle: the energy of gravitating systems. More precisely we want to consider, for gravitating systems, how to best describe energy-momentum and angular momentum/center-of-mass momentum (CoMM). It is known that these quantities cannot be given by a local density. The modern understanding is that (i) they are quasi-local (associated with a closed 2-surface), (ii) they have no unique formula, (iii) they have no reference frame independent description. In the first part of this work we review some early history, much of it not so well known, on the subject of gravitational energy in Einstein's general relativity (GR), noting especially Noether's contribution. In the second part we review (including some new results) much of our covariant Hamiltonian formalism and apply it to Poincar\\'e gauge theories (GR is a special case). The key point is that the Hamiltonian boundary term has two roles, it determines the quasi-local quantities, and, furthermore it determines the boundary con...
Scale Invariant Kaluza-Klein Theory and the Fate of the Gravitational Collapse
Quirós, I
2002-01-01
Pushing forward the similitudes between the gravitational collapse and the expansion of the universe (in the reversed sense of time), it should be expected that, during the collapse, eventually, a spacetime domain would be reached where attained energy scales are very high. In consequence some of the compactified extra dimensions may be decompactified and some presently broken symmetries may be restored. A more fundamental theory (of which Einstein's theory is a symmetry broken phase) is then expected to take account of further description of the collapse. I propose a simple (classical) model for the description of the late stages of the gravitational collapse: A non-Riemannian, scale-invariant version of 5-dimensional Kaluza-Klein theory in which the standard Riemann structure of the higher-dimensional manifold is replaced by a Weyl-integrable one. A class of solutions, that generalize the "soliton" one by Gross and Perry and Davidson and Owen, is found. This class contains both naked singularities and wormh...
Gravitational Waves and Inspiraling Compact Binaries in Alternative Theories of Gravity
Mirshekari, Saeed
2013-01-01
This dissertation consists of four parts. In Part I, we briefly review fundamental theories of gravity, performed experimental tests, and gravitational waves. The framework and the methods that we use in our calculations are discussed in Part II. This part includes reviewing the methods of the Parametrized Post-Newtonian (PPN) framework, Direct Integration of Relaxed Einstein Equations (DIRE), and Matched Filtering. In Part III, we calculate the explicit equations of motion for non-spinning compact objects (neutron stars or black holes) to 2.5 post-Newtonian order, or $O(v/c)^5$ beyond Newtonian gravity, in a general class of alternative theories to general relativity known as scalar-tensor theories. For the conservative part of the motion, we obtain the two-body Lagrangian and conserved energy and momentum through second post-Newtonian order. We find the contributions to gravitational radiation reaction to 1.5 post-Newtonian and 2.5 post-Newtonian orders, the former corresponding to the effects of dipole gra...
Redundancy of constraints in the classical and quantum theories of gravitation.
Moncrief, V.
1972-01-01
It is shown that in Dirac's version of the quantum theory of gravitation, the Hamiltonian constraints are greatly redundant. If the Hamiltonian constraint condition is satisfied at one point on the underlying, closed three-dimensional manifold, then it is automatically satisfied at every point, provided only that the momentum constraints are everywhere satisfied. This permits one to replace the usual infinity of Hamiltonian constraints by a single condition which may be taken in the form of an integral over the manifold. Analogous theorems are given for the classical Einstein Hamilton-Jacobi equations.
Scalar Field Model of Dark Energy In the Double Complex Symmetric Gravitational Theory
SHAO Ying; GUI Yuan-Xing; WANG Wei
2006-01-01
The scalar field model of dark energy is established in the double complex symmetric gravitational theory. The universe we live in is taken as the real part of double complex space M4C(J). The two cases of scalar field (ordinary and phantom scalar field) are discussed in a unified way. Not only can the double Friedmann equations be obtained, but also the equation of state for dark energy, potential V(φ) and scalar field φ can be expressed. Hence, a new method is proposed to study dark energy and the evolution of the universe.
Spatially Homogeneous Bianchi Type V Cosmological Model in the Scale-Covariant Theory of Gravitation
Shri Ram; M.K.Verma; Mohd.Zeyauddin
2009-01-01
We discuss spatially homogeneous and anisotropic Bianchi type-V spacetime filled with a perfect fluid in the framework of the scaie-covariant theory of gravitation proposed by Canuto et al.By applying the law of variation for Hubble's parameter,exact solutions of the field equations are obtained,which correspond to the model of the universe having a big-bang type singularity at the initial time t=0.The cosmological model,evolving from the initial singularity,expands with power-law expansion and gives essentially an empty space for a large time.The physical and dynamical properties of the model are also discussed.
Fubini instantons in Dilatonic Einstein-Gauss-Bonnet theory of gravitation
Ro, Daeho; Lee, Bum-Hoon
2016-01-01
We investigate various types of Fubini instantons in Dilatonic Einstein-Gauss-Bonnet theory of gravitation, which describe the decay of the vacuum state at a hilltop potential through the tunneling without a barrier. It is shown that the vacuum states are modified by the non-minimally coupled higher-curvature term. Accordingly, we present the new type of solutions describing the tunneling from new vacuum states in anti-de Sitter and de Sitter backgrounds. The decay probabilities of vacuum states are also influenced. Consequently, we show that the semiclassical exponents can be decreased for specific parameter ranges, which make the tunneling probabilities enhanced.
Anisotropic massive strings in the scalar-tensor theory of gravitation
Anil Kumar Yadav
2013-01-01
We present the model of an anisotropic universe with string fluid as the source of matter within the framework of the scalar-tensor theory of gravitation.An exact solution of field equations is obtained by applying Berman's law of variation to Hubble's parameter which yields a constant value of the deceleration parameter.The nature of classical potential is examined for the model under consideration.It has also been found that the massive strings dominate in the early universe and finally disappear from the universe.This is in agreement with current astronomical observations.The physical and dynamical properties of the model are also discussed.
Consequences of f(R)-theories of gravity on gravitational leptogenesis
Lambiase, G; Pizza, L
2012-01-01
f(R)-theories of gravity are reviewed in the framework of the matter-antimatter asymmetry in the Universe. The asymmetry is generated by the gravitational coupling of heavy (Majorana) neutrinos with the Ricci scalar curvature. In order that the mechanism works, a time varying non-zero Ricci curvature is necessary. The latter is provided by f(R) cosmology, whose Lagrangian density is of the form {\\cal L}(R)\\sim f(R). In particular we study the cases f(R)\\sim R+\\alpha R^n and f(R)\\sim R^{1+\\epsilon}.
