Global structure of Robinson-Trautman radiative space-times with cosmological constant
Bicák, J
1997-01-01
Robinson-Trautman radiative space-times of Petrov type II with a non-vanishing cosmological constant Lambda and mass parameter m>0 are studied using analytical methods. They are shown to approach the corresponding spherically symmetric Schwarzschild-de Sitter or Schwarzschild-anti-de Sitter solution at large retarded times. Their global structure is analyzed, and it is demonstrated that the smoothness of the extension of the metrics across the horizon, as compared with the case Lambda=0, is increased for Lambda>0 and decreased for Lambda0 exhibit explicitly the cosmic no-hair conjecture under the presence of gravitational waves.
Algebraic classification of Robinson-Trautman spacetimes
Podolsky, Jiri
2016-01-01
We consider a general class of four-dimensional geometries admitting a null vector field that has no twist and no shear but has an arbitrary expansion. We explicitly present the Petrov classification of such Robinson-Trautman (and Kundt) gravitational fields, based on the algebraic properties of the Weyl tensor. In particular, we determine all algebraically special subcases when the optically privileged null vector field is a multiple principal null direction (PND), as well as all the cases when it remains a single PND. No field equations are a priori applied, so that our classification scheme can be used in any metric theory of gravity in four dimensions. In the classic Einstein theory this reproduces previous results for vacuum spacetimes, possibly with a cosmological constant, pure radiation and electromagnetic field, but can be applied to an arbitrary matter content. As non-trivial explicit examples we investigate specific algebraic properties of the Robinson-Trautman spacetimes with a free scalar field, ...
Gravitational wave momentum extraction in non-axisymmetric Robinson-Trautman spacetimes
Aranha, R F; Tonini, E V
2014-01-01
We examine numerically the gravitational wave recoil in non-axisymmetric Robinson-Trautman spacetimes. We construct characteristic initial data for the Robinson-Trautman dynamics which are interpreted as corresponding to the early post-merger state of two boosted colliding black holes with a common apparent horizon. Our analysis is based on the Bondi-Sachs energy-momentum conservation laws which regulate the radiative transfer processes involved in the emission of gravitational waves. We evaluate the Bondi-Sachs momentum flux carried out by gravitational waves and the associated net kick velocity defined (in a zero-initial-Bondi-momentum frame) as proportional to the total gravitational wave impulse imparted on the system. The kick velocity distributions are obtained and analyzed for two distinct classes of initial data corresponding to the early post-merger state of (i) non-head-on collisions and (ii) head-on collisions of black holes. For the first class (i), the net gravitational wave momentum fluxes and a...
Gravitational wave recoils in non-axisymmetric Robinson-Trautman spacetimes
Aranha, R F; Tonini, E V
2014-01-01
We examine the gravitational wave recoil waves and the associated net kick velocities in non-axisymmetric Robinson-Trautman spacetimes. We use characteristic initial data for the dynamics corresponding to non-head-on collisions of black holes. We make a parameter study of the kick distributions, corresponding to an extended range of the incidence angle $\\rho_0$ in the initial data. For the range of $\\rho_0$ examined ($3^{\\circ} \\leq \\rho_0 \\leq 110^{\\circ}$) the kick distributions as a function of the symmetric mass parameter $\\eta$ satisfy a law obtained from an empirical modification of the Fitchett law, with a parameter $C$ that accounts for the non-zero net gravitational momentum wave fluxes for the equal mass case. The law fits accurately the kick distributions for the range of $\\rho_0$ examined, with a rms normalized error of the order of $5 \\%$. For the equal mass case the nonzero net gravitational wave momentum flux increases as $\\rho_0$ increases, up to $\\rho_0 \\simeq 55^{\\circ}$ beyond which it decr...
The role of the apparent horizon in the evolution of Robinson-Trautman Einstein-Maxwell spacetimes
Lun, A W C; Lun, A W C; Chow, E W M
1994-01-01
The `runaway solutions' of the Lorentz-Dirac equation of a charged particle interacting with its own field in classical electrodynamics are well-known. This type of self accelerated phenomena also exists in the solutions of the Einstein-Maxwell equations in general relativity. In particular, runaway solutions occur in a class of simple models known as the `Asymptotically Flat Robinson-Trautman Einstein-Maxwell' (AFRTEM) spacetimes. Consequently these spacetimes cannot evolve to their unique regular steady state, viz. a charged non-rotating black hole. This seems to contradict the established results that charged non-rotating black holes are stable under first order perturbations. We show that if an AFRTEM spacetime also possesses an apparent horizon, then it has a Lyapunov functional. This suggests that the evolution equations with additional constraints arising from the apparent horizon would evolve stably to a charged non-rotating black hole. We also demonstrate that the linearised equations of these restri...
Robinson-Trautman solutions to Einstein's equations
Davidson, William
2017-02-01
Solutions to Einstein's equations in the form of a Robinson-Trautman metric are presented. In particular, we derive a pure radiation solution which is non-stationary and involves a mass m, The resulting spacetime is of Petrov Type II A special selection of parametric values throws up the feature of the particle `rocket', a Type D metric. A suitable transformation of the complex coordinates allows the metrics to be expressed in real form. A modification, by setting m to zero, of the Type II metric thereby converting it to Type III, is then shown to admit a null Einstein-Maxwell electromagnetic field.
Robinson-Trautman solution with nonlinear electrodynamics
Tahamtan, T.; Svitek, O. [Charles University in Prague, Faculty of Mathematics and Physics, Institute of Theoretical Physics, Prague 8 (Czech Republic)
2016-06-15
Explicit Robinson-Trautman solutions with an electromagnetic field satisfying nonlinear field equations are derived and analyzed. The solutions are generated from the spherically symmetric ones. In all studied cases the electromagnetic field singularity is removed while the gravitational one persists. The models resolving the curvature singularity in spherically symmetric spacetimes could not be generalized to the Robinson-Trautman geometry using the generating method developed in this paper, which indicates that the removal of a singularity in the associated spherically symmetric case might be just a consequence of high symmetry. We show that the obtained solutions are generally of algebraic type II and reduce to type D in spherical symmetry. Asymptotically they tend to the spherically symmetric case as well. (orig.)
Note on a specific subcases of Robinson-Trautman solution with scalar hair
Tahamtan, T
2016-01-01
Explicit Robinson-Trautman solution with minimally coupled free scalar field was derived and analyzed recently. It was shown that this solution possesses curvature singularity which is initially naked but later the horizon envelopes it. However this study concentrated on the general branch of the solution where all the free constants are nonzero. Interesting special cases arise when some of the parameters are set to zero. In most of these cases the scalar field is still present. One of the cases is a static solution which represents a parametric limit of Janis-Newman-Winicour scalar field spacetime.
Lanczos spintensor for the Robinson-Trautman metrics of the vacuum space and Einstein-Maxwell fields
Gaftoi, V; Morales, J.; Ovando, G.; Pena, J. J. [Mexico city, Univ. Autonoma Metropolitana-Azcapotzalco (Mexico). Dept. de Ciencias Basicas. Area de Fisica
1998-10-01
Using the Newman-Penrose formalism, are obtained the {Omega}{sub r} projections of the Lanczos spintensor over the null tetrad for the Robinson-Trautman (RT) solutions of the vacuum space and Einstein-Maxwell fields. Specifically, the authors are concerned with the Weyl-Lanczos relationships for the II, III and D Petrov`s type of the RT afore-mentioned metrics. The presented approach considers the most general case of the functions P(x{sup 1}, x{sup 2}, u) and H(x{sup 1}, x{sup 2}, r, u), that characterize the metrics, resulting in a procedure by far simpler than equivalent methods that use spinors and tensors in order to determine the K{sub ijr} Lanczos spintensor.
Higher dimensional spacetimes with a geodesic, shearfree, twistfree and expanding null congruence
Ortaggio, M
2007-01-01
We present the complete family of higher dimensional spacetimes that admit a geodesic, shearfree, twistfree and expanding null congruence, thus extending the well-known D=4 class of Robinson-Trautman solutions. Einstein's equations are solved for empty space with an arbitrary cosmological constant and for aligned pure radiation. Main differences with respect to the D=4 case (such as the absence of type III/N solutions, related to ``violations'' of the Goldberg-Sachs theorem in D>4) are pointed out, also in connection with other recent works. A formal analogy with electromagnetic fields is briefly discussed in an appendix, where we demonstrate that multiple principal null directions of null Maxwell fields are necessarily geodesic, and that in D>4 they are also shearing if expanding.
Shear-free Null Quasi-Spherical Spacetimes
Bartnik, R A
1997-01-01
The residual gauge freedom within the null quasi-spherical coordinate condition is studied, for spacetimes admitting an {\\em expanding, shear-free} null foliation. The freedom consists of a boost and rotation at each coordinate sphere, corresponding to a specification of inertial frame at each sphere. Explicit formulae involving arbitrary functions of two variables are obtained for the accelerated Minkowski, Schwarzschild, and Robinson-Trautman spacetimes. These examples will be useful as test metrics in numerical relativity.
Radiation Transport in Dynamic Spacetimes
Schnittman, Jeremy; Baker, John G.; Etienne, Zachariah; Giacomazzo, Bruno; Kelly, Bernard J.
2017-08-01
We present early results from a new radiation transport calculation of gas accretion onto merging binary black holes. We use the Monte Carlo radiation transport code Pandurata, now generalized for application to dynamic spacetimes. The time variability of the metric requires careful numerical techniques for solving the geodesic equation, particularly with tabulated spacetime data from numerical relativity codes. Using a new series of general relativistic magneto-hydrodynamical simulations of magnetized flow onto binary black holes, we investigate the possibility for detecting and identifying unique electromagnetic counterparts to gravitational wave events.
Algebraic classification of higher dimensional spacetimes based on null alignment
Ortaggio, Marcello; Pravdova, Alena
2012-01-01
We review recent developments and applications of the classification of the Weyl tensor in higher dimensional Lorentzian geometries. First, we discuss the general setup, i.e. main definitions and methods for the classification, some refinements and the generalized Newman-Penrose and Geroch-Held-Penrose formalisms. Next, we summarize general results, such as a partial extension of the Goldberg-Sachs theorem, characterization of spacetimes with vanishing (or constant) curvature invariants and the peeling behaviour in asymptotically flat spacetimes. Finally, we discuss certain invariantly defined families of metrics and their relation with the Weyl tensor classification, including: Kundt and Robinson-Trautman spacetimes; the Kerr-Schild ansatz in a constant-curvature background; purely electric and purely magnetic spacetimes; direct and (some) warped products; and geometries with certain symmetries. To conclude, some applications to quadratic gravity are also overviewed.
Quantum Larmor radiation in de Sitter spacetime
Blaga, Robert; Busuioc, Sergiu [West University of Timisoara, Timisoara (Romania)
2016-09-15
We study the radiation emitted by inertial charge evolving on the expanding de Sitter spacetime. Performing a perturbative calculation, within scalar quantum electrodynamics (sQED), we obtain the transition amplitude for the process and using this we define the energy radiated by the source. In the non-relativistic limit we find that the leading term is compatible with the classical result (Larmor formula). The first quantum correction is found to be negative, a result which is in line with a number of similar quantum field theory results. For the ultra-relativistic case we find a logarithmic divergence of the emitted energy for large frequencies, which we link to the nature of the spacetime. We compare our results with that of Nomura et al. (JCAP 11:013, 2006), where the authors make a similar calculation for a general conformally flat spacetime. (orig.)
Hawking radiation in the kappa-spacetime
Harikumar, E
2016-01-01
In this paper, we analyze the Hawking radiation of kappa-deformed Schwarzchild black hole and obtain the deformed Hawking temperature. For this, we first derive deformed metric for the kappa-spacetime, which in the generic case, is not a symmetric tensor and also has a momentum dependence. We show that the Schwarzchild metric obtained in the kappa-deformed spacetime has a dependence on energy. We use the fact that the deformed metric is conformally flat in the 1+1 dimensions, to solve the kappa-deformed Klein-Gordon equation in the background of the Schwarzchild metric. The method of Boguliobov coefficients is then used to calculate the thermal spectrum of kappa-deformed-Schwarzchild black hole and show that the Hawking temperature is modified by the non-commutativity of the kappa-spacetime.
Relativistic Radiation Magnetohydrodynamics in Dynamical Spacetimes: Numerical Methods and Tests
2008-01-01
Many systems of current interest in relativistic astrophysics require a knowledge of radiative transfer in a magnetized gas flowing in a strongly-curved, dynamical spacetime. Such systems include coalescing compact binaries containing neutron stars or white dwarfs, disks around merging black holes, core collapse supernovae, collapsars, and gamma-ray burst sources. To model these phenomena, all of which involve general relativity, radiation (photon and/or neutrino), and magnetohydrodynamics, w...
Odyssey: Ray tracing and radiative transfer in Kerr spacetime
Pu, Hung-Yi; Yun, Kiyun; Younsi, Ziri; Yoon, Suk-Jin
2016-01-01
Odyssey is a GPU-based General Relativistic Radiative Transfer (GRRT) code for computing images and/or spectra in Kerr metric describing the spacetime around a rotating black hole. Odyssey is implemented in CUDA C/C++. For flexibility, the namespace structure in C++ is used for different tasks; the two default tasks presented in the source code are the redshift of a Keplerian disk and the image of a Keplerian rotating shell at 340GHz. Odyssey_Edu, an educational software package for visualizing the ray trajectories in the Kerr spacetime that uses Odyssey, is also available.
Classical Physics of Thermal Scalar Radiation in Two Spacetime Dimensions
Boyer, Timothy H
2010-01-01
Thermal scalar radiation in two spacetime dimensions is treated within relativistic classical physics. Part I involves an inertial frame where are given the analogues both of Boltzmann's derivation of the Stefan-Boltzmann law and also Wien's derivation of the displacement theorem using the scaling of relativitic radiation theory. Next the spectrum of classical scalar zero-point radiation in an inertial frame is derived both from scale invariance and from Lorentz invariance. Part II involves the behavior of thermal radiation in a coordinate frame undergoing (relativistic) constant acceleration, a Rindler frame. The radiation normal modes in a Rindler frame are obtained. The classical zero-point radiation of inertial frames is transformed over to the coordinates of a Rindler frame. Although for zero-point radiation the two-field correlation function at different spatial points at a single time is the same between inertial and Rindler frames, the correlation function at two different times at a single Rindler sp...
The Boulware-Deser class of spacetimes radiates
Brassel, Byron P.; Maharaj, Sunil D.; Goswami, Rituparno
2017-08-01
We establish the result that the standard Boulware-Deser spacetime can radiate. This allows us to model the dynamics of a spherically symmetric radiating dynamical star in five-dimensional Einstein-Gauss-Bonnet gravity with three spacetime regions. The local internal region is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the vacuum Boulware-Deser exterior. Our approach allows for all three spacetime regions to be modeled by the same class of metric functions. A large family of solutions to the field equations are presented for various realistic equations of state. A comparison of our solutions with earlier well known results is undertaken and we show that Einstein-Gauss-Bonnet analogues of these solutions, including those of Husain, are contained in our family. We also generalise our results to higher dimensions.
On Radiative Fluids in Anisotropic Spacetimes
Shogin, Dmitry
2016-01-01
We apply the second-order Israel-Stewart theory of relativistic fluid- and thermodynamics to a physically realistic model of a radiative fluid in a simple anisotropic cosmological background. We investigate the asymptotic future of the resulting cosmological model and review the role of the dissipative phenomena in the early Universe. We demonstrate that the transport properties of the fluid alone, if described appropriately, do not explain the presently observed accelerated expansion of the Universe. Also, we show that, in constrast to the mathematical fluid models widely used before, the radiative fluid does approach local thermal equilibrium at late times, although very slowly, due to the cosmological expansion.
Radiation reaction in curved space-time: local method
Gal'tsov, D; Staub, S; Gal'tsov, Dmitri; Spirin, Pavel; Staub, Simona
2006-01-01
Although consensus seems to exist about the validity of equations accounting for radiation reaction in curved space-time, their previous derivations were criticized recently as not fully satisfactory: some ambiguities were noticed in the procedure of integration of the field momentum over the tube surrounding the world-line. To avoid these problems we suggest a purely local derivation dealing with the field quantities defined only {\\em on the world-line}. We consider point particle interacting with scalar, vector (electromagnetic) and linearized gravitational fields in the (generally non-vacuum) curved space-time. To properly renormalize the self-action in the gravitational case, we use a manifestly reparameterization-invariant formulation of the theory. Scalar and vector divergences are shown to cancel for a certain ratio of the corresponding charges. We also report on a modest progress in extending the results for the gravitational radiation reaction to the case of non-vacuum background.