Path integral measure for gravitational interactions
Kazuo Fujikawa
1983-10-01
Full Text Available It is pointed out that the path-integral variables as well as the local measure for gravitational interactions are uniquely specified if one imposes the anomaly-free condition on the Becchi-Rouet-Stora supersymmetry associated with general coordinate transformations. This prescription is briefly illustrated for the Einstein gravity and supergravity in four space-time dimensions and the relativistic string theory in two dimensions.
Some Surprises in Relativistic Gravity
Santos, N O
2016-01-01
General Relativity has had tremendous success both on the theoretical and the experimental fronts for over a century now. However, the contents of the theory are far from exhausted. Only very recently, with the detection of gravitational waves from colliding black holes, we have started probing the behavior of gravity in the strongly non-linear regime. Even today, the studies of black holes keep revealing more and more paradoxes and bizarre results. In this paper, inspired by David Hilbert's startling observation, we show that, contrary to the conventional wisdom, a freely falling test particle feels gravitational repulsion by a black hole as seen by the asymptotic observer. We dig deeper into this surprising behavior of relativistic gravity and offer some explanations.
Cattaneo, Carlo
2011-01-01
This title includes: Pham Mau Quam: Problemes mathematiques en hydrodynamique relativiste; A. Lichnerowicz: Ondes de choc, ondes infinitesimales et rayons en hydrodynamique et magnetohydrodynamique relativistes; A.H. Taub: Variational principles in general relativity; J. Ehlers: General relativistic kinetic theory of gases; K. Marathe: Abstract Minkowski spaces as fibre bundles; and, G. Boillat: Sur la propagation de la chaleur en relativite.
无
2000-01-01
For a special use a new modelling method of evaluating external disturbing potential is presented in this paper. Being different from classical methods in physical geodesy this method is grounded upon the theory of unified representation of gravitational field. The models created in this way are particularly satisfactory for a high-speed computation of gravitational field in low altitude because they take account of topographic effects and have their kernel functions with simple structure and weak singularity.
Black Hole Spectroscopy: Testing General Relativity through Gravitational Wave Observations
Dreyer, O; Krishnan, B; Finn, L S; Garrison, D; López-Aleman, R; Dreyer, Olaf; Kelly, Bernard; Krishnan, Badri; Finn, Lee Samuel; Garrison, David; Lopez-Aleman, Ramon
2004-01-01
Assuming that general relativity is the correct theory of gravity in the strong field limit, can gravitational wave observations distinguish between black hole and other compact object sources? Alternatively, can gravitational wave observations provide a test of one of the fundamental predictions of general relativity? Here we describe a definitive test of the hypothesis that observations of damped, sinusoidal gravitational waves originated from a black hole or, alternatively, that nature respects the general relativistic no-hair theorem. For astrophysical black holes, which have a negligible charge-to-mass ratio, the black hole quasi-normal mode spectrum is characterized entirely by the black hole mass and angular momentum and is unique to black holes. In a different theory of gravity, or if the observed radiation arises from a different source (e.g., a neutron star, strange matter or boson star), the spectrum will be inconsistent with that predicted for general relativistic black holes. We give a statistica...
Grigoryan, L. S.; Saakyan, G. S.
1984-09-01
The existence of a special gravitational vacuum is considered in this paper. A phenomenological method differing from the traditional Einsteinian formalization is utilized. Vacuum, metric and matter form a complex determined by field equations and at great distances from gravitational masses vacuum effects are small but could be large in powerful fields. Singularities and black holes justify the approach as well as the Ambartsmyan theory concerning the existence of supermassive and superdense prestallar bodies that then disintegrate. A theory for these superdense bodies is developed involving gravitational field equations that describe the vacuum by an energy momentum tensor and define the field and mass distribution. Computations based on the theory for gravitational radii with incompressible liquid models adequately reflecting real conditions indicate that a gravitational vacuum could have considerable effects on superdense stars and could have radical effects for very large masses.
Chandel S; Ram Shri
2016-03-01
The paper deals with the study of particle creation and bulk viscosity in the evolution of spatially homogeneous and anisotropic Bianchi type-V cosmological models in the framework of Saez–Ballester theory of gravitation. Particle creation and bulk viscosity are considered as separate irreversible processes. The energy–momentum tensor is modified to accommodate the viscous pressure and creation pressure which is associated with the creation of matter out of gravitational field. A special law of variation of Hubble parameter is applied to obtain exact solutions of field equations in two types of cosmologies, one with power-law expansion and the other with exponential expansion. Cosmological model with power-law expansion has a Big-Bang singularity at time $t = 0$, whereas the model with exponential expansion has no finite singularity. We study bulk viscosity and particle creation in each model in four different cases. The bulk viscosity coefficient is obtained for full causal, Eckart’s and truncated theories. All physical parameters are calculated and thoroughly discussed in both models.
First test of Verlinde's theory of emergent gravity using weak gravitational lensing measurements
Brouwer, Margot M.; Visser, Manus R.; Dvornik, Andrej; Hoekstra, Henk; Kuijken, Konrad; Valentijn, Edwin A.; Bilicki, Maciej; Blake, Chris; Brough, Sarah; Buddelmeijer, Hugo; Erben, Thomas; Heymans, Catherine; Hildebrandt, Hendrik; Holwerda, Benne W.; Hopkins, Andrew M.; Klaes, Dominik; Liske, Jochen; Loveday, Jon; McFarland, John; Nakajima, Reiko; Sifón, Cristóbal; Taylor, Edward N.