On Radiative Fluids in Anisotropic Spacetimes
Shogin, Dmitry; Amundsen, Per Amund
2016-01-01
We apply the second-order Israel-Stewart theory of relativistic fluid- and thermodynamics to a physically realistic model of a radiative fluid in a simple anisotropic cosmological background. We investigate the asymptotic future of the resulting cosmological model and review the role of the dissipative phenomena in the early Universe. We demonstrate that the transport properties of the fluid alone, if described appropriately, do not explain the presently observed accelerated expansion of the ...
Stationarity of asymptotically flat non-radiating electrovacuum spacetimes
Enríquez, Rosemberg Toalá
2016-01-01
It is proven that a solution to the Einstein-Maxwell equations whose gravitational and electromagnetic radiation fields vanish is in fact stationary in a neighbourhood of spatial infinity. That is, if the Weyl and Faraday tensors decay suitably fast, then there exists a time-like Killing vector field in the region outside the bifurcate horizon of a sphere of sufficiently large radius. In particular, truly dynamical time-periodic electrovacuum spacetimes do not exist. This is an extension of earlier work by Alexakis and Schlue and Bi\\v{c}\\'{a}k, Sholtz and Tod to include electromagnetism.
Non-Riemannian effective spacetime effects on Hawking radiation in superfluids
Garcia de Andrade, L C
2005-01-01
Riemannian effective spacetime description of Hawking radiation in $^{3}He-A$ superfluids is extended to non-Riemannian effective spacetime. An example is given of non-Riemannian effective geometry of the rotational motion of the superfluid vacuum around the vortex where the effective spacetime Cartan torsion can be associated to the Hawking giving rise to a physical interpretation of effective torsion recently introduced in the literature in the form of an acoustic torsion in superfluid $^{4}He$ (PRD-70(2004),064004). Curvature and torsion singularities of this $^{3}He-A$ fermionic superfluid are investigated. This Lense-Thirring effective metric, representing the superfluid vacuum in rotational motion, is shown not support Hawking radiation when the isotropic $^{4}He$ is restored at far distances from the vortex axis. Hawking radiation can be expressed also in topological solitons (moving domain walls) in fermionic superfluids in non-Riemannian (teleparallel) $(1+1)$ dimensional effective spacetime. A telep...
Black-body radiation for twist-deformed space-time
Daszkiewicz, Marcin
2015-01-01
In this article we formally investigate the impact of twisted space-time on black-body radiation phenomena, i.e. we derive the $\\theta$-deformed Planck distribution function as well as we perform its numerical integration to the $\\theta$-deformed total radiation energy. In such a way we indicate that the space-time noncommutativity very strongly damps the black-body radiation process. Besides we provide for small parameter $\\theta$ the twisted counterparts of Rayleigh-Jeans and Wien distributions respectively.
Unpolarized radiative cylindrical spacetimes Trapped surfaces and quasilocal energy
Gonçalves, S M C V
2003-01-01
We consider the most general vacuum cylindrical spacetimes, which are defined by two global, spacelike, commuting, non-hypersurface-orthogonal Killing vector fields. The cylindrical waves in such spacetimes contain both + and $\\times$ polarizations, and are thus said to be unpolarized. We show that there are no trapped cylinders in the spacetime, and present a formal derivation of Thorne's C-energy, based on a Hamiltonian reduction approach. Using the Brown-York quasilocal energy prescription, we compute the actual physical energy (per unit Killing length) of the system, which corresponds to the value of the Hamiltonian that generates unit proper-time translations orthogonal to a given fixed spatial boundary. The C-energy turns out to be a monotonic non-polynomial function of the Brown-York quasilocal energy. Finally, we show that the Brown-York energy at spatial infinity is related to an asymptotic deficit angle in exactly the same manner as the specific mass of a straight cosmic string is to the former.
Gallo, Emanuel
2014-01-01
Here, we present a new definition of {intrinsic angular momentum} at future null infinity, based on the charge-integral approach. This definition is suitable for the general case of radiating spacetimes without symmetries, which does not suffer from supertranslations ambiguities. In the case of axial symmetry this new definition agrees with the Komar integral.
Radiation Rate of a Two-Level Atom in a Spacetime with a Reflecting Boundary
LU Shi-Zhuan; YU Hong-Wei
2005-01-01
@@ We study a two-level atom in interaction with a real massless scalar quantum field in a spacetime with a reflecting boundary. We calculate the rate of change of the atomic energy for the atom. The presence of the boundary modifies the quantum fluctuations of the scalar field, which in turn modifies the rate of change of the atomic energy.It is found that the modifications induced by the presence of a boundary make the spontaneous radiation rate of an excited atom to oscillate near the boundary and this oscillatory behaviour may offer a possible opportunity for experimental tests for geometrical (boundary) effects in flat spacetime.
Cai, Huabing; Ren, Zhongzhou
2017-09-01
We investigate the rate of change of energy for a static two-level atom interacting with a massless quantum scalar field in global monopole spacetime and separately calculate the contributions of thermal fluctuations and radiation reaction. We discuss two different kinds of atom-field interactions separately. The behaviors of the atomic transition rates are analyzed in different circumstances such as near distance and big solid angle deficit. Moreover, we compare the results with those in Minkowski spacetime so as to reveal the effects of the global monopole. In general, as the atom-monopole distance increases, the transition rates oscillate around the results in Minkowski spacetime and the amplitude of oscillation gradually decreases. The oscillation is more severe for larger solid angle deficit. Our works suggest that the transition rates can profoundly change with different atom-field interactions and different types of scalar field.
The space-time outside a source of gravitational radiation: the axially symmetric null fluid
Herrera, L. [Universidad Central de Venezuela, Escuela de Fisica, Facultad de Ciencias, Caracas (Venezuela, Bolivarian Republic of); Universidad de Salamanca, Instituto Universitario de Fisica Fundamental y Matematicas, Salamanca (Spain); Di Prisco, A. [Universidad Central de Venezuela, Escuela de Fisica, Facultad de Ciencias, Caracas (Venezuela, Bolivarian Republic of); Ospino, J. [Universidad de Salamanca, Departamento de Matematica Aplicada and Instituto Universitario de Fisica Fundamental y Matematicas, Salamanca (Spain)
2016-11-15
We carry out a study of the exterior of an axially and reflection symmetric source of gravitational radiation. The exterior of such a source is filled with a null fluid produced by the dissipative processes inherent to the emission of gravitational radiation, thereby representing a generalization of the Vaidya metric for axially and reflection symmetric space-times. The role of the vorticity, and its relationship with the presence of gravitational radiation is put in evidence. The spherically symmetric case (Vaidya) is, asymptotically, recovered within the context of the 1 + 3 formalism. (orig.)
The spacetime outside a source of gravitational radiation: The axially symmetric null fluid
Herrera, L; Ospino, J
2016-01-01
We carry out a study of the exterior of an axially and reflection symmetric source of gravitational radiation. The exterior of such a source is filled with a null fluid produced by the dissipative processes inherent to the emission of gravitational radiation, thereby representing a generalization of the Vaidya metric for axially and reflection symmetric spacetimes. The role of the vorticity, and its relationship with the presence of gravitational radiation is put in evidence. The spherically symmetric case (Vaidya) is, asymptotically, recovered within the context of the $1+3$ formalism.
The Lambda CDM-model in quantum field theory on curved spacetime and Dark Radiation
Hack, Thomas-Paul
2013-01-01
In the standard model of cosmology, the universe is described by a Robertson-Walker spacetime, while its matter/energy content is modeled by a perfect fluid with three components corresponding to matter/dust, radiation and a cosmological constant. On the other hand, in particle physics matter and radiation are described in terms of quantum field theory on Minkowski spacetime. We unify these seemingly different theoretical frameworks by analysing the standard model of cosmology from first principles within quantum field theory on curved spacetime: assuming that the universe is homogeneous and isotropic on large scales, we specify a class of quantum states whose expectation value of the energy density is qualitatively and quantitatively of the standard perfect fluid form up to potential corrections. Qualitatively, these corrections depend on new parameters not present in the standard Lambda CDM-model and can account for e.g. the phenomenon of Dark Radiation (N_eff>3.046), having a characteristic signature which...
Hawking radiation of charged Dirac particles in Vaidya-Bonner space-time
朱建阳; 张建华; 赵峥
1995-01-01
The dynamical properties of charged Dirac spinor particles in the Vaidya-Bonner space-time are investigated. The asymptotic solution to the radial part of the charged Dirac equation near the event horizon of the black hole is obtained. The Hawking temperature and the event horizon of the charged evaporating black hole, as well as the spectrum of the Hawking radiation of the Dirac particles, are exactly shown. Thereby, a new approach to the back-reaction of radiation from the non-stationary black holes is established.
Baryogenesis via Hawking-like Radiation in the FRW Space-time
Modak, Sujoy K
2014-01-01
We present a phenomenological model for baryogenesis based on particle creation in the Friedman-Robertson-Walker (FRW) space-time. This study is a continuation of our proposal that Hawking-like radiation in FRW space-time explains several physical aspects of the early Universe including inflation. In this model we study a coupling between the FRW space-time, in the form of the derivative of the Ricci scalar, and the $B-L$ current, $J^{\\mu} _{B-L}$, which leads to a different chemical potential between baryons and anti-baryons resulting in an excess of baryons over anti-baryons with the right order of magnitude. In this model the generation of baryon asymmetry, in principle, occurs over the entire history of the Universe starting from the beginning of the radiation phase. However, in practice, almost the entire contribution to the baryon asymmetry only comes from the very beginning of the Universe and is negligible thereafter. There is a free parameter in our model which can be interpreted as defining the boun...
General Relativistic Radiative Transfer Code in Rotating Black Hole Spacetime: {ARTIST}
Takahashi, Rohta; Umemura, Masayuki
2016-10-01
We present a general relativistic radiative transfer code, {ARTIST} (Authentic Radiative Transfer In Space-Time), which is a perfectly causal scheme to pursue the propagation of radiation with absorption and scattering around a Kerr black hole. The code explicitly solves the invariant radiation intensity along null geodesics in the Kerr-Schild coordinates, and therefore properly includes light bending, Doppler boosting, frame dragging, and gravitational redshifts. The notable aspect of {ARTIST} is that it conserves the radiative energy with high accuracy, and is not subject to the numerical diffusion, since the transfer is solved on long characteristics along null geodesics. We first solve the wavefront propagation around a Kerr black hole, which was originally explored by Hanni (1977). This demonstrates repeated wavefront collisions, light bending, and causal propagation of radiation with the speed of light. We show that the decay rate of the total energy of wavefronts near a black hole is determined solely by the black hole spin in late phases, in agreement with analytic expectations. As a result, the {ARTIST} turns out to correctly solve the general relativistic radiation fields until late phases as t ˜ 90M. We also explore the effects of absorption and scattering, and apply this code for a photon wall problem and an orbiting hot spot problem. All the simulations in the present study are performed in the equatorial plane around a Kerr black hole. The {ARTIST} is the first step to realize the general relativistic radiation hydrodynamics.
General relativistic radiative transfer code in rotating black hole space-time: ARTIST
Takahashi, Rohta; Umemura, Masayuki
2017-02-01
We present a general relativistic radiative transfer code, ARTIST (Authentic Radiative Transfer In Space-Time), that is a perfectly causal scheme to pursue the propagation of radiation with absorption and scattering around a Kerr black hole. The code explicitly solves the invariant radiation intensity along null geodesics in the Kerr-Schild coordinates, and therefore properly includes light bending, Doppler boosting, frame dragging, and gravitational redshifts. The notable aspect of ARTIST is that it conserves the radiative energy with high accuracy, and is not subject to the numerical diffusion, since the transfer is solved on long characteristics along null geodesics. We first solve the wavefront propagation around a Kerr black hole that was originally explored by Hanni. This demonstrates repeated wavefront collisions, light bending, and causal propagation of radiation with the speed of light. We show that the decay rate of the total energy of wavefronts near a black hole is determined solely by the black hole spin in late phases, in agreement with analytic expectations. As a result, the ARTIST turns out to correctly solve the general relativistic radiation fields until late phases as t ˜ 90 M. We also explore the effects of absorption and scattering, and apply this code for a photon wall problem and an orbiting hotspot problem. All the simulations in this study are performed in the equatorial plane around a Kerr black hole. The ARTIST is the first step to realize the general relativistic radiation hydrodynamics.
Krtous, Pavel; Podolský, Jirí
2004-12-01
We analyse the directional properties of general gravitational, electromagnetic and spin-s fields near conformal infinity \\scri . The fields are evaluated in normalized tetrads which are parallelly propagated along null geodesics which approach a point P of \\scri . The standard peeling-off property is recovered and its meaning is discussed and refined. When the (local) character of the conformal infinity is null, such as in asymptotically flat spacetimes, the dominant term which is identified with radiation is unique. However, for spacetimes with a non-vanishing cosmological constant the conformal infinity is spacelike (for Λ > 0) or timelike (for Λ 0 the radiation vanishes only along directions which are opposite to principal null directions. For Λ conformal infinity the corresponding directional structures differ, depending not only on the number and degeneracy of the principal null directions at P but also on their specific orientation with respect to \\scri . The directional structure of radiation near (anti-)de Sitter-like infinities supplements the standard peeling-off property of spin-s fields. This characterization offers a better understanding of the asymptotic behaviour of the fields near conformal infinity under the presence of a cosmological constant.
Asymptotic directional structure of radiative fields in spacetimes with a cosmological constant
Krtous, Pavel; Podolsky, JirI [Institute of Theoretical Physics, Charles University in Prague, V Holesovickach 2, 18000 Prague 8 (Czech Republic)
2004-12-21
We analyse the directional properties of general gravitational, electromagnetic and spin-s fields near conformal infinity I. The fields are evaluated in normalized tetrads which are parallelly propagated along null geodesics which approach a point P of I. The standard peeling-off property is recovered and its meaning is discussed and refined. When the (local) character of the conformal infinity is null, such as in asymptotically flat spacetimes, the dominant term which is identified with radiation is unique. However, for spacetimes with a non-vanishing cosmological constant the conformal infinity is spacelike (for {lambda} > 0) or timelike (for {lambda} < 0), and the radiative component of each field depends substantially on the null direction along which P is approached. The directional dependence of asymptotic fields near such de Sitter-like or anti-de Sitter-like I is explicitly found and described. We demonstrate that the corresponding directional structure of radiation has a universal character that is determined by the algebraic (Petrov) type of the field. In particular, when {lambda} > 0 the radiation vanishes only along directions which are opposite to principal null directions. For {lambda} < 0 the directional dependence is more complicated because it is necessary to distinguish outgoing and ingoing radiation. Near such anti-de Sitter-like conformal infinity the corresponding directional structures differ, depending not only on the number and degeneracy of the principal null directions at P but also on their specific orientation with respect to I. The directional structure of radiation near (anti-)de Sitter-like infinities supplements the standard peeling-off property of spin-s fields. This characterization offers a better understanding of the asymptotic behaviour of the fields near conformal infinity under the presence of a cosmological constant. (topical review)
Baryogenesis via Hawking-like radiation in the FRW space-time
Modak, Sujoy K. [Universidad Nacional Autonoma de Mexico, Instituto de Ciencias Nucleares, Mexico City, Distrito Federal (Mexico); Singleton, Douglas [Universidad Nacional Autonoma de Mexico, Instituto de Ciencias Nucleares, Mexico City, Distrito Federal (Mexico); California State University, Department of Physics, Fresno, CA (United States)
2015-05-15
We present a phenomenological model for baryogenesis based on particle creation in the Friedman-Robertson-Walker (FRW) space-time. This study is a continuation of our proposal that Hawking-like radiation in FRW space-time explains several physical aspects of the early Universe including inflation. In this model we study a coupling between the FRW space-time, in the form of the derivative of the Ricci scalar, and the B-L current, J{sub B-L}{sup μ}, which leads to a different chemical potential between baryons and anti-baryons, resulting in an excess of baryons over anti-baryons with the right order of magnitude. In this model the generation of baryon asymmetry, in principle, occurs over the entire history of the Universe, starting from the beginning of the radiation phase. However, in practice, almost the entire contribution to the baryon asymmetry only comes from the very beginning of the Universe and is negligible thereafter. There is a free parameter in our model which can be interpreted as defining the boundary between the unknown quantum gravity regime and the inflation/baryogenesis regime covered by our model. When this parameter is adjusted to give the observed value of baryon asymmetry we get a higher than usual energy scale for our inflation model which, however, may be in line with the Grand Unified Theory scale for inflation in view of the BICEP2 and Planck results. In addition our model provides the correct temperature for the CMB photons at the time of decoupling. (orig.)