2017-04-01
Verlinde proposed that the observed excess gravity in galaxies and clusters is the consequence of emergent gravity (EG). In this theory, the standard gravitational laws are modified on galactic and larger scales due to the displacement of dark energy by baryonic matter. EG gives an estimate of the excess gravity (described as an apparent dark matter density) in terms of the baryonic mass distribution and the Hubble parameter. In this work, we present the first test of EG using weak gravitational lensing, within the regime of validity of the current model. Although there is no direct description of lensing and cosmology in EG yet, we can make a reasonable estimate of the expected lensing signal of low-redshift galaxies by assuming a background Lambda cold dark matter cosmology. We measure the (apparent) average surface mass density profiles of 33 613 isolated central galaxies and compare them to those predicted by EG based on the galaxies' baryonic masses. To this end, we employ the ∼180 deg2 overlap of the Kilo-Degree Survey with the spectroscopic Galaxy And Mass Assembly survey. We find that the prediction from EG, despite requiring no free parameters, is in good agreement with the observed galaxy-galaxy lensing profiles in four different stellar mass bins. Although this performance is remarkable, this study is only a first step. Further advancements on both the theoretical framework and observational tests of EG are needed before it can be considered a fully developed and solidly tested theory.
Relativistic theory of the Jahn-Teller effect: p-orbitals in tetrahedral and trigonal systems
Domcke, Wolfgang; Opalka, Daniel; Poluyanov, Leonid V.
2016-03-01
A relativistic generalization of Jahn-Teller theory is presented which includes spin-orbit coupling effects beyond low-order Taylor expansions in vibrational coordinates. For the example of a p-electron in tetrahedral and trigonal environments, the matrix elements of the Breit-Pauli spin-orbit-coupling operator are expressed in terms of the matrix elements of the electrostatic electronic potential. Employing expansions of the latter in invariant polynomials in symmetry-adapted nuclear coordinates, the spin-orbit induced Jahn-Teller coupling terms are derived for the T2 × (t2 + e) and (E + A) × (e + a) Jahn-Teller problems up to arbitrarily high orders. The linear G3/2 × (t2 + e) Jahn-Teller Hamiltonian of Moffitt and Thorson [Phys. Rev. 108, 1251 (1957)] for tetrahedral systems is generalized to higher orders in vibrational displacements. The Jahn-Teller Hamiltonians derived in the present work are useful for the interpolation and extrapolation of Jahn-Teller distorted potential-energy surfaces of molecules and complexes with heavy elements as well as for the calculation of vibronic spectra of such systems.
Fan, Peifeng; Liu, Jian; Xiang, Nong; Yu, Zhi
2016-01-01
A manifestly covariant, or geometric, field theory for relativistic classical particle-field system is developed. The connection between space-time symmetry and energy-momentum conservation laws for the system is established geometrically without splitting the space and time coordinates, i.e., space-time is treated as one identity without choosing a coordinate system. To achieve this goal, we need to overcome two difficulties. The first difficulty arises from the fact that particles and field reside on different manifold. As a result, the geometric Lagrangian density of the system is a function of the 4-potential of electromagnetic fields and also a functional of particles' world-lines. The other difficulty associated with the geometric setting is due to the mass-shell condition. The standard Euler-Lagrange (EL) equation for a particle is generalized into the geometric EL equation when the mass-shell condition is imposed. For the particle-field system, the geometric EL equation is further generalized into a w...
Properties and structure of N=Z nuclei within relativistic mean field theory
GAO Yuan; DONG Jian-Min; ZHANG Hong-Fei; ZUO Wei; LI Jun-Qing
2009-01-01
The axially deformed relativistic mean field theory with the force NLSH has been performed in the blocked BCS approximation to investigate the properties and structure of N=Z nuclei from Z=20 to Z=48.Some ground state quantities such as binding energies, quadrupole deformations, one/two-nucleon separation energies, root-mean-square (rms) radii of charge and neutron, and shell gaps have been calculated.The results suggest that large deformations can be found in medium-heavy nuclei with N=Z=38-42.The charge and neutron rms radii increase rapidly beyond the magic number N=Z=28 until Z=42 with increasing nucleon number, which is similar to isotope shift, yet beyond Z=42, they decrease dramatically as the structure changes greatly from Z=42 to Z=43.The evolution of shell gaps with proton number Z can be clearly observed.Besides the appearance of possible new shell closures, some conventional shell closures have been found to disappear in some region.In addition, we found that the Coulomb interaction is not strong enough to breakdown the shell structure of protons in the current region.
Komorovsky, Stanislav; Repisky, Michal; Ruud, Kenneth; Malkina, Olga L; Malkin, Vladimir G
2013-12-27
A four-component relativistic method for the calculation of NMR shielding constants of paramagnetic doublet systems has been developed and implemented in the ReSpect program package. The method uses a Kramer unrestricted noncollinear formulation of density functional theory (DFT), providing the best DFT framework for property calculations of open-shell species. The evaluation of paramagnetic nuclear magnetic resonance (pNMR) tensors reduces to the calculation of electronic g tensors, hyperfine coupling tensors, and NMR shielding tensors. For all properties, modern four-component formulations were adopted. The use of both restricted kinetically and magnetically balanced basis sets along with gauge-including atomic orbitals ensures rapid basis-set convergence. These approaches are exact in the framework of the Dirac-Coulomb Hamiltonian, thus providing useful reference data for more approximate methods. Benchmark calculations on Ru(III) complexes demonstrate good performance of the method in reproducing experimental data and also its applicability to chemically relevant medium-sized systems. Decomposition of the temperature-dependent part of the pNMR tensor into the traditional contact and pseudocontact terms is proposed.
Cannoni, Mirco
2015-01-01
We find an exact formula for the thermally averaged cross section times the relative velocity $\\langle \\sigma v_{\\text{rel}} \\rangle$ with relativistic Maxwell-Boltzmann statistics. The formula is valid in the effective field theory approach when the masses of the annihilation products can be neglected compared with the dark matter mass and cut-off scale. The expansion at $x=m/T\\gg 1$ directly gives the nonrelativistic limit of $\\langle \\sigma v_{\\text{rel}}\\rangle$ which is usually used to compute the relic abundance for heavy particles that decouple when they are nonrelativistic. We compare this expansion with the one obtained by expanding the total cross section $\\sigma(s)$ in powers of the nonrelativistic relative velocity $v_r$. We show the correct invariant procedure that gives the nonrelativistic average $\\langle \\sigma_{nr} v_r \\rangle_{nr}$ coinciding with the large $x$ expansion of $\\langle \\sigma v_{\\text{rel}}\\rangle$ in the comoving frame. We explicitly formulate flux, cross section, thermal aver...