Odyssey: A Public GPU-Based Code for General-Relativistic Radiative Transfer in Kerr Spacetime
Pu, Hung-Yi; Younsi, Ziri; Yoon, Suk-Jin
2016-01-01
General-relativistic radiative transfer (GRRT) calculations coupled with the calculation of geodesics in the Kerr spacetime are an essential tool for determining the images, spectra and light curves from matter in the vicinity of black holes. Such studies are especially important for ongoing and upcoming millimeter/submillimeter (mm/sub-mm) Very Long Baseline Interferometry (VLBI) observations of the supermassive black holes at the centres of Sgr A^{*} and M87. To this end we introduce Odyssey, a Graphics Processing Unit(GPU)-based code for ray tracing and radiative transfer in the Kerr spacetime. On a single GPU, the performance of Odyssey can exceed 1 nanosecond per photon, per Runge-Kutta integration step. Odyssey is publicly available, fast, accurate, and flexible enough to be modified to suit the specific needs of new users. Along with a Graphical User Interface (GUI) powered by a video-accelerated display architecture, we also present an educational software tool, Odyssey_Edu, for showing in real time h...
Odyssey: A Public GPU-based Code for General Relativistic Radiative Transfer in Kerr Spacetime
Pu, Hung-Yi; Yun, Kiyun; Younsi, Ziri; Yoon, Suk-Jin
2016-04-01
General relativistic radiative transfer calculations coupled with the calculation of geodesics in the Kerr spacetime are an essential tool for determining the images, spectra, and light curves from matter in the vicinity of black holes. Such studies are especially important for ongoing and upcoming millimeter/submillimeter very long baseline interferometry observations of the supermassive black holes at the centers of Sgr A* and M87. To this end we introduce Odyssey, a graphics processing unit (GPU) based code for ray tracing and radiative transfer in the Kerr spacetime. On a single GPU, the performance of Odyssey can exceed 1 ns per photon, per Runge-Kutta integration step. Odyssey is publicly available, fast, accurate, and flexible enough to be modified to suit the specific needs of new users. Along with a Graphical User Interface powered by a video-accelerated display architecture, we also present an educational software tool, Odyssey_Edu, for showing in real time how null geodesics around a Kerr black hole vary as a function of black hole spin and angle of incidence onto the black hole.
ODYSSEY: A PUBLIC GPU-BASED CODE FOR GENERAL RELATIVISTIC RADIATIVE TRANSFER IN KERR SPACETIME
Pu, Hung-Yi [Institute of Astronomy and Astrophysics, Academia Sinica, 11F of Astronomy-Mathematics Building, AS/NTU No. 1, Taipei 10617, Taiwan (China); Yun, Kiyun; Yoon, Suk-Jin [Department of Astronomy and Center for Galaxy Evolution Research, Yonsei University, Seoul 120-749 (Korea, Republic of); Younsi, Ziri [Institut für Theoretische Physik, Max-von-Laue-Straße 1, D-60438 Frankfurt am Main (Germany)
2016-04-01
General relativistic radiative transfer calculations coupled with the calculation of geodesics in the Kerr spacetime are an essential tool for determining the images, spectra, and light curves from matter in the vicinity of black holes. Such studies are especially important for ongoing and upcoming millimeter/submillimeter very long baseline interferometry observations of the supermassive black holes at the centers of Sgr A* and M87. To this end we introduce Odyssey, a graphics processing unit (GPU) based code for ray tracing and radiative transfer in the Kerr spacetime. On a single GPU, the performance of Odyssey can exceed 1 ns per photon, per Runge–Kutta integration step. Odyssey is publicly available, fast, accurate, and flexible enough to be modified to suit the specific needs of new users. Along with a Graphical User Interface powered by a video-accelerated display architecture, we also present an educational software tool, Odyssey-Edu, for showing in real time how null geodesics around a Kerr black hole vary as a function of black hole spin and angle of incidence onto the black hole.
Understanding the "antikick" in the merger of binary black holes.
Rezzolla, Luciano; Macedo, Rodrigo P; Jaramillo, José Luis
2010-06-04
The generation of a large recoil velocity from the inspiral and merger of binary black holes represents one of the most exciting results of numerical-relativity calculations. While many aspects of this process have been investigated and explained, the "antikick," namely, the sudden deceleration after the merger, has not yet found a simple explanation. We show that the antikick can be understood in terms of the radiation from a deformed black hole where the anisotropic curvature distribution on the horizon correlates with the direction and intensity of the recoil. Our analysis is focused on Robinson-Trautman spacetimes and allows us to measure both the energies and momenta radiated in a gauge-invariant manner. At the same time, this simpler setup provides the qualitative and quantitative features of merging black holes, opening the way to a deeper understanding of the nonlinear dynamics of black-hole spacetimes.
Understanding the "anti-kick" in the merger of binary black holes
Rezzolla, Luciano; Jaramillo, José Luis
2010-01-01
The generation of a large recoil velocity from the inspiral and merger of binary black holes represents one of the most exciting results of numerical-relativity calculations. While many aspects of this process have been investigated and explained, the "anti-kick", namely the sudden deceleration after the merger, has not yet found a simple explanation. We show that the anti-kick can be easily understood in terms of the radiation from a deformed black hole where the intrinsically anisotropic curvature distribution on the horizon determines the direction and intensity of the recoil. Our analysis is focussed on the properties of Robinson-Trautman spacetimes and allows us to measure both the energies and momenta radiated in a gauge-invariant manner. At the same time, this simpler setup provides all the qualitative but also quantitative features of inspiralling black hole binaries, thus opening the way to a deeper understanding of the nonlinear dynamics of black-hole spacetimes.
Benini, Marco; Murro, Simone
2014-01-01
We discuss the quantization of linearized gravity on globally hyperbolic, asymptotically flat, vacuum spacetimes and the construction of distinguished states which are both of Hadamard form and invariant under the action of all bulk isometries. The procedure, we follow, consists of looking for a realization of the observables of the theory as a sub-algebra of an auxiliary, non-dynamical algebra constructed on future null infinity $\\Im^+$. The applicability of this scheme is tantamount to proving that a solution of the equations of motion for linearized gravity can be extended smoothly to $\\Im^+$. This has been claimed to be possible provided that a suitable gauge fixing condition, first written by Geroch and Xanthopoulos, is imposed. We review its definition critically showing that there exists a previously unnoticed obstruction in its implementation leading us to introducing the concept of radiative observables. These constitute an algebra for which a Hadamard state induced from null infinity and invariant u...
Hawking radiation via tunneling from the spacetime of a spinning cosmic string black holes
Jusufi, Kimet
2015-01-01
In this paper, we study Hawking radiation as a massless particles tunneling process across the event horizon from the Schwarzschild and Reissner-Nordstr\\"om black holes pierced by an infinitely long spinning cosmic string and a global monopole. Applying the WKB approximation and using a generalized Painlev\\'e line element for stationary axisymmetric spacetimes, also by taking into account that the ADM mass of the black hole decreases due to the presence of topological defects, it is shown that the Hawking temperature remains unchanged for these black holes. The tunneling of charged massive particles from Reissner-Nordstr\\"om black holes is also studied, in both cases the tunneling rate is related to the change of the Bekenstein-Hawking entropy. The results extend the work of Parikh and Wilczek and are consistent with an underlying unitary theory.
Nonsymmetric Dynamical Thin-Shell Wormhole
Svitek, O
2016-01-01
The thin-shell wormhole created using the Darmois--Israel formalism applied to Robinson--Trautman family of spacetimes is presented. The stress energy tensor created on the throat is interpreted in terms of two dust streams and it is shown that asymptotically this wormhole settles to the Schwarzschild wormhole with throat on the horizon.
On the Existence of Radiation Gauges in Petrov type II spacetimes
Price, L R; Whiting, B F; Price, Larry R.; Shankar, Karthik; Whiting, Bernard F.
2006-01-01
The radiation gauges used by Chrzanowski (his IRG/ORG) for metric reconstruction in the Kerr spacetime seem to be over-specified. Their specification consists of five conditions: four (which we treat here as) ``gauge'' conditions plus an additional condition on the trace of the metric perturbation. In this work, we utilize a newly developed form of the perturbed Einstein equations to establish a condition -- on a particular tetrad component of the stress-energy tensor -- under which one can impose the full IRG/ORG. In a Petrov type II background, imposing the IRG/ORG additionally requires (consistently) setting a particular component of the metric perturbation to zero ``by hand''. By contrast, in a generic type D background, gauge freedom can generally be used to achieve this. As a specific example, we work through the process of imposing the IRG in a Schwarzschild background, using a more traditional approach. Implications for metric reconstruction using the Teukolsky curvature perturbations in type D spacet...
Boyer, Timothy H
2011-01-01
The analysis of this article is entirely within classical physics. Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation so as to account for the Casimir forces between parallel conducting plates at low temperatures. Furthermore, conformal symmetry carries solutions of Maxwell's equations into solutions. In an inertial frame, conformal symmetry leaves zero-point radiation invariant and does not connect it to non-zero-temperature; time-dilating conformal transformations carry the Lorentz-invariant zero-point radiation spectrum into zero-point radiation and carry the thermal radiation spectrum at non-zero temperature into thermal radiation at a different non-zero-temperature. However, in a non-inertial frame, a time-dilating conformal transformation carries classical zero-point radiation into thermal radiation at a finite non-zero-temperature. By taking the no-acceleration limit, one can obtain the Planck radiation spect...
Ibragimov, N H; Wessels, E J H; Ellis, George F. R.; Ibragimov, Nail H.; Wessels, Ewald J. H.
2006-01-01
We carry out a Lie group analysis of the Sachs equations for a time-dependent axisymmetric non-rotating space-time in which the Ricci tensor vanishes. These equations, which are the first two members of the set of Newman-Penrose equations, define the characteristic initial-value problem for the space-time. We find a particular form for the initial data such that these equations admit a Lie symmetry, and so defines a geometrically special class of such spacetimes. These should additionally be of particular physical interest because of this special geometric feature.
Calculation of radiation reaction effect on orbital parameters in Kerr spacetime
Sago, Norichika
2015-01-01
We calculate the secular changes of the orbital parameters of a point particle orbiting a Kerr black hole, due to the gravitational radiation reaction. For this purpose, we use the post-Newtonian (PN) approximation in the first order black hole perturbation theory, with the expansion with respect to the orbital eccentricity. In this work, the calculation is done up to the fourth post-Newtonian (4PN) order and to the sixth order of the eccentricity, including the effect of the absorption of gravitational waves by the black hole. We confirm that, in the Kerr case, the effect of the absorption appears at the 2.5PN order beyond the leading order in the secular change of the particle's energy and may induce a superradiance, as known previously for circular orbits. In addition, we find that the superradiance may be suppressed when the orbital plane inclines with respect to the equatorial plane of the central black hole. We also investigate the accuracy of the 4PN formulae by comparing to numerical results. If we re...
Aranha, R F; Soares, I Damião; Tonini, E V
2008-01-01
We examine the efficiency of gravitational bremsstrahlung production in the process of head-on collision of two boosted Schwarzschild black holes. We constructed initial data for the characteristic initial value problem in Robinson-Trautman spacetimes, that represent two instantaneously stationary Schwarzschild black holes in motion towards each other with the same velocity. The Robinson-Trautman equation was integrated for these initial data using a numerical code based on the Galerkin method. The final resulting configuration is a boosted black hole with Bondi mass greater than the sum of the individual mass of each initial black hole. Two relevant aspects of the process are presented. The first relates the efficiency $\\Delta$ of the energy extraction by gravitational wave emission to the mass of the final black hole. This relation is fitted by a distribution function of non-extensive thermostatistics with entropic parameter $q \\simeq 1/2$; the result extends and validates analysis based on the linearized t...
Aranha, Rafael Fernandes; Soares, Ivano Damião; Tonini, Eduardo Valentino
2016-09-01
We show that gravitational wave radiative patterns from a point test particle falling radially into a Schwarzschild black hole, as derived by Davis, Ruffini, Press and Price [M. Davis et al., Phys. Rev. Lett. 27, 1466 (1971).], are present in the nonlinear regime of head-on mergers of black holes. We use the Bondi-Sachs characteristic formulation and express the gravitational wave luminosity and the net momentum flux in terms of the news functions. We then evaluate the (-2 )-spin-weighted ℓ-multipole decomposition of these quantities via exact expressions valid in the nonlinear regime and defined at future null infinity. Our treatment is made in the realm of Robinson-Trautman dynamics, with characteristic initial data corresponding to the head-on merger of two black holes. We consider mass ratios in the range 0.01 ≤α ≤1 . We obtain the exponential decay with ℓ of the total energy contributed by each multipole ℓ, with an accurate linear correlation in the log-linear plot of the points up to α ≃0.7 . Above this mass ratio the contribution of the odd modes to the energy decreases faster than that of the even modes, leading to the breaking of the linear correlation; for α =1 the energy in all odd modes is zero. The dominant contribution to the total radiated energy comes from the quadrupole mode ℓ=2 corresponding, for instance, to about ≃84 % for small mass ratios up to ≃99.8 % for the limit case α =1 . The total rescaled radiated energy EWtotal/m0α2 decreases linearly with decreasing α , yielding for the point particle limit α →0 the value ≃0.0484 , about 5 times larger than the result of Davis et al. [1]. The mode decomposition of the net momentum flux and of the associated gravitational wave impulses results in an adjacent-even-odd mode-mixing pattern. We obtain that the impulses contributed by each (ℓ,ℓ+1 ) mixed mode also accurately satisfy the exponential decay with ℓ, for the whole mass ratio domain considered, 0.01 ≤α 0
Ibragimov, Nail H [Research Centre ALGA: Advances in Lie Group Analysis, Blekinge Institute of Technology, SE-37179 Karlskrona (Sweden); Wessels, Ewald J H [Department of Applied Mathematics, University of Cape Town, Cape Town (South Africa); Ellis, George F R [Department of Applied Mathematics, University of Cape Town, Cape Town (South Africa)
2007-12-07
We carry out a Lie group analysis of the Sachs equations for a time-dependent axisymmetric non-rotating spacetime in which the Ricci tensor vanishes. These equations, which are the first two members of the set of Newman-Penrose equations, define the characteristic initial-value problem for the spacetime. We find that the equations admit a five-dimensional equivalence Lie algebra. The initial value function that allows the equations to admit a non-trivial Lie symmetry separates into three disjoint equivalence classes.
Self-force driven motion in curved spacetimeS
Spallicci, Alessandro D A M; Aoudia, S
2014-01-01
We adopt the Dirac-Detweiler-Whiting radiative and regular effective field in curved spacetime. Thereby, we derive straightforwardly the first order perturbative correction to the geodesic of the background in a covariant form, for the extreme mass ratio two-body problem. The correction contains the self-force contribution and a background metric dependent term.
Chakraborty, Subenoy; Saha, Subhajit; Corda, Christian
2016-01-01
The present work deals with the semi-classical tunnelling approach and the Hamilton-Jacobi method to study Hawking radiation from the dynamical horizon of both the homogeneous Friedmann-Robertson-Walker (FRW...
Hawking evaporation and space-time structure
Balbinot, R.; Bergamini, R. (Consiglio Nazionale delle Ricerche, Bologna (Italy). Lab. di Radioastronomia); Giorgini, B. (Bologna Univ. (Italy). Ist. di Fisica)
1982-08-11
The Vaidya radiating metric is used to model an evaporating black-hole space-time. It is shown that, thus, a wormhole is produced in analogy with the Einstein-Rosen bridge. Its physical consequences are discussed.
Exact solutions to quadratic gravity generated by a conformal method
Pravda, Vojtech; Podolsky, Jiri; Svarc, Robert
2016-01-01
We study the role of conformal transformations in constructing vacuum solutions to quadratic gravity. We find that such solutions can be obtained by solving one non-linear partial differential equation for the conformal factor on any Einstein spacetime or, more generally, on any background with vanishing Bach tensor. We show that all spacetimes conformal to Kundt are either Kundt or Robinson--Trautmann, and we provide explicit Kundt and Robinson--Trautman solutions to quadratic gravity by solving the above mentioned equation on certain Kundt backgrounds.
Quantum Radiation of a Non-stationary Kerr-Newman Black Hole in de Sitter Space-Time
JIANG Qing-Quan; YANG Shu-Zheng
2006-01-01
Hawking radiation of Klein-Gordon and Dirac particles in a non-stationary Kerr-Newman-de-Sitter black hole is studied by introducing a new tortoise coordinate transformation. The result shows that the Fermi-Dirac radiant spectrum displays a new term that represents the interaction between the spin of spinor particles and the rotation of black holes, which is absent in the Bose-Einstein distribution of Klein-Gordon particles.
Tipler, F.J.
1977-08-01
Causally symmetric spacetimes are spacetimes with J/sup +/(S) isometric to J/sup -/(S) for some set S. We discuss certain properties of these spacetimes, showing for example that, if S is a maximal Cauchy surface with matter everywhere on S, then the spacetime has singularities in both J/sup +/(S) and J/sup -/(S). We also consider totally vicious spacetimes, a class of causally symmetric spacetimes for which I/sup +/(p) =I/sup -/(p) = M for any point p in M. Two different notions of stability in general relativity are discussed, using various types of causally symmetric spacetimes as starting points for perturbations.
Cosmological power spectrum in a noncommutative spacetime
Kothari, Rahul; Rath, Pranati K.; Jain, Pankaj
2016-09-01
We propose a generalized star product that deviates from the standard one when the fields are considered at different spacetime points by introducing a form factor in the standard star product. We also introduce a recursive definition by which we calculate the explicit form of the generalized star product at any number of spacetime points. We show that our generalized star product is associative and cyclic at linear order. As a special case, we demonstrate that our recursive approach can be used to prove the associativity of standard star products for same or different spacetime points. The introduction of a form factor has no effect on the standard Lagrangian density in a noncommutative spacetime because it reduces to the standard star product when spacetime points become the same. We show that the generalized star product leads to physically consistent results and can fit the observed data on hemispherical anisotropy in the cosmic microwave background radiation.
Cosmic strings in an expanding spacetime
Stein-Schabes, J.A.; Burd, A.B.
1988-03-15
We study string solutions in an expanding Friedmann-Robertson-Walker (FRW) spacetime. The back reaction of the string on the spacetime has been ignored so that the background stays Friedmannian throughout the evolution. By numerically integrating the field equations in both radiation- and matter-dominated eras, we discover some new oscillatory solutions. The possible damping of these oscillations is discussed. For late times the solution becomes identical to the static one.
Asymptotic symmetries of de Sitter space-time
Chrusciel, P.T. (Polska Akademia Nauk, Warsaw. Inst. Fizyki)
1981-01-01
The general form of the metric of an axially-symmetrical asymptotically de Sitter space-time fulfilling a radiation condition was found. Using the Bondi-Metzner method, the group of asymptotic symmetries of de Sitter space-time was found. The results obtained in this work agree only partially with Penrose's theory.
Lin, De-Hone
2015-01-01
This paper is concerned with the application of a spacetime structure to a three-dimensional quantum system. There are three components. First, the main part of this paper presents the constraint conditions which build the relation of a spacetime structure and a form invariance solution to the covariant Dirac equation. The second is to devise a spacetime cage for fermions with chosen constraints. The third part discusses the feasibility of the cage with an experiment.
Finsler spacetimes and gravity
Pfeifer, Christian
2012-01-01
We consider the geometry of spacetime based on a non-metric, Finslerian, length measure, which, in terms of physics, represents a generalized clock. Our defnition of Finsler spacetimes ensure a well defined notion of causality, a precise description of observers and a geometric background for field theories. Moreover we present our Finsler geometric extension of the Einstein equations, which determine the geometry of Finsler spacetimes dynamically.
Fractional and noncommutative spacetimes
Arzano, M.; Calcagni, M.; Oriti, D.; Scalisi, M.
2011-01-01
We establish a mapping between fractional and noncommutative spacetimes in configuration space. Depending on the scale at which the relation is considered, there arise two possibilities. For a fractional spacetime with log-oscillatory measure, the effective measure near the fundamental scale determi
Spacetime and Euclidean Geometry
Brill, D R; Brill, Dieter; Jacobson, Ted
2004-01-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the "spacetime Pythagoras theorem".
Spacetime and Euclidean geometry
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
Space-Time radar waveforms: circulating codes
Babur, G.; Aubry, P.; Le Chevalier, F.
2013-01-01
This paper describes a concept of the circulating codes covering the whole class of the space-time codes. The circulating codes do not narrow the radiated pattern of the antenna array, thus providing a wide angular coverage, possibly tunable. In turn, the beam-forming on transmit is achievable by me
Visser, Matt
2013-01-01
Analogue spacetimes, (and more boldly, analogue models both of and for gravity), have attracted significant and increasing attention over the last decade and a half. Perhaps the most straightforward physical example, which serves as a template for most of the others, is Bill Unruh's model for a dumb hole, (mute black hole, acoustic black hole), wherein sound is dragged along by a moving fluid --- and can even be trapped behind an acoustic horizon. This and related analogue models for curved spacetimes are useful in many ways: Analogue spacetimes provide general relativists with extremely concrete physical models to help focus their thinking, and conversely the techniques of curved spacetime can sometimes help improve our understanding of condensed matter and/or optical systems by providing an unexpected and countervailing viewpoint. In this introductory chapter, I shall provide a few simple examples of analogue spacetimes as general background for the rest of the contributions.
Partition Function of Spacetime
Makela, Jarmo
2008-01-01
We consider a microscopic model of spacetime, where spacetime is assumed to be a specific graph with Planck size quantum black holes on its vertices. As a thermodynamical system under consideration we take a certain uniformly accelerating, spacelike two-surface of spacetime which we call, for the sake of brevity and simplicity, as {\\it acceleration surface}. Using our model we manage to obtain an explicit and surprisingly simple expression for the partition function of an acceleration surface. Our partition function implies, among other things, the Unruh and the Hawking effects. It turns out that the Unruh and the Hawking effects are consequences of a specific phase transition, which takes place in spacetime, when the temperature of spacetime equals, from the point of view of an observer at rest with respect to an acceleration surface, to the Unruh temperature measured by that observer. When constructing the partition function of an acceleration surface we are forced to introduce a quantity which plays the ro...
Perko, Howard
2017-01-01
Concepts from physical chemistry and more specifically surface tension are introduced to spacetime. Lagrangian equations of motion for membranes of curved spacetime manifold are derived. The equations of motion in spatial directions are dispersion equations and can be rearranged to Schrodinger's equation where Plank's constant is related to membrane elastic modulus. The equation of motion in the time-direction has two immediately recognizable solutions: electromagnetic waves and corpuscles. The corpuscular membrane solution can assume different genus depending on quantized amounts of surface energy. A metric tensor that relates empty flat spacetime to energetic curved spacetime is found that satisfies general relativity. Application of the surface tension to quantum electrodynamics and implications for quantum chromodynamics are discussed. Although much work remains, it is suggested that spacetime surface tension may provide a classical explanation that combines general relativity with field theories in quantum mechanics and atomic particle physics.
Fractional and noncommutative spacetimes
Arzano, Michele; Calcagni, Gianluca; Oriti, Daniele; Scalisi, Marco
2011-12-01
We establish a mapping between fractional and noncommutative spacetimes in configuration space. Depending on the scale at which the relation is considered, there arise two possibilities. For a fractional spacetime with log-oscillatory measure, the effective measure near the fundamental scale determining the log-period coincides with the nonrotation-invariant but cyclicity-preserving measure of κ-Minkowski spacetime. At scales larger than the log-period, the fractional measure is averaged and becomes a power law with real exponent. This can be also regarded as the cyclicity-inducing measure in a noncommutative spacetime defined by a certain nonlinear algebra of the coordinates, which interpolates between κ-Minkowski and canonical spacetime. These results are based upon a braiding formula valid for any nonlinear algebra which can be mapped onto the Heisenberg algebra.
Residual Representations of Spacetime
Saller, H
2001-01-01
Spacetime is modelled by binary relations - by the classes of the automorphisms $\\GL(\\C^2)$ of a complex 2-dimensional vector space with respect to the definite unitary subgroup $\\U(2)$. In extension of Feynman propagators for particle quantum fields representing only the tangent spacetime structure, global spacetime representations are given, formulated as residues using energy-momentum distributions with the invariants as singularities. The associatated quantum fields are characterized by two invariant masses - for time and position - supplementing the one mass for the definite unitary particle sector with another mass for the indefinite unitary interaction sector without asymptotic particle interpretation.
Beal, Jacob; Viroli, Mirko
2015-01-01
... in terms of individual devices. This paper aims to provide a unified approach for the investigation and engineering of computations programmed with the aid of space-time abstractions, by bringing together a number of recent results...
Fractional and noncommutative spacetimes
Arzano, Michele; Oriti, Daniele; Scalisi, Marco
2011-01-01
We establish a mapping between fractional and noncommutative spacetimes in configuration space. Depending on the scale at which the relation is considered, there arise two possibilities. For a fractional spacetime with log-oscillatory measure, the effective measure near the fundamental scale determining the log-period coincides with the non-rotation-invariant but cyclicity-preserving measure of \\kappa-Minkowski. At scales larger than the log-period, the fractional measure is averaged and becomes a power-law with real exponent. This can be also regarded as the cyclicity-inducing measure in a noncommutative spacetime defined by a certain nonlinear algebra of the coordinates, which interpolates between \\kappa-Minkowski and canonical spacetime. These results are based upon a braiding formula valid for any nonlinear algebra which can be mapped onto the Heisenberg algebra.
Physics on noncommutative spacetimes
Padmanabhan, Pramod
The structure of spacetime at the Planck scale remains a mystery to this date with a lot of insightful attempts to unravel this puzzle. One such attempt is the proposition of a 'pointless' structure for spacetime at this scale. This is done by studying the geometry of the spacetime through a noncommutative algebra of functions defined on it. We call such spacetimes 'noncommutative spacetimes'. This dissertation probes physics on several such spacetimes. These include compact noncommutative spaces called fuzzy spaces and noncompact spacetimes. The compact examples we look at are the fuzzy sphere and the fuzzy Higg's manifold. The noncompact spacetimes we study are the Groenewold-Moyal plane and the Bcn⃗ plane. A broad range of physical effects are studied on these exotic spacetimes. We study spin systems on the fuzzy sphere. The construction of Dirac and chirality operators for an arbitrary spin j is studied on both S2F and S2 in detail. We compute the spectrums of the spin 1 and spin 32 Dirac operators on S2F . These systems have novel thermodynamical properties which have no higher dimensional analogs, making them interesting models. The fuzzy Higg's manifold is found to exhibit topology change, an important property for any theory attempting to quantize gravity. We study how this change occurs in the classical setting and how quantizing this manifold smoothens the classical conical singularity. We also show the construction of the star product on this manifold using coherent states on the noncommutative algebra describing this noncommutative space. On the Moyal plane we develop the LSZ formulation of scalar quantum field theory. We compute scattering amplitudes and remark on renormalization of this theory. We show that the LSZ formalism is equivalent to the interaction representation formalism for computing scattering amplitudes on the Moyal plane. This result is true for on-shell Green's functions and fails to hold for off-shell Green's functions. With the
Cylindrically symmetric dust spacetime
Senovilla, J M M; Senovilla, Jose M. M.; Vera, Raul
2000-01-01
We present an explicit exact solution of Einstein's equations for an inhomogeneous dust universe with cylindrical symmetry. The spacetime is extremely simple but nonetheless it has new surprising features. The universe is ``closed'' in the sense that the dust expands from a big-bang singularity but recollapses to a big-crunch singularity. In fact, both singularities are connected so that the whole spacetime is ``enclosed'' within a single singularity of general character. The big-bang is not simultaneous for the dust, and in fact the age of the universe as measured by the dust particles depends on the spatial position, an effect due to the inhomogeneity, and their total lifetime has no non-zero lower limit. Part of the big-crunch singularity is naked. The metric depends on a parameter and contains flat spacetime as a non-singular particular case. For appropriate values of the parameter the spacetime is a small perturbation of Minkowski spacetime. This seems to indicate that flat spacetime may be unstable agai...
Cylindrically symmetric dust spacetime
Senovilla, José M. M.
2000-07-01
We present an explicit exact solution of Einstein's equations for an inhomogeneous dust universe with cylindrical symmetry. The spacetime is extremely simple but nonetheless it has surprising new features. The universe is `closed' in the sense that the dust expands from a big-bang singularity but recollapses to a big-crunch singularity. In fact, both singularities are connected so that the whole spacetime is `enclosed' within a single singularity of general character. The big-bang is not simultaneous for the dust, and in fact the age of the universe as measured by the dust particles depends on the spatial position, an effect due to the inhomogeneity, and their total lifetime has no non-zero lower limit. Part of the big-crunch singularity is naked. The metric depends on a parameter and contains flat spacetime as a non-singular particular case. For appropriate values of the parameter the spacetime is a small perturbation of Minkowski spacetime. This seems to indicate that flat spacetime may be unstable against some global non-vacuum perturbations.
Aranha, R F; Tonini, E V
2011-01-01
We examine numerically the post-merger regime of two Schwarzschild black holes in non head-on collision. Our treatment is made in the realm of non-axisymmetric Robinson-Trautman spacetimes which are appropriate for the description of the system. Characteristic initial data for the system are constructed and the Robinson-Trautman equation is integrated using a numerical code based on the Galerkin spectral method. The collision is planar, restricted to the plane determined by the directions of the two initial colliding black holes, with the net momentum fluxes of gravitational waves confined to this plane. We evaluate the efficiency of mass-energy extraction, the total energy and momentum carried out by gravitational waves and the momentum distribution of the remnant black hole. Our analysis is based on the Bondi-Sachs four momentum conservation laws. Head-on collisions and orthogonal collisions constitute, respectively, upper and lower bounds to the power emission and to the efficiency of mass-energy extractio...
Superfluids in Curved Spacetime
Villegas, Kristian Hauser A
2015-01-01
Superfluids under an intense gravitational field are typically found in neutron star and quark star cores. Most treatments of these superfluids, however, are done in a flat spacetime background. In this paper, the effect of spacetime curvature on superfluidity is investigated. An effective four-fermion interaction is derived by integrating out the mediating scalar field. The fermions interacting via the mediating gauge vector bosons is also discussed. Two possible cases are considered in the mean-field treatment: antifermion-fermion and fermion-fermion pairings. An effective action, quadratic in fermion field, and a self-consistent equation are derived for both cases. The effective Euclidean action and the matrix elements of the heat kernel operator, which are very useful in curved-spacetime QFT calculations, are derived for the fermion-fermion pairing. Finally, explicit numerical calculation of the gravitational correction to the pairing order parameter is performed for the scalar superfluid case. It is foun...
Ashtekar, Abhay
In general relativity space-time ends at singularities. The big bang is considered as the Beginning and the big crunch, the End. However these conclusions are arrived at by using general relativity in regimes which lie well beyond its physical domain of validity. Examples where detailed analysis is possible show that these singularities are naturally resolved by quantum geometry effects. Quantum space-times can be vastly larger than what Einstein had us believe. These non-trivial space-time extensions enable us to answer of some long standing questions and resolve of some puzzles in fundamental physics. Thus, a century after Minkowski's revolutionary ideas on the nature of space and time, yet another paradigm shift appears to await us in the wings.
Comment on "Spacetime Information"
Kent, A
1996-01-01
A recent paper by Hartle [Phys. Rev. D 51, 1800 (1995)] proposes a definition of ``spacetime information'' --- the information available about a quantum system's boundary conditions in the various sets of decohering histories it may display --- and investigates its properties. We note here that Hartle's analysis contains errors which invalidate several of the conclusions. In particular, the proof that the proposed definition agrees with the standard definition for ordinary quantum mechanics is invalid, the evaluations of the spacetime information for time-neutral generalized quantum theories and for generalized quantum theories with non-unitary evolution are incorrect, and the argument that spacetime information is conserved on spacelike surfaces in these last theories is erroneous. We show however that the proposed definition does, in fact, agree with the standard definition for ordinary quantum mechanics. Hartle's definition relies on choosing, case by case, a class of fine-grained consistent sets of histor...
Quantization of the space-time with topological defect
高长军; 沈有根
2003-01-01
We present the classical solution of Lagrange equations for the black hole with a global monopole or with a cosmic string. Then we obtain the wavefunction of the space-time by solving the Wheeler-De Witt equation. De Broglie-Bohm interpretation applied to the wavefunction gives the quantum solution of the space-time. In the end, the quantum effect on Hawking radiation is studied.
Classical limits of boot-rotation symmetric spacetimes
Kofron, David
2010-01-01
Boost-rotation symmetric spacetimes are exceptional as they are the only exact asymptotically flat solutions to the Einstein equations describing spatially bounded sources ("point-like" particles, black holes) undergoing non-trivial motion ("uniform acceleration") with radiation. We construct the Newtonian limit of these spacetimes: it yields fields of uniformly accelerated sources in classical mechanics. We also study the special-relativistic limit of the charged rotating C-metric and so find accelerating electromagnetic magic field.
Emergent Spacetime: Reality or Illusion?
Yang, Hyun Seok
2015-01-01
The contemporary physics has revealed growing evidences that the emergence can be applied to not only biology and condensed matter systems but also gravity and spacetime. We observe that noncommutative spacetime necessarily implies emergent spacetime if spacetime at microscopic scales should be viewed as noncommutative. Since the emergent spacetime is a new fundamental paradigm for quantum gravity, it is necessary to reexamine all the rationales to introduce the multiverse hypothesis from the standpoint of emergent spacetime. We argue that the emergent spacetime certainly opens a new perspective that may cripple all the rationales to introduce the multiverse picture. Moreover the emergent spacetime may rescue us from the doomsday of metastable multiverse as quantum mechanics did from the catastrophic collapse of classical atoms.