Scott, Tony C.
It has been shown that the Fokker-Wheeler-Feynman (FWF) model could be rewritten to yield a physically acceptable relativistic many-particle Lagrangian. Contrary to Wheeler and Feynman's postulates, the model satisfies causality and can be generalised to include arbitrary forces. The 1/c power series of the FWF Lagrangian to order (1/c) ^4 contains accelerations. A procedure of quantizing the theory for such a Lagrangian is presented and it is then found that the accelerations approximately introduce an independent harmonic mode which is in agreement with resonances recently observed in Positronium collisions processes. This result may be of fundamental physical importance and requires further investigation. However, the refinement of this calculation requires the creation of new computational tools. To this end, a new method is presented in which both the eigenfunctions and eigenenergies are determined algebraically as power series in the order parameter, where each coefficient of the series is obtained in closed form. This method avoids the complications of a basis set and makes extensive use of symbolic computation. It is then applied to two model problems, namely the one-body Dirac equation for testing purposes and a special case of the two-body Dirac equation for which one obtains previously unknown closed form solutions.
Some cosmological models coming from gravitational theories having torsional degrees of freedom
Espiro, J. Lorca; Vásquez, Yerko
2016-09-01
In this work we consider gravitational theories in which the effect of coupling characteristic classes, appropriately introduced as operators in the Einstein-Hilbert action, has been taken into account. As it is well known, this approach strays from the framework of general relativity since it results in theories in which torsion can be present. We consider here all the characteristic classes that are consistent with a four-dimensional space-time manifold. Then, we present explicit expressions for the contortion 1-form and torsion 2-form for a broad class of conditions in various cases of interest. Additionally, we use the same framework to study cosmological scenarios that are obtained mainly by selecting the flat FLRW metric and an ideal fluid.
Detection of gravitational waves from black holes: Is there a window for alternative theories?
Konoplya, Roman, E-mail: konoplya@th.physik.uni-frankfurt.de [Institute for Theoretical Physics, Goethe University, Max-von-Laue-Str. 1, 60438 Frankfurt (Germany); Zhidenko, Alexander, E-mail: zhidenko@th.physik.uni-frankfurt.de [Institute for Theoretical Physics, Goethe University, Max-von-Laue-Str. 1, 60438 Frankfurt (Germany); Centro de Matemática, Computação e Cognição, Universidade Federal do ABC (UFABC), Rua Abolição, CEP: 09210-180, Santo André, SP (Brazil)
2016-05-10
Recently the LIGO and VIRGO Collaborations reported the observation of gravitational-wave signal corresponding to the inspiral and merger of two black holes, resulting into formation of the final black hole. It was shown that the observations are consistent with the Einstein theory of gravity with high accuracy, limited mainly by the statistical error. Angular momentum and mass of the final black hole were determined with rather large allowance of tens of percents. Here we shall show that this indeterminacy in the range of the black-hole parameters allows for some non-negligible deformations of the Kerr spacetime leading to the same frequencies of the black-hole ringing. This means that at the current precision of the experiment there remains some possibility for alternative theories of gravity.
Gravitational Collapse In Vaidya Space-time For Galileon Gravity Theory
Rudra, Prabir
2014-01-01
The motive of this work is to study gravitational collapse in Vaidya space-time embedded in Galileon gravity theory. Galileon gravity is in fact an infrared modification of Einstein gravity, which was proposed as a generalization of the 4D effective theory in DGP brane model. Vaidya's metric is used all over to follow the nature of future outgoing radial null geodesics. Detecting whether the central singularity is naked or wrapped by an event horizon, by the existence of future directed radial null geodesic emitted in past from the singularity is the basic objective. To point out the existence of positive trajectory tangent solution, both particular parametric cases (through tabular forms) and wide range contouring process have been applied. Precisely, the EoS in perfect fluid satisfies a wide range of phenomena: from dust to exotic fluid like dark energy. We have used the EoS parameter $k$ to determine the end collapse state in different cosmological era.
The particle spectrum of parity-violating Poincar\\'e gravitational theory
Karananas, Georgios K
2014-01-01
In this paper we investigate the physical spectrum of the gravitational theory based on the Poincar\\'e group with terms which are at most quadratic in tetrad and spin connection, allowing for the presence of parity-even as well as parity-odd invariants. We determine restrictions on the parameters of the action so that all degrees of freedom propagate and are neither ghosts nor tachyons. We show that the addition of parity non-conserving invariants extends the healthy parameter space of the theory. To accomplish our goal, we apply the weak field approximation around flat spacetime and in order to facilitate the analysis, we separate the bilinear action for the excitations into completely independent spin sectors. For this purpose, we employ the spin-projection operator formalism and extend the original basis built previously, to be able to handle the parity-odd pieces.
Distinguishing f(R) theories from general relativity by gravitational lensing effect
Liu, Hongguang; Li, Haida; Ma, Yongge
2015-01-01
The post-Newtonian formulation of a general class of f(R) theories is set up to 3rd order approximation. It turns out that the information of a specific form of f(R) gravity is encoded in the Yukawa potential, which is contained in the perturbative expansion of the metric components. It is shown that the Yukawa potantial does appear in the 3rd order expression of the effective refraction index of light, although it is cancelled in the 2nd order expression. Therefore the f(R) theories are distinguishable from general relativity by gravitational lensing effect at the 3rd order post-Newtonian approximation. Our result opens the possibility to bring new insights into the issue of dark matter from f(R) gravity.
Detection of gravitational waves from black holes: Is there a window for alternative theories?
Roman Konoplya
2016-05-01
Full Text Available Recently the LIGO and VIRGO Collaborations reported the observation of gravitational-wave signal corresponding to the inspiral and merger of two black holes, resulting into formation of the final black hole. It was shown that the observations are consistent with the Einstein theory of gravity with high accuracy, limited mainly by the statistical error. Angular momentum and mass of the final black hole were determined with rather large allowance of tens of percents. Here we shall show that this indeterminacy in the range of the black-hole parameters allows for some non-negligible deformations of the Kerr spacetime leading to the same frequencies of the black-hole ringing. This means that at the current precision of the experiment there remains some possibility for alternative theories of gravity.