Symmetry, structure, and spacetime
Rickles, Dean
2007-01-01
In this book Rickles considers several interpretative difficulties raised by gauge-type symmetries (those that correspond to no change in physical state). The ubiquity of such symmetries in modern physics renders them an urgent topic in philosophy of physics. Rickles focuses on spacetime physics, and in particular classical and quantum general relativity. Here the problems posed are at their most pathological, involving the apparent disappearance of spacetime! Rickles argues that both traditional ontological positions should be replaced by a structuralist account according to which relational
Axially Symmetric, Spatially Homothetic Spacetimes
Wagh, S M; Wagh, Sanjay M.; Govinder, Keshlan S.
2002-01-01
We show that the existence of appropriate spatial homothetic Killing vectors is directly related to the separability of the metric functions for axially symmetric spacetimes. The density profile for such spacetimes is (spatially) arbitrary and admits any equation of state for the matter in the spacetime. When used for studying axisymmetric gravitational collapse, such solutions do not result in a locally naked singularity.
YANG Shu-Zheng; JIANG Qing-Quan; LI Hui-Ling
2006-01-01
Applying Parikh-Wilzcek's semi-classical quantum tunneling model, we study the Hawking radiation of charged particles as tunneling from the event horizon of a cylindrically symmetric black hole in anti-de Sitter space-time.The derived result shows that the tunneling rate of charged particles is related to the change of Bekenstein-Hawking entropy and that the radiation spectrum is not strictly pure thermal after taking the black hole background dynamical and self-gravitation interaction into account, but is consistent with the underlying unitary theory.
The Planck Blackbody Spectrum Follows from the Structure of Relativistic Spacetime
Boyer, Timothy H
2016-01-01
Here we show that within classical physics, the Planck blackbody spectrum can be derived directly from the structure of relativistic spacetime. In noninertial frames, thermal radiation at positive temperature is connected directly to zero-point radiation whose spectrum follows from the geodesic structure of the spacetime. The connection between zero-point radiation and thermal radiation at postive temperature is through a time-dilating conformal transformation in the noninertial frame. Transferring the spectrum back to Minskowski spacetime, the Planck spectrum is obtained.
Spectral geometry of spacetime
Kopf, T
2000-01-01
Spacetime, understood as a globally hyperbolic manifold, may be characterized by spectral data using a 3+1 splitting into space and time, a description of space by spectral triples and by employing causal relationships, as proposed earlier. Here, it is proposed to use the Hadamard condition of quantum field theory as a smoothness principle.
Schrödinger, Erwin
1985-01-01
In response to repeated requests this classic book on space-time structure by Professor Erwin Schrödinger is now available in the Cambridge Science Classics series. First published in 1950, and reprinted in 1954 and 1960, this lucid and profound exposition of Einstein's 1915 theory of gravitation still provides valuable reading for students and research workers in the field.
Emergent Spacetime for Quantum Gravity
Yang, Hyun Seok
2016-01-01
We emphasize that noncommutative (NC) spacetime necessarily implies emergent spacetime if spacetime at microscopic scales should be viewed as NC. In order to understand NC spacetime correctly, we need to deactivate the thought patterns that we have installed in our brains and taken for granted for so many years. Emergent spacetime allows a background-independent formulation of quantum gravity that will open a new perspective to resolve the notorious problems in theoretical physics such as the cosmological constant problem, hierarchy problem, dark energy, dark matter, and cosmic inflation.
Quantum Singularity of Quasiregular Spacetimes
Konkowski, Deborah A.; Helliwell, Thomas M.
2001-04-01
A quasiregular spacetime is a spacetime with a classical quasiregular singularity, the mildest form of true singularity [G.F.R. Ellis and B.G. Schmidt, Gen. Rel. Grav. 8, 915 (1977)]. The definition of G.T. Horowitz and D. Marolf [Phys. Rev. D52, 5670 (1995)] for a quantum-mechanically singular spacetime is one in which the spatial-derivative operator in the Klein-Gordon equation for a massive scalar field is not essentially self-adjoint. In such a quantum-mechanically singular spacetime, the time evolution of a quantum test particle is not uniquely determined. Horowitz and Marolf showed that a two-dimensional spacetime with a classical conical singularity (i.e., a two-dimensional quasiregular singularity) is also quantum-mechanically singular. Here we show that a class of static quasiregular spacetimes possessing disclinations and dislocations [R.A.Puntigam and H.H. Soleng , Class. Quantum Grav. 14, 1129 (1997)] is quantum-mechanically singular, since the scalar wave operator is not essentially self-adjoint. These spacetimes include an idealized cosmic string spacetime, i.e., a four-dimensional spacetime with conical singularity, and a Galtsov/Letelier/Tod spacetime featuring a screw dislocation [K.P. Tod, Class. Quantum Grav. 11, 1331 (1994); D.V. Galtsov and P.S. Letelier, Phys. Rev. D47, 4273 (1993)]. In addition, we show that the definition of quantum-mechanically singular spacetimes can be extended to include Maxwell and Dirac fields.
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...
Lovelady, Benjamin C
2015-01-01
According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dim Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected SO(n) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an SO(n-1,1) connection on the spacetime. The principal fiber bundle character of the original SO(n) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.
Computation and Spacetime Structure
Stannett, Mike
2011-01-01
We investigate the relationship between computation and spacetime structure, focussing on the role of closed timelike curves (CTCs) in promoting computational speedup. We note first that CTC traversal can be interpreted in two distinct ways, depending on ones understanding of spacetime. Focussing on one interpretation leads us to develop a toy universe in which no CTC can be traversed more than once, whence no computational speedup is possible. Focussing on the second (and more standard) interpretation leads to the surprising conclusion that CTCs act as perfect information repositories: just as black holes have entropy, so do CTCs. If we also assume that P is not equal to NP, we find that all observers agree that, even if unbounded time travel existed in their youth, this capability eventually vanishes as they grow older. Thus the computational assumption "P is not NP" is also an assumption concerning cosmological structure.
Lovelady, Benjamin C.; Wheeler, James T.
2016-04-01
According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dimensional Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected S O (n ) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an S O (n -1 ,1 ) connection on the spacetime. The principal fiber bundle character of the original S O (n ) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.
Black hole evaporation rates without spacetime.
Braunstein, Samuel L; Patra, Manas K
2011-08-12
Verlinde recently suggested that gravity, inertia, and even spacetime may be emergent properties of an underlying thermodynamic theory. This vision was motivated in part by Jacobson's 1995 surprise result that the Einstein equations of gravity follow from the thermodynamic properties of event horizons. Taking a first tentative step in such a program, we derive the evaporation rate (or radiation spectrum) from black hole event horizons in a spacetime-free manner. Our result relies on a Hilbert space description of black hole evaporation, symmetries therein which follow from the inherent high dimensionality of black holes, global conservation of the no-hair quantities, and the existence of Penrose processes. Our analysis is not wedded to standard general relativity and so should apply to extended gravity theories where we find that the black hole area must be replaced by some other property in any generalized area theorem.
Hydrodynamics in Class B Warped Spacetimes
Carot, J
2005-01-01
We discuss certain general features of type B warped spacetimes which have important consequences on the material content they may admit and its associated dynamics. We show that, for Warped B spacetimes, if shear and anisotropy are nonvanishing, they have to be proportional. We also study some of the physics related to the warping factor and of the underlying decomposable metric. Finally we explore the only possible cases compatible with a type B Warped geometry which satisfy the dominant energy conditions. As an example of the above mentioned consequences we consider a radiating fluid and two non-spherically symmetric metrics which depend upon an arbitrary parameter, such that if the parameter vanishes the spherical symmetry is recovered.
Introducing surface tension to spacetime
Perko, H. A.
2017-05-01
Concepts from physical chemistry of surfaces and surface tension are applied to spacetime. More specifically, spacetime is modeled as a spatial fluid continuum bound together by a multi-dimensional membrane of time. A metric tensor that relates empty flat spacetime to energetic curved spacetime is found. Equations of motion for an infinitesimal unit of spacetime are derived. The equation of motion in a time-like direction is a Klein-Gordon type equation. The equations of motion in space-like directions take the form of Schrodinger’s equation where Plank’s constant is related to membrane elastic modulus. Although much work remains, it is suggested that the spacetime surface tension may serve as a mechanical model for many phenomena in quantum mechanics and atomic particle physics.
Spacetime in modern physical theories
Klatt, Carrie
In this thesis we examine the relationship between the gravitational field and spacetime in three modern physical theories: general relativity, the field theoretic approach, and geometrodynamics. Our analysis is based on two questions: first, is gravity best understood as a field in a spacetime background or is the gravitational field indistinguishable from spacetime? Here we compare the field theoretic approach to gravity presented by Feynman and Weinberg, where spacetime is at first taken to be a flat background, to general relativity, where we find that the equivalence principle in conjunction with the geodesic hypothesis allows us to consider the gravitational field as being indistinguishable from curved spacetime. Second, what does it mean to say that spacetime (or alternatively, matter) has a privileged status in a theory? That is, is it sensible to say that one object in a theory, such as spacetime, can be derived from another object in the theory, for example, matter? Here we compare general relativity, where matter and spacetime are considered to be primary notions in the theory, to Wheeler's geometrodynamics, where all objects in the universe, including matter, charge and electromagnetism, are to be explained as manifestations of curved spacetime. By considering these issues, it is hoped that we will be able to contribute to the analysis of similar topics in theories of quantum gravity such as string theory.
Multipole Moments of numerical spacetimes
Pappas, George
2012-01-01
In this article we present some recent results on identifying correctly the relativistic multipole moments of numerically constructed spacetimes, and the consequences that this correction has on searching for appropriate analytic spacetimes that can approximate well the previously mentioned numerical spacetimes. We also present expressions that give the quadrupole and the spin octupole as functions of the spin parameter of a neutron star for various equations of state and in a range of masses for every equation of state used. These results are relevant for describing the exterior spacetime of rotating neutron stars that are made up of matter obeying realistic equations of state.
Asymptotically flat space-times: an enigma
Newman, Ezra T.
2016-07-01
We begin by emphasizing that we are dealing with standard Einstein or Einstein-Maxwell theory—absolutely no new physics has been inserted. The fresh item is that the well-known asymptotically flat solutions of the Einstein-Maxwell theory are transformed to a new coordinate system with surprising and (seemingly) inexplicable results. We begin with the standard description of (Null) asymptotically flat space-times described in conventional Bondi-coordinates. After transforming the variables (mainly the asymptotic Weyl tensor components) to a very special set of Newman-Unti (NU) coordinates, we find a series of relations totally mimicking standard Newtonian classical mechanics and Maxwell theory. The surprising and troubling aspect of these relations is that the associated motion and radiation does not take place in physical space-time. Instead these relations takes place in an unusual inherited complex four-dimensional manifold referred to as H-space that has no immediate relationship with space-time. In fact these relations appear in two such spaces, H-space and its dual space \\bar{H}.
Spherically symmetric brane spacetime with bulk gravity
Chakraborty, Sumanta; SenGupta, Soumitra
2015-01-01
Introducing term in the five-dimensional bulk action we derive effective Einstein's equation on the brane using Gauss-Codazzi equation. This effective equation is then solved for different conditions on dark radiation and dark pressure to obtain various spherically symmetric solutions. Some of these static spherically symmetric solutions correspond to black hole solutions, with parameters induced from the bulk. Specially, the dark pressure and dark radiation terms (electric part of Weyl curvature) affect the brane spherically symmetric solutions significantly. We have solved for one parameter group of conformal motions where the dark radiation and dark pressure terms are exactly obtained exploiting the corresponding Lie symmetry. Various thermodynamic features of these spherically symmetric space-times are studied, showing existence of second order phase transition. This phenomenon has its origin in the higher curvature term with gravity in the bulk.
Computer algebra in spacetime embedding
Roque, Waldir L
2014-01-01
In this paper we describe an algorithm to determine the vectors normal to a space-time V4 embedded in a pseudo-Euclidean manifold M4+n. An application of this algorithm is given considering the Schwarzchild space-time geometry embedded in a 6 dimensional pseudo-Euclidean manifold, using the algebraic computing system REDUCE.
Stability problem in Rindler spacetime
2007-01-01
The stability problem of the Rindler spacetime is carefully studies by using the scalar wave perturbation. Using two different coordinate systems, the scalar wave equation is investigated. The results are different in the two cases.They are analysed and compared with each other in detail. The following conclusions are obtained: (a) the Rindler spacetime as a whole is not stable; (b) the Rindler spacetime can exist stably only as part of the Minkowski spacetime,and the Minkowski spacetime can be a real entity independently; (c) there are some defects for the scalar wave equation written by the Rindler coordinates, and it is unsuitable for the investigation of the stability properties of the Rindler spacetime. All these results may shed some light on the stability properties of the Schwarzschild black hole. It is natural and reasonable for one to infer that: (a) perhaps the Regge-Wheeler equation is not sufficient to determine the stable properties; (b) the Schwarzschild black hole as a whole might be really unstable; (c) the Kruskal spacetime is stable and can exist as a real physical entity; whereas the Schwarzschild black hole can occur only as part of the Kruskal spacetime.
Causal Behaviour on Carter spacetime
Blanco, Oihane F
2015-01-01
In this work we will focus on the causal character of Carter Spacetime (see B. Carter, Causal structure in space-time, Gen. Rel. Grav. 1 4 337-406, 1971). The importance of this spacetime is the following: for the causally best well behaved spacetimes (the globally hyperbolic ones), there are several characterizations or alternative definitions. In some cases, it has been shown that some of the causal properties required in these characterizations can be weakened. But Carter spacetime provides a counterexample for an impossible relaxation in one of them. We studied the possibility of Carter spacetime to be a counterexample for impossible lessening in another characterization, based on the previous results. In particular, we will prove that the time-separation or Lorentzian distance between two chosen points in Carter spacetime is infinite. Although this spacetime turned out not to be the counterexample we were looking for, the found result is interesting per se and provides ideas for alternate approaches to t...
Chapline, George
It has been shown that a nonlinear Schrödinger equation in 2+1 dimensions equipped with an SU(N) Chern-Simons gauge field can provide an exact description of certain self-dual Einstein spaces in the limit N-=∞. Ricci flat Einstein spaces can then be viewed as arising from a quantum pairing of the classical self-dual and anti-self-dual solutions. In this chapter, we will outline how this theory of empty space-time might be generalized to include matter and vacuum energy by transplanting the nonlinear Schrödinger equation used to construct Einstein spaces to the 25+1-dimensional Lorentzian Leech lattice. If the distinguished 2 spatial dimensions underlying the construction of Einstein spaces are identified with a hexagonal lattice section of the Leech lattice, the wave-function becomes an 11 × 11 matrix that can represent fermion and boson degrees of freedom (DOF) associated with 2-form and Yang-Mills gauge symmetries. The resulting theory of gravity and matter in 3+1 dimensions is not supersymmetric, which provides an entry for a vacuum energy. Indeed, in the case of a Lemaitre cosmological model, the emergent space-time will naturally have a vacuum energy on the order of the observed cosmological constant.
Emergent Spacetime and Cosmic Inflation
Yang, Hyun Seok
2015-01-01
We propose a background-independent formulation of cosmic inflation. The inflation in this picture corresponds to a dynamical process to generate space and time while the conventional inflation is simply an (exponential) expansion of a preexisting spacetime owing to the vacuum energy carried by an inflaton field. We observe that the cosmic inflation is triggered by the condensate of Planck energy into vacuum responsible for the generation of spacetime and must be a single event according to the exclusion principle of noncommutative spacetime caused by the Planck energy condensate in vacuum. The emergent spacetime picture admits a background-independent formulation so that the inflation can be described by a conformal Hamiltonian system characterized by an exponential phase space expansion without introducing any inflaton field as well as an ad hoc inflation potential. This implies that the emergent spacetime may incapacitate all the rationales to introduce the multiverse hypothesis.
Polarized electrogowdy spacetimes censored
Nungesser, Ernesto, E-mail: ernesto.nungesser@aei.mpg.d [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, 14476 Potsdam (Germany)
2010-05-01
A sketch of the proof of strong cosmic censorship is presented for a class of solutions of the Einstein-Maxwell equations, those with polarized Gowdy symmetry. A key element of the argument is the observation that by means of a suitable choice of variables the central equations in this problem can be written in a form where they are identical to the central equations for general (i.e. non-polarized) vacuum Gowdy spacetimes. Using this it is seen that the results of Ringstroem on strong cosmic censorship in the vacuum case have implications for the Einstein-Maxwell case. Working out the geometrical meaning of these analytical results leads to the main conclusion.
Springer handbook of spacetime
Petkov, Vesselin
2014-01-01
The Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courses on these subjects. The Han...