Wachter, H
2007-01-01
This is the second part of a paper about a q-deformed analog of non-relativistic Schroedinger theory. It applies the general ideas of part I and tries to give a description of one-particle states on q-deformed quantum spaces like the braided line or the q-deformed Euclidean space in three dimensions. Hamiltonian operators for the free q-deformed particle in one as well as three dimensions are introduced. Plane waves as solutions to the corresponding Schroedinger equations are considered. Their completeness and orthonormality relations are written down. Expectation values of position and momentum observables are taken with respect to one-particle states and their time-dependence is discussed. A potential is added to the free-particle Hamiltonians and q-analogs of the Ehrenfest theorem are derived from the Heisenberg equations of motion. The conservation of probability is proved.
Helmich-Paris, Benjamin; Visscher, Lucas
2016-01-01
We present a formulation of Laplace-transformed atomic orbital-based second-order M{\\o}ller-Plesset perturbation theory (MP2) energies for two-component Hamiltonians in the Kramers-restricted formalism. This low-order scaling technique can be used to enable correlated relativistic calculations for large molecular systems. We show that the working equations to compute the relativistic MP2 energy differ by merely a change of algebra (quaternion instead of real) from their non-relativistic counterparts. With a proof-of-principle implementation we study the effect of the nuclear charge on the magnitude of half-transformed integrals and show that for light elements spin-free and spin-orbit MP2 energies are almost identical. Furthermore, we investigate the effect of separation of charge distributions on the Coulomb and exchange energy con- tributions, which show the same long-range decay with the inter-electronic / atomic distance as for non-relativistic MP2. A linearly scaling implementation is possible if the pro...
Lorentz covariant reduced-density-operator theory for relativistic quantum information processing
Ahn, D; Hwang, S W; Ahn, Doyeol; Lee, Hyuk-jae; Hwang, Sung Woo
2003-01-01
In this paper, we derived Lorentz covariant quantum Liouville equation for the density operator which describes the relativistic quantum information processing from Tomonaga-Schwinger equation and an exact formal solution for the reduced-density-operator is obtained using the projector operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of non-relativistic case which is valid only in some specified reference frame. The formulation presented in this work is general and might be applied to related fields such as quantum electrodynamics and relativistic statistical mechanics.
André, Raíla
2014-01-01
In this work we analyze the dynamics of collisionless self-gravitating systems described by the f(R)-gravity and Boltzmann equation in the weak field approximation, focusing on the Jeans instability for theses systems. The field equations in this approximation were obtained within the Palatini formalism. Through the solution of coupled equations we achieved the collapse criterion for infinite homogeneous fluid and stellar systems, which is given by a dispersion relation. This result is compared with the results of the standard case and the case for f(R)-gravity in metric formalism, in order to see the difference among them. The limit of instability varies according to which theory of gravity is adopted.
The Work and the Energy in Special Theory of Relativistic Dynamics%相对论中的功和能
籍延坤; 郭红
2001-01-01
以经典力学某些量为线索,根据经典动力学的基本方程,采用物理上常用的类比的方法建立了狭义相对论动力学的基本方程,由该基本方程对空间的累积效应,可以引入相对论动力学中质点和质点系的质量、运动质量、动量、动能、静能、机械能、相对论能量和力以及力的功的基本概念。得到了相对论动力学中的功和能关系式即质点和质点系的动能定理、质点系的功能原理、机械能守恒定律与能量守恒定律以及能量准守恒定律。%Some quantities in classical mechanics being taken as clue, a fundamental equation of special theory of relativistic dynamics has been established based on the fundamental equation of classical mechanics and by using analogy method . From the accumulative effect of this equation to space, the basic concepts of rest mass, moving mass, momentum, kinetic energy, rest energy, mechanical energy, relativistic energy , force, and the work of force of particle or particle system in special theory of relativistic dynamics can be introduced. The relation formula between work and energy in special theory of relativistic dynamics, i.e. kinetic energy theorem of particle or particle system, the principle of work and energy, the conservation law of mechanical energy and quasi-conservation law of energy in particle system have been obtained as well.
Luciano, Rezzolla
2013-01-01
Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solut...
Kawazura, Yohei; Morrison, Philip J
2016-01-01
Two types of Eulerian action principles for relativistic extended magnetohydrodynamics (MHD) are formulated. With the first, the action is extremized under the constraints of density, entropy, and Lagrangian label conservation, which leads to a Clebsch representation for a generalized momentum and a generalized vector potential. The second action arises upon transformation to physical field variables, giving rise to a covariant bracket action principle, i.e., a variational principle in which constrained variations are generated by a degenerate Poisson bracket. Upon taking appropriate limits, the action principles lead to relativistic Hall MHD and well-known relativistic ideal MHD. For the first time, the Hamiltonian formulation of relativistic Hall MHD with electron thermal inertia (akin to [Comisso \\textit{et al.}, Phys. Rev. Lett. {\\bf 113}, 045001 (2014)] for the electron--positron plasma) is introduced. This thermal inertia effect allows for violation of the frozen-in magnetic flux condition in marked con...
Iliaš, M.; Jensen, Hans Jørgen Aagaard; Bast, R.;
2013-01-01
better convergence of magnetisabilities with respect to the basis set size is observed compared to calculations employing a common gauge origin. In fact, it is mandatory to use London atomic orbitals unless you want to use ridiculously large basis sets. Relativistic effects on magnetisabilities are found......The use of magnetic-field dependent London atomic orbitals, also called gauge including atomic orbitals, is known to be an efficient choice for accurate non-relativistic calculations of magnetisabilities. In this work, the appropriate formulas were extended and implemented in the framework...... of the four-component relativistic linear response method at the self-consistent field single reference level. Benefits of employing the London atomic orbitals in relativistic calculations are illustrated with Hartree-Fock wave functions on the XF3 (X = N, P, As, Sb, Bi) series of molecules. Significantly...
Quantum gravitational anomaly as a dark matter
Kazinski, P O
2015-01-01
The general properties of a perfect relativistic fluid resulting from the quantum gravitational anomaly are investigated. It is found that, in the limit of a weak gravitational field, this fluid possesses a polytropic equation of state characterized by two universal constants: the polytropic constant and the natural polytropic index. Based on the astrophysical data, the estimates for the polytropic constant are given. It is shown that this fluid can describe a considerable part of the cold dark matter. The quantum theory of such a fluid is constructed in the framework of the background field method. The Ward identities associated with the entropy and vorticity conservation laws are derived. The leading gradient corrections to the pressure of the perfect fluid are found and the restrictions on their form are obtained. These restrictions guarantee, in particular, the absence of ghosts in the model. The second order nonlinear corrections to the equations of motion of a perfect relativistic fluid are analyzed and...
Kutepov, A L
2004-01-08
Linear-response (LR) theory in combination with the first-principles band structure codes allows to calculate phonons in an efficient way. In this report a formalism which enables us to apply LR theory within an all-electron framework utilizing the relativistic full-potential linearized augmented plane-wave (RFLAPW) method is presented. As first part, the equations for the calculations of the atomic forces are given and they are used for the calculation of forces in {alpha}-Pu. As a second step, a complete set of formulaes for the dynamic matrices calculation is presented.
Relativistic four-component multiconfigurational self-consistent-field theory for molecules
Jensen, Hans Jørgen Aa; Dyall, Kenneth G.; Saue, Trond
1996-01-01
A formalism for relativistic four-component multiconfigurational self-consistent-field calculations on molecules is presented. The formalism parallels a direct second-order restricted-step algorithm developed for nonrelativistic molecular calculations. The presentation here focuses on the differe......A formalism for relativistic four-component multiconfigurational self-consistent-field calculations on molecules is presented. The formalism parallels a direct second-order restricted-step algorithm developed for nonrelativistic molecular calculations. The presentation here focuses...
Radiationless transitions to atomic M 1,2,3 shells - Results of relativistic theory
Chen, M. H.; Crasemann, B.; Mark, H.
1983-01-01
Radiationless transitions filling vacancies in atomic M1, M2, and M3 subshells have been calculated relativistically with Dirac-Hartree-Slater wave functions for ten elements with atomic numbers 67-95. Results are compared with those of nonrelativistic calculations and experiment. Relativistic effects are found to be significant. Limitations of an independent-particle model for the calculation of Coster-Kronig rates are noted.
Relativistic quantum mechanics
Wachter, Armin
2010-01-01
Which problems do arise within relativistic enhancements of the Schrödinger theory, especially if one adheres to the usual one-particle interpretation, and to what extent can these problems be overcome? And what is the physical necessity of quantum field theories? In many books, answers to these fundamental questions are given highly insufficiently by treating the relativistic quantum mechanical one-particle concept very superficially and instead introducing field quantization as soon as possible. By contrast, this monograph emphasizes relativistic quantum mechanics in the narrow sense: it extensively discusses relativistic one-particle concepts and reveals their problems and limitations, therefore motivating the necessity of quantized fields in a physically comprehensible way. The first chapters contain a detailed presentation and comparison of the Klein-Gordon and Dirac theory, always in view of the non-relativistic theory. In the third chapter, we consider relativistic scattering processes and develop the...
Reissner-Nordstr\\"om Spacetime in the Tetrad Theory of Gravitation
Nashed, Gamal G L
2007-01-01
We give two classes of spherically symmetric exact solutions of the couple gravitational and electromagnetic fields with charged source in the tetrad theory of gravitation. The first solution depends on an arbitrary function $H({R},t)$. The second solution depends on a constant parameter $\\eta$. These solutions reproduce the same metric, i.e., the Reissner--Nordstr$\\ddot{o}$m metric. If the arbitrary function which characterizes the first solution and the arbitrary constant of the second solution are set to be zero, then the two exact solutions will coincide with each other. We then calculate the energy content associated with these analytic solutions using the superpotential method. In particular, we examine whether these solutions meet the condition which M{\\o}ller required for a consistent energy-momentum complex: Namely, we check whether the total four-momentum of an isolated system behaves as a four-vector under Lorentz transformations. It is then found that the arbitrary function should decrease faster ...
Relativistic quantum information
Mann, R. B.; Ralph, T. C.
2012-11-01
Over the past few years, a new field of high research intensity has emerged that blends together concepts from gravitational physics and quantum computing. Known as relativistic quantum information, or RQI, the field aims to understand the relationship between special and general relativity and quantum information. Since the original discoveries of Hawking radiation and the Unruh effect, it has been known that incorporating the concepts of quantum theory into relativistic settings can produce new and surprising effects. However it is only in recent years that it has become appreciated that the basic concepts involved in quantum information science undergo significant revision in relativistic settings, and that new phenomena arise when quantum entanglement is combined with relativity. A number of examples illustrate that point. Quantum teleportation fidelity is affected between observers in uniform relative acceleration. Entanglement is an observer-dependent property that is degraded from the perspective of accelerated observers moving in flat spacetime. Entanglement can also be extracted from the vacuum of relativistic quantum field theories, and used to distinguish peculiar motion from cosmological expansion. The new quantum information-theoretic framework of quantum channels in terms of completely positive maps and operator algebras now provides powerful tools for studying matters of causality and information flow in quantum field theory in curved spacetimes. This focus issue provides a sample of the state of the art in research in RQI. Some of the articles in this issue review the subject while others provide interesting new results that will stimulate further research. What makes the subject all the more exciting is that it is beginning to enter the stage at which actual experiments can be contemplated, and some of the articles appearing in this issue discuss some of these exciting new developments. The subject of RQI pulls together concepts and ideas from
Relativistic theory of nuclear magnetic resonance parameters in a Gaussian basis representation.