Clocks, computers, black holes, spacetime foam, and holographic principle
Ng, Y J
2000-01-01
What do simple clocks, simple computers, black holes, space-time foam, and holographic principle have in common? I will show that the physics behind them is inter-related, linking together our concepts of information, gravity, and quantum uncertainty. Thus, the physics that sets the limits to computation and clock precision also yields Hawking radiation of black holes and the holographic principle. Moreover, the latter two strongly imply that space-time undergoes much larger quantum fluctuations than what the folklore suggests --- large enough to be detected with modern gravitational-wave interferometers through future refinements.
Mesoscopic Fluctuations in Stochastic Spacetime
Shiokawa, K
2000-01-01
Mesoscopic effects associated with wave propagation in spacetime with metric stochasticity are studied. We show that the scalar and spinor waves in a stochastic spacetime behave similarly to the electrons in a disordered system. Viewing this as the quantum transport problem, mesoscopic fluctuations in such a spacetime are discussed. The conductance and its fluctuations are expressed in terms of a nonlinear sigma model in the closed time path formalism. We show that the conductance fluctuations are universal, independent of the volume of the stochastic region and the amount of stochasticity.
Ambient cosmology and spacetime singularities
Antoniadis, Ignatios
2015-01-01
We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary.
Ambient cosmology and spacetime singularities
Antoniadis, Ignatios [Bern University, Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern (Switzerland); Ecole Polytechnique, Palaiseau (France); Cotsakis, Spiros [CERN, Theory Division, Department of Physics, Geneva 23 (Switzerland); National Technical University, School of Applied Mathematics and Physical Sciences, Athens (Greece)
2015-01-01
We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary. (orig.)
Nonlocal gravity: Conformally flat spacetimes
Bini, Donato
2016-01-01
The field equations of the recent nonlocal generalization of Einstein's theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of conformally flat spacetimes. Even in this simple case, the field equations are intractable. Therefore, to gain insight into the nature of these equations, we investigate the structure of nonlocal gravity in two-dimensional spacetimes. While any smooth 2D spacetime is conformally flat and satisfies Einstein's field equations, only a subset containing either a Killing vector or a homothetic Killing vector can satisfy the field equations of nonlocal gravity.
Interactions Between Real and Virtual Spacetimes
Javadi, Hossein; Forouzbakhsh, Farshid
2014-01-01
. In this article, we analyzed that c is the edge of visible and invisible particles such as virtual photons and graviton. It leads us passing the real spacetime and enter into the virtual spacetime and describe interactions between real spacetime and virtual spacetime and reach to non-obvious space....
Gaussian quantum steering and its asymmetry in curved spacetime
Wang, Jieci; Jing, Jiliang; Fan, Heng
2015-01-01
We study Gaussian quantum steering and its asymmetry in the background of a Schwarzschild black hole. We present a Gaussian channel description of quantum state evolution under the influence of Hawking radiation. We find that thermal noise introduced by Hawking effect will destroy the steerability between an inertial observer Alice and an accelerated observer Bob who hovers outside an event horizon, while it generates steerability between Bob and a hypothetical observer Anti-Bob inside the event horizon. Besides, unlike entanglement behaviors in curved spacetime, here the steering from Alice to Bob suffers from a ``sudden death" and the steering from Anti-Bob to Bob appears a ``sudden birth" with the increasing of Hawking temperature. We also find that the Gaussian steering is always asymmetric and the maximum steering asymmetry can \\emph{ exceed} $\\ln 2$ in curved spacetime, which is quite different from the flat spacetime case [Phys. Rev. Lett. 114, 060403 (2015)] where the steering asymmetry can \\emph{neve...
Spherically Symmetric, Self-Similar Spacetimes
Wagh, S M; Wagh, Sanjay M.; Govinder, Keshlan S.
2001-01-01
Self-similar spacetimes are of importance to cosmology and to gravitational collapse problems. We show that self-similarity or the existence of a homothetic Killing vector field for spherically symmetric spacetimes implies the separability of the spacetime metric in terms of the co-moving coordinates and that the metric is, uniquely, the one recently reported in [cqg1]. The spacetime, in general, has non-vanishing energy-flux and shear. The spacetime admits matter with any equation of state.
Quasilocal Energy in Kerr Spacetime
Liu, Jian-Liang
2016-01-01
In this work we study the quasilocal energy as in [11] for a constant radius surface in Kerr spacetime in Boyer-Lindquist coordinates. We show that under suitable conditions for isometric embedding, for a stationary observer the quasilocal energy defined in [11] for constant radius in a Kerr like spacetime is exactly equal to the Brown-York quasilocal energy [2]. By some careful estimations, we show that for a constant radius surface in the Kerr spacetime which is outside the ergosphere the embedding conditions for the previous result are satisfied. Finally we discuss extremal solutions as described in [14] and show that near the horizon of the Kerr spacetime for the small rotation case the extremal solutions are trivial.
Romero, Gustavo E
2015-01-01
I present a discussion of some issues in the ontology of spacetime. After a characterisation of the controversies among relationists, substantivalists, eternalists, and presentists, I offer a new argument for rejecting presentism, the doctrine that only present objects exist. Then, I outline and defend a form of spacetime realism that I call event substantivalism. I propose an ontological theory for the emergence of spacetime from more basic entities (timeless and spaceless `events'). Finally, I argue that a relational theory of pre-geometric entities can give rise to substantival spacetime in such a way that relationism and substantivalism are not necessarily opposed positions, but rather complementary. In an appendix I give axiomatic formulations of my ontological views.
Ronald E Meyers; Keith S Deacon
2015-01-01
.... The ghost imaging experiments are performed both with and without turbulence. A discussion of the physics of the space-time imaging is presented in terms of quantum nonlocal two-photon analysis to support the experimental results...
Visualizing spacetimes via embedding diagrams
Hledik, Stanislav; Cipko, Alois
2016-01-01
It is hard to imagine curved spacetimes of General Relativity. A simple but powerful way how to achieve this is visualizing them via embedding diagrams of both ordinary geometry and optical reference geometry. They facilitate to gain an intuitive insight into the gravitational field rendered into a curved spacetime, and to assess the influence of parameters like electric charge and spin of a black hole, magnetic field or cosmological constant. Optical reference geometry and related inertial forces and their relationship to embedding diagrams are particularly useful for investigation of test particles motion. Embedding diagrams of static and spherically symmetric, or stationary and axially symmetric black-hole and naked-singularity spacetimes thus present a useful concept for intuitive understanding of these spacetimes' nature. We concentrate on general way of embedding into 3-dimensional Euclidean space, and give a set of illustrative examples.
Prather B.
2013-07-01
Full Text Available This paper considers the possibility of a teleparallel approximation of general relativity where the underlying space-time of a compact massive source is related to the isotropic coordinate chart rather than the geometric chart. This results in a 20 percent reduction of the expected shadow radius of compact objects. The observation of the shadow radius of Sagittarius A* should be possible in the near future using VLBI. The theoretical reduction is within the uncertainty of the expected shadow radius, however any observation less than a critical radius would indicate that gravity is not the result of space-time curvature alone. If space-time curvature does not act alone it is simpler to adopt the teleparallel view, with the tetrad ﬁeld representing the index of refraction of the required material ﬁeld in a ﬂat space-time.
Asymptotic behaviour of electro-$\\Lambda$ spacetimes
Saw, Vee-Liem
2016-01-01
We derive the asymptotic solutions for vacuum spacetimes with non-zero cosmological constant $\\Lambda$ coupled to Maxwell fields, using the Newman-Penrose formalism. This extends a recent work that dealt with the vacuum Einstein (Newman-Penrose) equations with $\\Lambda=0$. Using these asymptotic solutions, we discuss the mass-loss of an isolated electro-gravitating system with cosmological constant. In a universe with $\\Lambda>0$, the physics of electromagnetic (EM) radiation is relatively straightforward compared to those of gravitational radiation: 1) It is clear that outgoing EM radiation results in a decrease to the Bondi mass of the isolated system. 2) It is also perspicuous that if any incoming EM radiation from elsewhere is present, those beyond the isolated system's cosmological horizon would eventually arrive at the spacelike $\\mathcal{I}$ and increase the Bondi mass of the isolated system. Hence, the (outgoing and incoming) EM radiation fields do not couple with the Bondi mass-loss formula in any un...
Mapping curved spacetimes into Dirac spinors
Sabín, Carlos
2016-01-01
We show how to transform a Dirac equation in curved spacetime into a Dirac equation in flat spacetime. In particular, we show that any solution of the free massless Dirac equation in a 1+1 dimensional flat spacetime can be transformed via a local phase transformation into a solution of the corresponding Dirac equation in a curved background, where the spacetime metric is encoded into the phase. In this way, the existing quantum simulators of the Dirac equation can naturally incorporate curved spacetimes. As a first example we use our technique to obtain solutions of the Dirac equation in a particular family of interesting spacetimes in 1+1 dimensions.
Global solutions of Yang-Mills equations on anti-de Sitter spacetime
Choquet-Bruhat, Y. (Paris Univ. (France). Mecanique Relativiste)
1989-12-01
Anti-de Sitter spacetime is a C{sup {infinity}} manifold diffeomorphic to R{sup 4}, endowed with a C{sup {infinity}} metric of hyperbolic signature. However this spacetime is not globally hyperbolic, and the known results about the solution of the Cauchy problem for wave equations on Lorentzian manifolds do not apply, even for a small interval of time and even for linear equations. We prove the global existence of a solution of the Cauchy problem for the Yang-Mills-Higgs equations on anti-de Sitter spacetime, under the condition that there is no radiation at timelike infinity, a condition that is explained mathematically. (author).
Various Facets of Spacetime Foam
Ng, Y Jack
2011-01-01
Spacetime foam manifests itself in a variety of ways. It has some attributes of a turbulent fluid. It is the source of the holographic principle. Cosmologically it may play a role in explaining why the energy density has the critical value, why dark energy/matter exists, and why the effective dynamical cosmological constant has the value as observed. Astrophysically the physics of spacetime foam helps to elucidate why the critical acceleration in modified Newtonian dynamics has the observed value; and it provides a possible connection between global physics and local galactic dynamics involving the phenomenon of flat rotation curves of galaxies and the observed Tully-Fisher relation. Spacetime foam physics also sheds light on nonlocal gravitational dynamics.
Thermal dimension of quantum spacetime
Amelino-Camelia, Giovanni; Gubitosi, Giulia; Santos, Grasiele
2016-01-01
Recent results suggest that a crucial crossroad for quantum gravity is the characterization of the effective dimension of spacetime at short distances, where quantum properties of spacetime become significant. This is relevant in particular for various scenarios of "dynamical dimensional reduction" which have been discussed in the literature. We are here concerned with the fact that the related research effort has been based exclusively on analyses of the "spectral dimension", which involves an unphysical Euclideanization of spacetime and is highly sensitive to the off-shell properties of a theory. As here shown, different formulations of the same physical theory can have wildly different spectral dimension. We propose that dynamical dimensional reduction should be described in terms of the "thermal dimension" which we here introduce, a notion that only depends on the physical content of the theory. We analyze a few models with dynamical reduction both of the spectral dimension and of our thermal dimension, f...
Geodesics of Spherical Dilaton Spacetimes
ZENG Yi; L(U) Jun-Li; WANG Yong-Jiu
2006-01-01
The properties of spherical dilaton black hole spacetimes are investigated through a study of their geodesies. The closed and non-closed orbits of test particles are analysed using the effective potential and phase-plane method. The stability and types of orbits are determined in terms of the energy and angular momentum of the test particles. The conditions of the existence of circular orbits for a spherical dilaton spacetime with an arbitrary dilaton coupling constant a are obtained. The properties of the orbits and in particular the position of the innermost stable circular orbit are compared to those of the Reissner-Nordstrom spacetime. The circumferential radius of innermost stable circular orbit and the corresponding angular momentum of the test particles increase for a≠0.
Szpak, Nikodem
2014-01-01
We present some new ideas on how to design analogue models of quantum fields living in curved spacetimes using ultra-cold atoms in optical lattices. We discuss various types of static and dynamical curved spacetimes achievable by simple manipulations of the optical setup. Examples presented here contain two-dimensional spaces of positive and negative curvature as well as homogeneous cosmological models and metric waves. Most of them are extendable to three spatial dimensions. We mention some interesting phenomena of quantum field theory in curved spacetimes which might be simulated in such optical lattices loaded with bosonic or fermionic ultra-cold atoms. We also argue that methods of differential geometry can be used, as an alternative mathematical approach, for dealing with realistic inhomogeneous optical lattices.
Anisotropic inflation in Finsler spacetime
Li, Xin; Chang, Zhe
2015-01-01
We suggest the universe is Finslerian in the stage of inflation. The Finslerian background spacetime breaks rotational symmetry and induces parity violation. The primordial power spectrum is given for quantum fluctuation of the inflation field. It depends not only on the magnitude of wavenumber but also on the preferred direction. We derive the gravitational field equations in the perturbed Finslerian background spacetime, and obtain a conserved quantity outside the Hubble horizon. The angular correlation coefficients are presented in our anisotropic inflation model. The parity violation feature of Finslerian background spacetime requires that the anisotropic effect only appears in angular correlation coefficients if $l'=l+1$. The numerical results of the angular correlation coefficients are given to describe the anisotropic effect.
Is Quantum Spacetime Foam Unstable?
Redmount, I H; Redmount, Ian H.; Suen, Wai-Mo
1993-01-01
A very simple wormhole geometry is considered as a model of a mode of topological fluctutation in Planck-scale spacetime foam. Quantum dynamics of the hole reduces to quantum mechanics of one variable, throat radius, and admits a WKB analysis. The hole is quantum-mechanically unstable: It has no bound states. Wormhole wave functions must eventually leak to large radii. This suggests that stability considerations along these lines may place strong constraints on the nature and even the existence of spacetime foam.
Tensor networks for dynamic spacetimes
May, Alex
2016-01-01
Existing tensor network models of holography are limited to representing the geometry of constant time slices of static spacetimes. We study the possibility of describing the geometry of a dynamic spacetime using tensor networks. We find it is necessary to give a new definition of length in the network, and propose a definition based on the mutual information. We show that by associating a set of networks with a single quantum state and making use of the mutual information based definition of length, a network analogue of the maximin formula can be used to calculate the entropy of boundary regions.
Black holes and warped spacetime
Kaufmann, W.J. III
1979-01-01
Black holes (BHs) and their warping effect on spacetime are described, beginning with a discussion on stellar evolution that includes white dwarfs, supernovas and neutron stars. The structure of static, rotating, and electrically charged BHs are considered, as well as the general theory of relativity, quantum mechanics, the Einstein-Rosen bridge, and wormholes in spacetime. Attention is also given to gravitational lenses, various space geometries, quasars, Seyfert galaxies, supermassive black holes, the evaporation and particle emission of BHs, and primordial BHs, including their temperature and lifetime.
The Motion of Point Particles in Curved Spacetime
Poisson Eric
2004-01-01
Full Text Available This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The self-force contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. The work done by the self-force matches the energy radiated away by the particle. The field's action on the particle is difficult to calculate because of its singular nature: The field diverges at the position of the particle. But it is possible to isolate the field's singular part and show that it exerts no force on the particle -- its only effect is to contribute to the particle's inertia. What remains after subtraction is a smooth field that is fully responsible for the self-force. Because this field satisfies a homogeneous wave equation, it can be thought of as a free (radiative field that interacts with the particle; it is this interaction that gives rise to the self-force. The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime are developed here from scratch. The review begins with a discussion of the basic theory of bitensors (Section 2. It then applies the theory to the construction of convenient coordinate systems to chart a neighbourhood of the particle's word line (Section 3. It continues with a thorough discussion of Green's functions in curved spacetime (Section 4. The review concludes with a detailed derivation of each of the three equations of motion (Section 5.
Trapping Horizons as inner boundary conditions for black hole spacetimes
Jaramillo, J L; Cordero-Carrion, I; Ibáñez, J M
2007-01-01
We present a set of inner boundary conditions for the numerical construction of dynamical black hole space-times, when employing a 3+1 constrained evolution scheme and an excision technique. These inner boundary conditions are heuristically motivated by the dynamical trapping horizon framework and are enforced in an elliptic subsystem of the full Einstein equation. In the stationary limit they reduce to existing isolated horizon boundary conditions. A characteristic analysis completes the discussion of inner boundary conditions for the radiative modes.