Kutzelnigg, Werner; Liu, Wenjian
2009-07-28
The calculation of NMR parameters from relativistic quantum theory in a Gaussian basis expansion requires some care. While in the absence of a magnetic field the expansion in a kinetically balanced basis converges for the wave function in the mean and for the energy with any desired accuracy, this is not necessarily the case for magnetic properties. The results for the magnetizability or the nuclear magnetic shielding are not even correct in the nonrelativistic limit (nrl) if one expands the original Dirac equation in a kinetically balanced Gaussian basis. This defect disappears if one starts from the unitary transformed Dirac equation as suggested by Kutzelnigg [Phys. Rev. A 67, 032109 (2003)]. However, a new difficulty can arise instead if one applies the transformation in the presence of the magnetic field of a point nucleus. If one decomposes certain contributions, the individual terms may diverge, although their sum is regular. A controlled cancellation may become difficult and numerical instabilities can arise. Various ways exist to avoid these singularities and at the same time get the correct nrl. There are essentially three approaches intermediate between the transformed and the untransformed formulation, namely, the bispinor decomposition, the decomposition of the lower component, and the hybrid unitary transformation partially at operator and partially at matrix level. All three possibilities were first considered by Xiao et al. [J. Chem. Phys. 126, 214101 (2007)] in a different context and in a different nomenclature. Their analysis and classification in a more general context are given here for the first time. Use of an extended balanced basis has no advantages and has other drawbacks and is not competitive, while the use of a restricted magnetic balance basis can be justified.
ZHANG Peng-Fei; RUAN Tu-Nan
2001-01-01
A systematic theory on the appropriate spin operators for the relativistic states is developed. For a massive relativistic particle with arbitrary nonzero spin, the spin operator should be replaced with the relativistic one, which is called in this paper as moving spin. Further the concept of moving spin is discussed in the quantum field theory. A new is constructed. It is shown that, in virtue of the two operators, problems in quantum field concerned spin can be neatly settled.
Mahdi Afshar
2013-11-01
Full Text Available We have demonstrated electronic structure and magnetic properties of Cu3, Ag3 and Au3 trimers using a full potential local orbital method in the framework of relativistic density functional theory. We have also shown that the non-relativistic generalized gradient approximation for the exchange-correlation energy functional gives reliable magnetic properties in coinage metal trimers compared to experiment. In addition we have indicated that the spin-orbit coupling changes the structure and magnetic properties of gold trimer while the structure and magnetic properties of copper and silver trimers are marginally affected. A significant orbital moment of 0.21μB was found for most stable geometry of the gold trimer whereas orbital magnetism is almost quenched in the copper and silver trimers.
Verma, M. K.; Chandel, S.; Ram, Shri
2017-01-01
The present study deals with hypersurface-homogeneous cosmological models with anisotropic dark energy in Saez-Ballester theory of gravitation. Exact solutions of field equations are obtained by applying a special law of variation of Hubble's parameter that yields a constant negative value of the deceleration parameter. Three physically viable cosmological models of the Universe are presented for the values of parameter K occurring in the metric of the space-time. The model for K = 0 corresponds to an accelerating Universe with isotropic dark energy. The other two models for K = 1 and -1 represent accelerating Universe with anisotropic dark energy, which isotropize for large time. The physical and geometric behaviours of the models are also discussed.
Axially symmetric anisotropic string cosmological models in Saez-Ballester theory of gravitation
Kanakavalli, T.; Rao, G. Ananda; Reddy, D. R. K.
2017-02-01
Field equations of a scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A 113:467, 1986) are derived with the help of a spatially homogeneous axially symmetric anisotropic Bianchi type metric in the presence of cosmic string source. To obtain determinate solutions of the field equations we have used the fact that the scalar expansion is proportional to shear scalar and the equations of state which correspond to geometric, Takabayasi and massive strings. It is found that geometric and massive strings do not coexist with the Saez-Ballester Scalar field. However, Takabayasi string which survives has been determined. Also, physical discussion of the dynamical parameters of the model is presented.
M K VERMA; S CHANDEL; SHRI RAM
2017-01-01
The present study deals with hypersurface-homogeneous cosmological models with anisotropic dark energy in Saez–Ballester theory of gravitation. Exact solutions of field equations are obtained by applying a special law of variation of Hubble’s parameter that yields a constant negative value of the deceleration parameter. Three physically viable cosmological models of the Universe are presented for the values of parameter $K$ occurring in the metric of the space–time. The model for $K = 0$ corresponds to an accelerating Universe with isotropic dark energy. The other two models for $K = 1$ and $−1$ represent accelerating Universe with anisotropic dark energy, which isotropize for large time. The physical and geometric behaviours of the models are also discussed.
Kovalenko A. V.
2015-01-01
Full Text Available In the article, we have suggested a general mathematical model of non-stationary and non-isothermal process of a binary electrolyte transfer in dilute solutions in an electro-membrane system (EMS, taking into account the joint action of gravitational convection, forced convection and electro convection in potential dynamic mode. This model is a boundary problem for a system of two-dimensional quasi-linear Navier-Stokes equation and Nernst-Planck-Poisson in partial derivatives equation. We have developed a theory of similarity of the process of heat and mass transfer in electro-membrane systems, specifically, in a desalting channel of electro dialysis apparatus, taking into account joint actions of concentration polarization, space charge, gravity convection, forced convection and electro convection. It is shown that the criterion of electro convection does not directly depend on the initial concentration, and, therefore, electro convection occurs at any initial concentration. At the same time, the criterion of concentration convection linearly dependents on the initial concentration, and, therefore, at high concentrations, concentration convection prevails, while at lower concentrations, the role of gravitational convection begins to fall whereas the role of electro convection increases. The theory of similarity of the process of heat and mass transfer in the desalting channel of electro dialysis apparatus built in this work taking into account the joint action of concentration polarization, space charge, gravity convection, forced convection and electro convection is important for engineering calculations, for scaling the results of experiments in an electro-membrane cell for industrial electro dialysis water desalting apparatus
'Antigravity' Propulsion and Relativistic Hyperdrive
Felber, F S
2006-01-01
Exact payload trajectories in the strong gravitational fields of compact masses moving with constant relativistic velocities are calculated. The strong field of a suitable driver mass at relativistic speeds can quickly propel a heavy payload from rest to a speed significantly faster than the driver, a condition called hyperdrive. Hyperdrive thresholds and maxima are calculated as functions of driver mass and velocity.
Gravitational radiation from compact binary systems in the massive Brans-Dicke theory of gravity
Alsing, Justin; Will, Clifford; Zaglauer, Helmut
2011-01-01
We derive the equations of motion, the periastron shift, and the gravitational radiation damping for quasicircular compact binaries in a massive variant of the Brans-Dicke theory of gravity. We also study the Shapiro time delay and the Nordtvedt effect in this theory. By comparing with recent observational data, we put bounds on the two parameters of the theory: the Brans-Dicke coupling parameter \\omega_{BD} and the scalar mass m_s. We find that the most stringent bounds come from Cassini measurements of the Shapiro time delay in the Solar System, that yield a lower bound \\omega_{BD}>40000 for scalar masses m_s1000 for m_s1250 for m_s<10^{-20} eV. A first estimate suggests that bounds comparable to the Shapiro time delay may come from observations of radiation damping in the eccentric white dwarf-neutron star binary PSR J1141-6545, but a quantitative prediction requires the extension of our work to eccentric orbits.