Leptogenesis from loop effects in curved spacetime
McDonald, Jamie I
2015-01-01
We describe a new mechanism -- radiatively-induced gravitational leptogenesis -- for generating the matter-antimatter asymmetry of the Universe. We show how quantum loop effects in C and CP violating theories cause matter and antimatter to propagate differently in the presence of gravity, and prove this is forbidden in flat space by CPT and translation symmetry. This generates a curvature-dependent chemical potential for leptons, allowing a matter-antimatter asymmetry to be generated in thermal equilibrium in the early Universe. The time-dependent dynamics necessary for leptogenesis is provided by the interaction of the virtual self-energy cloud of the leptons with the expanding curved spacetime background, which violates the strong equivalence principle and allows a distinction between matter and antimatter. We show here how this mechanism is realised in a particular BSM theory, the see-saw model, where the quantum loops involve the heavy sterile neutrinos responsible for light neutrino masses. We demonstrat...
Non-Relativistic Spacetimes with Cosmological Constant
Aldrovandi, R.; Barbosa, A. L.; Crispino, L.C.B.; Pereira, J. G.
1998-01-01
Recent data on supernovae favor high values of the cosmological constant. Spacetimes with a cosmological constant have non-relativistic kinematics quite different from Galilean kinematics. De Sitter spacetimes, vacuum solutions of Einstein's equations with a cosmological constant, reduce in the non-relativistic limit to Newton-Hooke spacetimes, which are non-metric homogeneous spacetimes with non-vanishing curvature. The whole non-relativistic kinematics would then be modified, with possible ...
Numerical simulations of black-hole spacetimes
Chu, Tony
This thesis covers various aspects of the numerical simulation of black-hole spacetimes according to Einstein's general theory of relativity, using the Spectral Einstein Code developed by the Caltech-Cornell-CITA collaboration. The first topic is improvement of binary-black-hole initial data. One such issue is the construction of binary-black-hole initial data with nearly extremal spins that remain nearly constant during the initial relaxation in an evolution. Another concern is the inclusion of physically realistic tidal deformations of the black holes to reduce the high-frequency components of the spurious gravitational radiation content, and represents a first step in incorporating post-Newtonian results in constraint-satisfying initial data. The next topic is the evolution of black-hole binaries and the gravitational waves they emit. The first spectral simulation of two inspiralling black holes through merger and ringdown is presented, in which the black holes are nonspinning and have equal masses. This work is extended to perform the first spectral simulations of two inspiralling black holes with moderate spins and equal masses, including the merger and ringdown. Two configurations are considered, in which both spins are either anti-aligned or aligned with the orbital angular momentum. Highly accurate gravitational waveforms are computed for all these cases, and are used to calibrate waveforms in the effective-one-body model. The final topic is the behavior of quasilocal black-hole horizons in highly dynamical situations. Simulations of a rotating black hole that is distort ed by a pulse of ingoing gravitational radiation are performed. Multiple marginally outer trapped surfaces are seen to appear and annihilate with each other during the evolution, and the world tubes th ey trace out are all dynamical horizons. The dynamical horizon and angular momentum flux laws are evaluated in this context, and the dynamical horizons are contrasted with the event horizon
Topology and incompleteness for 2+1-dimensional cosmological spacetimes
Fajman, David
2016-12-01
We study the long-time behavior of the Einstein flow coupled to matter on 2-dimensional surfaces. We consider massless matter models such as collisionless matter composed of massless particles, massless scalar fields and radiation fluids and show that the maximal globally hyperbolic development of homogeneous and isotropic initial data on the 2-sphere is geodesically incomplete in both time directions, i.e. the spacetime recollapses. This behavior also holds for open sets of initial data. In particular, we construct classes of recollapsing 2+1-dimensional spacetimes with spherical spatial topology which provide evidence for a closed universe recollapse conjecture for massless matter models in 2+1 dimensions. Furthermore, we construct solutions with toroidal and higher genus topology for the massless matter fields, which in both cases are future complete. The spacetimes with toroidal topology are 2+1-dimensional analogies of the Einstein-de Sitter model. In addition, we point out a general relation between the energy-momentum tensor and the Kretschmann scalar in 2+1 dimensions and use it to infer strong cosmic censorship for all these models. In view of this relation, we also recall corresponding models containing massive particles, constructed in a previous work and determine the nature of their initial singularities. We conclude that the global structure of non-vacuum cosmological spacetimes in 2+1 dimensions is determined by the mass of particles and—in the homogeneous and isotropic setting studied here—verifies strong cosmic censorship.
Quantum fields in curved spacetime
Hollands, Stefan, E-mail: stefan.hollands@uni-leipzig.de [Universität Leipzig, Institut für Theoretische Physik, Brüderstrasse 16, D-04103 Leipzig (Germany); Wald, Robert M., E-mail: rmwa@uchicago.edu [Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL 60637 (United States)
2015-04-16
We review the theory of quantum fields propagating in an arbitrary, classical, globally hyperbolic spacetime. Our review emphasizes the conceptual issues arising in the formulation of the theory and presents known results in a mathematically precise way. Particular attention is paid to the distributional nature of quantum fields, to their local and covariant character, and to microlocal spectrum conditions satisfied by physically reasonable states. We review the Unruh and Hawking effects for free fields, as well as the behavior of free fields in deSitter spacetime and FLRW spacetimes with an exponential phase of expansion. We review how nonlinear observables of a free field, such as the stress–energy tensor, are defined, as well as time-ordered-products. The “renormalization ambiguities” involved in the definition of time-ordered products are fully characterized. Interacting fields are then perturbatively constructed. Our main focus is on the theory of a scalar field, but a brief discussion of gauge fields is included. We conclude with a brief discussion of a possible approach towards a nonperturbative formulation of quantum field theory in curved spacetime and some remarks on the formulation of quantum gravity.
Jing, Yindi
2014-01-01
Distributed Space-Time Coding (DSTC) is a cooperative relaying scheme that enables high reliability in wireless networks. This brief presents the basic concept of DSTC, its achievable performance, generalizations, code design, and differential use. Recent results on training design and channel estimation for DSTC and the performance of training-based DSTC are also discussed.
Observers in Spacetime and Nonlocality
Mashhoon, B
2012-01-01
Characteristics of observers in relativity theory are critically examined. For field measurements in Minkowski spacetime, the Bohr-Rosenfeld principle implies that the connection between actual (i.e., noninertial) and inertial observers must be nonlocal. Nonlocal electrodynamics of non-uniformly rotating observers is discussed and the consequences of this theory for the phenomenon of spin-rotation coupling are briefly explored.
Accelerating in de Sitter spacetimes
Cotaescu, Ion I
2014-01-01
We propose a definition of uniform accelerated frames in de Sitter spacetimes exploiting the Nachtmann group theoretical method of introducing coordinates on these manifolds. Requiring the transformation between the static frame and the accelerated one to depend continuously on acceleration in order to recover the well-known Rindler approach in the flat limit, we obtain a result with a reasonable physical meaning.
Spacetime compactification induced by scalars
Gell-Mann, M.; Zwiebach, B.
1984-07-05
It is shown that scalars of a nonlinear sigma model coupled to gravity can trigger spontaneous compactification of spacetime if the scalar manifold has an Einstein metric and the scalar self-coupling constant takes a specific value. The compactified space becomes isomorphic to the scalar manifold and the four-dimensional space has no cosmological term at the classical level.
On spacetime structure and electrodynamics
Ni, Wei-Tou
2016-01-01
Since almost all phenomena electrodynamics deal with have energy scales much lower than the Higgs mass energy and intermediate boson energy, electrodynamics of continuous media should be applicable and the constitutive relation of spacetime/vacuum should be local and linear. What is the key characteristic of the spacetime/vacuum? It is the Weak Equivalence Principle (WEP I) for photons/wave packets of light which states that the spacetime trajectory of light in a gravitational field depends only on its initial position and direction of propagation, and does not depend on its frequency (energy) and polarization, i.e. nonbirefringence of light propagation in spacetime/vacuum. With this principle it is proved by the author in 1981 in the weak field limit, and by Lammerzahl and Hehl in 2004 together with Favaro and Bergamin in 2011 without assuming the weak-field condition that the constitutive tensor must be of the core metric form with only two additional degrees of freedom - the pseudoscalar (Abelian axion or ...
Affine conformal vectors in space-time
Coley, A. A.; Tupper, B. O. J.
1992-05-01
All space-times admitting a proper affine conformal vector (ACV) are found. By using a theorem of Hall and da Costa, it is shown that such space-times either (i) admit a covariantly constant vector (timelike, spacelike, or null) and the ACV is the sum of a proper affine vector and a conformal Killing vector or (ii) the space-time is 2+2 decomposable, in which case it is shown that no ACV can exist (unless the space-time decomposes further). Furthermore, it is proved that all space-times admitting an ACV and a null covariantly constant vector (which are necessarily generalized pp-wave space-times) must have Ricci tensor of Segré type {2,(1,1)}. It follows that, among space-times admitting proper ACV, the Einstein static universe is the only perfect fluid space-time, there are no non-null Einstein-Maxwell space-times, and only the pp-wave space-times are representative of null Einstein-Maxwell solutions. Otherwise, the space-times can represent anisotropic fluids and viscous heat-conducting fluids, but only with restricted equations of state in each case.
Spacetime Meshing for Discontinuous Galerkin Methods
Thite, Shripad Vidyadhar
2008-01-01
Spacetime discontinuous Galerkin (SDG) finite element methods are used to solve such PDEs involving space and time variables arising from wave propagation phenomena in important applications in science and engineering. To support an accurate and efficient solution procedure using SDG methods and to exploit the flexibility of these methods, we give a meshing algorithm to construct an unstructured simplicial spacetime mesh over an arbitrary simplicial space domain. Our algorithm is the first spacetime meshing algorithm suitable for efficient solution of nonlinear phenomena in anisotropic media using novel discontinuous Galerkin finite element methods for implicit solutions directly in spacetime. Given a triangulated d-dimensional Euclidean space domain M (a simplicial complex) and initial conditions of the underlying hyperbolic spacetime PDE, we construct an unstructured simplicial mesh of the (d+1)-dimensional spacetime domain M x [0,infinity). Our algorithm uses a near-optimal number of spacetime elements, ea...
高长军; 沈有根
2002-01-01
We present the classical solution of Lagrange equations for the Reissner-Nordstrom black hole with a global monopole in the background of de Sitter space-time. Then we obtain the wavefunction of the space-time by solving the Wheeler-De Witt equation. De Broglie-Bohm interpretation applied to the wavefunction gives the quantum solution of the space-time. Finally, the quantum effect on Hawking radiation is studied.
Embedding Graphs in Lorentzian Spacetime
Clough, James R
2016-01-01
Geometric approaches to network analysis combine simply defined models with great descriptive power. In this work we provide a method for embedding directed acyclic graphs into Minkowski spacetime using Multidimensional scaling (MDS). First we generalise the classical MDS algorithm, defined only for metrics with a Euclidean signature, to manifolds of any metric signature. We then use this general method to develop an algorithm to be used on networks which have causal structure allowing them to be embedded in Lorentzian manifolds. The method is demonstrated by calculating embeddings for both causal sets and citation networks in Minkowski spacetime. We finally suggest a number of applications in citation analysis such as paper recommendation, identifying missing citations and fitting citation models to data using this geometric approach.
Energy conditions and spacetime singularities
Tipler, F.J.
1978-05-15
In this paper, a number of theorems are proven which collectively show that singularities will occur in spacetime under weaker energy conditions than the strong energy condition. In particular, the Penrose theorem, which uses only the weak energy condition but which applies only to open universes, is extended to all closed universes which have a Cauchy surface whose universal covering manifold is not a three-sphere. Furthermore, it is shown that the strong energy condition in the Hawking-Penrose theorem can be replaced by the weak energy condition and the assumption that the strong energy condition holds only on the average. In addition, it is demonstrated that if the Universe is closed, then the existence of singularities follows from the averaged strong energy condition alone. It is argued that any globally hyperbolic spacetime which satisfies the weak energy condition and which contains a black hole must be null geodesically incomplete.
Antigravity from a spacetime defect
Klinkhamer, F R
2013-01-01
A nonsingular localized static classical solution is constructed for standard Einstein gravity coupled to an SO(3)\\times SO(3) chiral model of scalars [Skyrme model]. The construction proceeds in three steps. First, an Ansatz is presented for a solution with nontrivial topology of the spacetime manifold. Second, an exact vacuum solution of the reduced field equations is obtained. Third, matter fields are included and a numerical solution is found. This numerical solution has a negative effective mass, meaning that the gravitational force on a distant point mass is repulsive. The origin of the negative effective mass must lie in the surgery needed to create the "defect" from Minkowski spacetime, but this process involves topology change and lies outside the realm of classical Einstein gravity.
Swimming versus swinging in spacetime
Guéron, E; Matsas, G E A; Gueron, Eduardo; Maia, Clovis A. S.; Matsas, George E. A.
2006-01-01
Wisdom has recently unveiled a new relativistic effect, called ``spacetime swimming'', where quasi-rigid free bodies in curved spacetimes can "speed up", "slow down" or "deviate" their falls by performing "local" cyclic shape deformations. We show here that for fast enough cycles this effect dominates over a non-relativistic related one, named here ``space swinging'', where the fall is altered through "nonlocal" cyclic deformations in Newtonian gravitational fields. We expect, therefore, to clarify the distinction between both effects leaving no room to controversy. Moreover, the leading contribution to the swimming effect predicted by Wisdom is enriched with a higher order term and the whole result is generalized to be applicable in cases where the tripod is in large red-shift regions.
Ray trajectories for Alcubierre spacetime
Anderson, Tom H; Lakhtakia, Akhlesh
2011-01-01
The Alcubierre spacetime was simulated by means of a Tamm medium which is asymptotically identical to vacuum and has constitutive parameters which are ontinuous functions of the spatial coordinates. Accordingly, the Tamm medium is amenable to physical realization as a nanostructured metamaterial. A comprehensive characterization of ray trajectories in the Tamm medium was undertaken, within the geometric-optics regime. Propagation directions corresponding to evanescent waves were identified: these occur in the region of the Tamm medium which corresponds to the warp bubble of the Alcubierre spacetime, especially for directions perpendicular to the velocity of the warp bubble at high speeds of that bubble. Ray trajectories are acutely sensitive to the magnitude and direction of the warp bubble's velocity, but rather less sensitive to the thickness of the transition zone between the warp bubble and its background. In particular, for rays which travel in the same direction as the warp bubble, the latter acts as a ...
Supersymmetric Spacetimes from Curved Superspace
Kuzenko, Sergei M
2015-01-01
We review the superspace technique to determine supersymmetric spacetimes in the framework of off-shell formulations for supergravity in diverse dimensions using the case of 3D N=2 supergravity theories as an illustrative example. This geometric formalism has several advantages over other approaches advocated in the last four years. Firstly, the infinitesimal isometry transformations of a given curved superspace form, by construction, a finite-dimensional Lie superalgebra, with its odd part corresponding to the rigid supersymmetry transformations. Secondly, the generalised Killing spinor equation, which must be obeyed by the supersymmetry parameters, is a consequence of the more fundamental superfield Killing equation. Thirdly, general rigid supersymmetric theories on a curved spacetime are readily constructed in superspace by making use of the known off-shell supergravity-matter couplings and restricting them to the background chosen. It is the superspace techniques which make it possible to generate arbitra...
Penrose Limits and Spacetime Singularities
Blau, Matthias; O'Loughlin, M; Papadopoulos, G; Blau, Matthias; Borunda, Monica; Loughlin, Martin O'; Papadopoulos, George
2003-01-01
We give a covariant characterisation of the Penrose plane wave limit: the plane wave profile matrix $A(u)$ is the restriction of the null geodesic deviation matrix (curvature tensor) of the original spacetime metric to the null geodesic, evaluated in a comoving frame. We also consider the Penrose limits of spacetime singularities and show that for a large class of black hole, cosmological and null singularities (of Szekeres-Iyers ``power-law type''), including those of the FRW and Schwarzschild metrics, the result is a singular homogeneous plane wave with profile $A(u)\\sim u^{-2}$, the scale invariance of the latter reflecting the power-law behaviour of the singularities.
From Horismos to Relativistic Spacetimes
Stoica, Ovidiu Cristinel
2015-01-01
A set endowed with a reflexive relation has surprisingly many features in common with the causal structure of a spacetime in General Relativity. If we identify this relation as the relation between lightlike separated events (the horismos relation), we can construct in a natural way the entire causal structure: causal and chronological relations, causal curves, and a topology. By imposing a simple additional condition, the structure gains a definite number of dimensions. This construction works both with continuous and discrete spacetimes. The dimensionality is obtained with ease also in the discrete case, in contrast with the causal set approach, which starts with a discrete set of events endowed with partial order relation representing the causal relation, but has severe difficulties in recovering the number of dimensions. Other simple conditions make it into a differentiable manifold with a conformal structure (the metric up to a scaling factor) just like in General Relativity. This structure provides a si...