On the horizons in a viable vector-tensor theory of gravitation
Dale, Roberto; Sáez, Diego
2015-01-01
A certain vector-tensor (VT) theory of gravitation was tested in previous papers. In the background universe, the vector field of the theory has a certain energy density, which is appropriate to play the role of vacuum energy (cosmological constant). Moreover, this background and its perturbations may explain the temperature angular power spectrum of the cosmic microwave background (CMB) obtained with WMAP (Wilkinson Map Anisotropy Probe), and other observations, as e.g., the Ia supernova luminosities. The parametrized post-Newtonian limit of the VT theory has been proved to be identical to that of general relativity (GR), and there are no quantum ghosts and classical instabilities. Here, the stationary spherically symmetric solution, in the absence of any matter content, is derived and studied. The metric of this solution is formally identical to that of the Reissner-Nordstr\\"om-de Sitter solution of GR, but the role of the electrical charge is played by a certain quantity $\\Gamma $ depending on both the vec...
Minotti, F O
2013-01-01
The scalar-tensor theory of gravitation proposed by Mbelek and Lachi\\`{e}ze-Rey have been recently shown to lead to some remarkable effects beyond those initially explored by its authors. These new effects include a possible explanation of the forces measured in asymmetric resonant microwave cavities, and the variation of the amplitude of electromagnetic waves as they propagate in static electric or magnetic fields. These rather unique effects are excelent candidates for laboratory tests of this particular type of scalar-tensor theory. In the present work we introduce an additional remarkable effect of the theory: the generation of pulsed gravitational forces by transient, quasi-stationary electromagnetic fields. In particular, we explore the possible measurable effects of the simple experiment of turning on and off the current in a coil. We show that with the proposed values of the constant in the theory, this effect could resonantly excite a pendulum oscillation up to an easily measurable magnitude.
A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory
Lindesay, James V
2001-05-11
We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a non-perturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the non-relativistic limit to the non-relativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require ''renormalization'' or ''dressing'' of these parameters to connect them to the boundary states.
Palmer, T N
2012-01-01
A realistic measurement-free theory for the quantum physics of multiple qubits is proposed. This theory is based on a symbolic representation of a fractal state-space geometry which is invariant under the action of deterministic and locally causal dynamics. This symbolic representation is constructed from self-similar families of quaternionic operators. Using number-theoretic properties of the cosine function, the statistical properties of the symbolic representation of the invariant set are shown to be consistent with the contextual requirements of the Kochen-Specker theorem, are not constrained by Bell inequalities, and mirror the statistics of entangled qubits. These number-theoretic properties in turn reflect the sparseness of the invariant set in state space, and relate to the metaphysical notion of counterfactual incompleteness. Using the concept of probability, the complex Hilbert Space can be considered the completion of this symbolic representation into the state space continuum. As a result, it is p...
Solar rotation gravitational moments
A. Ajabshirizadeh
2005-09-01
Full Text Available Gravitational multipole moments of the Sun are still poorly known. Theoretically, the difficulty is mainly due to the differential rotation for which the velocity rate varies both on the surface and with the depth. From an observational point of view, the multipole moments cannot be directly measured. However, recent progresses have been made proving the existence of a strong radial differential rotation in a thin layer near the solar surface (the leptocline. Applying the theory of rotating stars, we will first compute values of J2 and J4 taking into account the radial gradient of rotation, then we will compare these values with the existing ones, giving a more complete review. We will explain some astrophysical outcomes, mainly on the relativistic Post Newtonian parameters. Finally we will conclude by indicating how space experiments (balloon SDS flights, Golf NG, Beppi-Colombo, Gaia... will be essential to unambiguously determine these parameters.
Ji, Min; Lan, Xin; Han, Zhenping; Hao, Ce; Qiu, Jieshan
2012-11-19
The electronically excited state and luminescence property of metal-organic framework MOF-5 were investigated using relativistic density functional theory (DFT) and time-dependent DFT (TDDFT). The geometry, IR spectra, and UV-vis spectra of MOF-5 in the ground state were calculated using relativistic DFT, leading to good agreement between the experimental and theoretical results. The frontier molecular orbitals and electronic configuration indicated that the luminescence mechanism in MOF-5 follows ligand-to-ligand charge transfer (LLCT), namely, π* → π, rather than emission with the ZnO quantum dot (QD) proposed by Bordiga et al. The geometry and IR spectra of MOF-5 in the electronically excited state have been calculated using the relativistic TDDFT and compared with those for the ground state. The comparison reveals that the Zn4O13 QD is rigid, whereas the ligands BDC(2-) are nonrigid. In addition, the calculated emission band of MOF-5 is in good agreement with the experimental result and is similar to that of the ligand H2BDC. The combined results confirmed that the luminescence mechanism for MOF-5 should be LLCT with little mixing of the ligand-to-metal charge transfer. The reason for the MOF-5 luminescence is explained by the excellent coplanarity between the six-membered ring consisting of zinc, oxygen, carbon, and the benzene ring.
L-shell Auger and Coster-Kronig spectra from relativistic theory
Chen, M. H.; Crasemann, B.; Aoyagi, M.; Mark, H.
1979-01-01
The intensities of L-shell Auger and Coster-Kronig transitions in heavy atoms have been calculated relativistically. A detailed comparison is made with measured Auger spectra of Pt and U. The pertinent transition energies were computed from relativistic wave functions with inclusion of the Breit interaction, self-energy, a vacuum-polarization correction, and complete atomic relaxation. Multiplet splitting is found to distribute Auger electrons from certain transitions among several lines. The analysis leads to reassignment of a number of lines in the measured spectra. Lines originally identified as L2-L3Ni in the U spectrum are shown to arise from M4,5 Auger transitions instead.