Geometry of black hole spacetimes
Andersson, Lars; Blue, Pieter
2016-01-01
These notes, based on lectures given at the summer school on Asymptotic Analysis in General Relativity, collect material on the Einstein equations, the geometry of black hole spacetimes, and the analysis of fields on black hole backgrounds. The Kerr model of a rotating black hole in vacuum is expected to be unique and stable. The problem of proving these fundamental facts provides the background for the material presented in these notes. Among the many topics which are relevant for the uniqueness and stability problems are the theory of fields on black hole spacetimes, in particular for gravitational perturbations of the Kerr black hole, and more generally, the study of nonlinear field equations in the presence of trapping. The study of these questions requires tools from several different fields, including Lorentzian geometry, hyperbolic differential equations and spin geometry, which are all relevant to the black hole stability problem.
Multiscale spacetimes from first principles
Calcagni, Gianluca
2016-01-01
We formulate a theorem for the general profile of the Hausdorff and the spectral dimension of multiscale geometries, assuming a smooth and slow change of spacetime dimensionality at large scales. Agreement with various scenarios of quantum gravity is found. In particular, we derive uniquely the multiscale measure with log oscillations of theories of multifractional geometry. Predictivity of this class of models and falsifiability of their abundant phenomenology are thus established.
Dual geometries and spacetime singularities
Quirós, I
2000-01-01
The concept of geometrical duality is disscused in the context of Brans-Dicke theory and extended to general relativity. It is shown, in some generic cases, that spacetime singularities that arise in usual Riemannian general relativity, may be avoided in its dual representation: Weyl-like general relativity, thus providing a singularity-free picture of the World that is physicaly equivalent to the canonical general relativistic one.
Black Hole: The Interior Spacetime
Ong, Yen Chin
2016-01-01
The information loss paradox is often discussed from the perspective of the observers who stay outside of a black hole. However, the interior spacetime of a black hole can be rather nontrivial. We discuss the open problems regarding the volume of a black hole, and whether it plays any role in information storage. We also emphasize the importance of resolving the black hole singularity, if one were to resolve the information loss paradox.
Leptogenesis from loop effects in curved spacetime
McDonald, Jamie I.; Shore, Graham M.
2016-04-01
We describe a new mechanism — radiatively-induced gravitational leptogenesis — for generating the matter-antimatter asymmetry of the Universe. We show how quantum loop effects in C and CP violating theories cause matter and antimatter to propagate differently in the presence of gravity, and prove this is forbidden in flat space by CPT and translation symmetry. This generates a curvature-dependent chemical potential for leptons, allowing a matter-antimatter asymmetry to be generated in thermal equilibrium in the early Universe. The time-dependent dynamics necessary for leptogenesis is provided by the interaction of the virtual self-energy cloud of the leptons with the expanding curved spacetime background, which violates the strong equivalence principle and allows a distinction between matter and antimatter. We show here how this mechanism is realised in a particular BSM theory, the see-saw model, where the quantum loops involve the heavy sterile neutrinos responsible for light neutrino masses. We demonstrate by explicit computation of the relevant two-loop Feynman diagrams how the size of the radiative corrections relevant for leptogenesis becomes enhanced by increasing the mass hierarchy of the sterile neutrinos, and show how the induced lepton asymmetry may be sufficiently large to play an important rôle in determining the baryon-to-photon ratio of the Universe.
Leptogenesis from loop effects in curved spacetime
McDonald, Jamie I.; Shore, Graham M. [Department of Physics, Swansea University,Singleton Park, Swansea, SA2 8PP (United Kingdom)
2016-04-05
We describe a new mechanism — radiatively-induced gravitational leptogenesis — for generating the matter-antimatter asymmetry of the Universe. We show how quantum loop effects in C and CP violating theories cause matter and antimatter to propagate differently in the presence of gravity, and prove this is forbidden in flat space by CPT and translation symmetry. This generates a curvature-dependent chemical potential for leptons, allowing a matter-antimatter asymmetry to be generated in thermal equilibrium in the early Universe. The time-dependent dynamics necessary for leptogenesis is provided by the interaction of the virtual self-energy cloud of the leptons with the expanding curved spacetime background, which violates the strong equivalence principle and allows a distinction between matter and antimatter. We show here how this mechanism is realised in a particular BSM theory, the see-saw model, where the quantum loops involve the heavy sterile neutrinos responsible for light neutrino masses. We demonstrate by explicit computation of the relevant two-loop Feynman diagrams how the size of the radiative corrections relevant for leptogenesis becomes enhanced by increasing the mass hierarchy of the sterile neutrinos, and show how the induced lepton asymmetry may be sufficiently large to play an important rôle in determining the baryon-to-photon ratio of the Universe.
Intertial Frame Dragging in an Acoustic Analogue spacetime
Chakraborty, Chandrachur; Majumdar, Parthasarathi
2015-01-01
We report an incipient exploration of the Lense-Thirring precession effect in a rotating {\\it acoustic analogue black hole} spacetime. An exact formula is deduced for the precession frequency of a gyroscope due to inertial frame dragging, close to the ergosphere of a `Draining Bathtub' acoustic spacetime which has been studied extensively for acoustic Hawking radiation of phonons and also for `superresonance'. The formula is verified by embedding the two dimensional spatial (acoustic) geometry into a three dimensional one where the similarity with standard Lense-Thirring precession results within a strong gravity framework is well known. Prospects of experimental detection of this new `fixed-metric' effect in acoustic geometries, are briefly discussed.
Lorentz violations in multifractal spacetimes
Calcagni, Gianluca
2016-01-01
Using the recent observation of gravitational waves (GW) produced by a black-hole merger, we place a lower bound on the energy above which a multifractal spacetime would manifest an anomalous geometry and, in particular, violations of Lorentz invariance. In the so-called multifractional theory with $q$-derivatives, we show that the deformation of dispersion relations is much stronger than in generic quantum-gravity approaches (including loop quantum gravity) and, contrary to the latter, present observations on GWs can place very strong bounds on the characteristic scales at which spacetime deviates from standard Minkowski. The energy at which multifractal effects should become apparent is $E_*>10^{14}\\,\\text{GeV}$ (thus improving previous bounds by 12 orders of magnitude) when the exponents in the measure are fixed to their central value $1/2$. We also estimate, for the first time, the effect of logarithmic oscillations in the measure (corresponding to a discrete spacetime structure) and find that they do not...
Lorentz violations in multifractal spacetimes
Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, Madrid (Spain)
2017-05-15
Using the recent observation of gravitational waves (GW) produced by a black-hole merger, we place a lower bound on the energy above which a multifractal spacetime would display an anomalous geometry and, in particular, violations of Lorentz invariance. In the so-called multifractional theory with q-derivatives, we show that the deformation of dispersion relations is much stronger than in generic quantum-gravity approaches (including loop quantum gravity) and, contrary to the latter, present observations on GWs can place very strong bounds on the characteristic scales at which spacetime deviates from standard Minkowski. The energy at which multifractal effects should become apparent is E{sub *} > 10{sup 14} GeV (thus improving previous bounds by 12 orders of magnitude) when the exponents in the measure are fixed to their central value 1 / 2. We also estimate, for the first time, the effect of logarithmic oscillations in the measure (corresponding to a discrete spacetime structure) and find that they do not change much the bounds obtained in their absence, unless the amplitude of the oscillations is fine tuned. This feature, unavailable in known quantum-gravity scenarios, may help the theory to avoid being ruled out by gamma-ray burst (GRB) observations, for which E{sub *} > 10{sup 17} GeV or greater. (orig.)
Spacetime Singularities in Quantum Gravity
Minassian, Eric A.
2000-04-01
Recent advances in 2+1 dimensional quantum gravity have provided tools to study the effects of quantization of spacetime on black hole and big bang/big crunch type singularities. I investigate effects of quantization of spacetime on singularities of the 2+1 dimensional BTZ black hole and the 2+1 dimensional torus universe. Hosoya has considered the BTZ black hole, and using a "quantum generalized affine parameter" (QGAP), has shown that, for some specific paths, quantum effects "smear" the singularities. Using gaussian wave functions as generic wave functions, I found that, for both BTZ black hole and the torus universe, there are families of paths that still reach the singularities with a finite QGAP, suggesting that singularities persist in quantum gravity. More realistic calculations, using modular invariant wave functions of Carlip and Nelson for the torus universe, offer further support for this conclusion. Currently work is in progress to study more realistic quantum gravity effects for BTZ black holes and other spacetime models.
Ronald E. Meyers
2015-03-01
Full Text Available We report on an experimental and theoretical investigation of quantum imaging where the images are stored in both space and time. Ghost images of remote objects are produced with either one or two beams of chaotic laser light generated by a rotating ground glass and two sensors measuring the reference field and bucket field at different space-time points. We further observe that the ghost images translate depending on the time delay between the sensor measurements. The ghost imaging experiments are performed both with and without turbulence. A discussion of the physics of the space-time imaging is presented in terms of quantum nonlocal two-photon analysis to support the experimental results. The theoretical model includes certain phase factors of the rotating ground glass. These experiments demonstrated a means to investigate the time and space aspects of ghost imaging and showed that ghost imaging contains more information per measured photon than was previously recognized where multiple ghost images are stored within the same ghost imaging data sets. This suggests new pathways to explore quantum information stored not only in multi-photon coincidence information but also in time delayed multi-photon interference. The research is applicable to making enhanced space-time quantum images and videos of moving objects where the images are stored in both space and time.
Lorentz violations in multifractal spacetimes
Calcagni, Gianluca
2017-05-01
Using the recent observation of gravitational waves (GW) produced by a black-hole merger, we place a lower bound on the energy above which a multifractal spacetime would display an anomalous geometry and, in particular, violations of Lorentz invariance. In the so-called multifractional theory with q-derivatives, we show that the deformation of dispersion relations is much stronger than in generic quantum-gravity approaches (including loop quantum gravity) and, contrary to the latter, present observations on GWs can place very strong bounds on the characteristic scales at which spacetime deviates from standard Minkowski. The energy at which multifractal effects should become apparent is E_{*}>10^{14} {GeV} (thus improving previous bounds by 12 orders of magnitude) when the exponents in the measure are fixed to their central value 1 / 2. We also estimate, for the first time, the effect of logarithmic oscillations in the measure (corresponding to a discrete spacetime structure) and find that they do not change much the bounds obtained in their absence, unless the amplitude of the oscillations is fine tuned. This feature, unavailable in known quantum-gravity scenarios, may help the theory to avoid being ruled out by gamma-ray burst (GRB) observations, for which E_{*}> 10^{17} {GeV} or greater.
Killing tensors in pp-wave spacetimes
Keane, Aidan J [87 Carlton Place, Glasgow G5 9TD, Scotland (United Kingdom); Tupper, Brian O J, E-mail: aidan@countingthoughts.co, E-mail: bt32@rogers.co [Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3 (Canada)
2010-12-21
The formal solution of the second-order Killing tensor equations for the general pp-wave spacetime is given. The Killing tensor equations are integrated fully for some specific pp-wave spacetimes. In particular, the complete solution is given for the conformally flat plane wave spacetimes and we find that irreducible Killing tensors arise for specific classes. The maximum number of independent irreducible Killing tensors admitted by a conformally flat plane wave spacetime is shown to be six. It is shown that every pp-wave spacetime that admits an homothety will admit a Killing tensor of Koutras type and, with the exception of the singular scale-invariant plane wave spacetimes, this Killing tensor is irreducible.
Toward a Holographic Theory for General Spacetimes
Nomura, Yasunori; Sanches, Fabio; Weinberg, Sean J
2016-01-01
We study a holographic theory of general spacetimes that does not rely on the existence of asymptotic regions. This theory is to be formulated in a holographic space. When a semiclassical description is applicable, the holographic space is assumed to be a holographic screen: a codimension-1 surface that is capable of encoding states of the gravitational spacetime. Our analysis is guided by conjectured relationships between gravitational spacetime and quantum entanglement in the holographic description. To understand basic features of this picture, we catalog predictions for the holographic entanglement structure of cosmological spacetimes. We find that qualitative features of holographic entanglement entropies for such spacetimes differ from those in AdS/CFT but that the former reduce to the latter in the appropriate limit. The Hilbert space of the theory is analyzed, and two plausible structures are found: a direct sum and "spacetime equals entanglement" structure. The former preserves a naive relationship b...
A macroscopic challenge for quantum spacetime
Amelino-Camelia, Giovanni
2013-01-01
Over the last decade a growing number of quantum-gravity researchers has been looking for opportunities for the first ever experimental evidence of a Planck-length quantum property of spacetime. These studies are usually based on the analysis of some candidate indirect implications of spacetime quantization, such as a possible curvature of momentum space. Some recent proposals have raised hope that we might also gain direct experimental access to quantum properties of spacetime, by finding evidence of limitations to the measurability of the center-of-mass coordinates of some macroscopic bodies. However I here observe that the arguments that originally lead to speculating about spacetime quantization do not apply to the localization of the center of mass of a macroscopic body. And I also analyze some popular formalizations of the notion of quantum spacetime, finding that when the quantization of spacetime is Planckian for the constituent particles then for the composite macroscopic body the quantization of spa...
Noncommutative Spacetime Symmetries from Covariant Quantum Mechanics
Alessandro Moia
2017-01-01
Full Text Available In the last decades, noncommutative spacetimes and their deformed relativistic symmetries have usually been studied in the context of field theory, replacing the ordinary Minkowski background with an algebra of noncommutative coordinates. However, spacetime noncommutativity can also be introduced into single-particle covariant quantum mechanics, replacing the commuting operators representing the particle’s spacetime coordinates with noncommuting ones. In this paper, we provide a full characterization of a wide class of physically sensible single-particle noncommutative spacetime models and the associated deformed relativistic symmetries. In particular, we prove that they can all be obtained from the standard Minkowski model and the usual Poincaré transformations via a suitable change of variables. Contrary to previous studies, we find that spacetime noncommutativity does not affect the dispersion relation of a relativistic quantum particle, but only the transformation properties of its spacetime coordinates under translations and Lorentz transformations.
Geodesics in the static Mallett spacetime
Olum, Ken D
2010-01-01
Mallett has exhibited a cylindrically symmetric spacetime containing closed timelike curves produced by a light beam circulating around a line singularity. I analyze the static version of this spacetime obtained by setting the intensity of the light to zero. Some null geodesics can escape to infinity, but all timelike geodesics in this spacetime originate and terminate at the singularity. Freely falling matter originally at rest quickly attains relativistic velocity inward and is destroyed at the singularity.
Theory and Phenomenology of Spacetime Defects
Hossenfelder, Sabine
2014-01-01
Whether or not space-time is fundamentally discrete is of central importance for the development of the theory of quantum gravity. If the fundamental description of space-time is discrete, typically represented in terms of a graph or network, then the apparent smoothness of geometry on large scales should be imperfect -- it should have defects. Here, we review a model for space-time defects and summarize the constraints on the prevalence of these defects that can be derived from observation.
Quantum field theory on locally noncommutative spacetimes
Lechner, Gandalf [Univ. Leipzig (Germany). Inst. fuer Theoretische Physik; Waldmann, Stefan [Leuven Univ. (Belgium)
2012-07-01
A class of spacetimes which are noncommutative only in a prescribed region is presented. These spacetimes are obtained by a generalization of Rieffel's deformation procedure to deformations of locally convex algebras and modules by smooth polynomially bounded R{sup n}-actions with compact support. Extending previous results of Bahns and Waldmann, it is shown how to perform such deformations in a strict sense. Some results on quantum fields propagating on locally noncommutative spacetimes are also given.
Geometrodynamics: The Nonlinear Dynamics of Curved Spacetime
Scheel, Mark A.; Thorne, Kip S.
2017-01-01
We review discoveries in the nonlinear dynamics of curved spacetime, largely made possible by numerical solutions of Einstein's equations. We discuss critical phenomena and self-similarity in gravitational collapse, the behavior of spacetime curvature near singularities, the instability of black strings in 5 spacetime dimensions, and the collision of four-dimensional black holes. We also discuss the prospects for further discoveries in geometrodynamics via observation of gravitational waves.
Experimental observation of Minkowski spacetime melting
Smolyaninov, Igor I
2015-01-01
Cobalt nanoparticle-based ferrofluid in the presence of an external magnetic field forms a self-assembled hyperbolic metamaterial, which may be described as an effective 3D Minkowski spacetime for extraordinary photons. If the magnetic field is not strong enough, this effective Minkowski spacetime gradually melts under the influence of thermal fluctuations. On the other hand, it may restore itself if the magnetic field is increased back to its original value. Here we present direct microscopic visualization of such a Minkowski spacetime melting/crystallization, which is somewhat similar to hypothesized formation of the Minkowski spacetime in loop quantum cosmology.
Hyperbolic statics in space-time
Pavlov, Dmitry
2015-01-01
Based on the concept of material event as an elementary material source that is concentrated on metric sphere of zero radius --- light-cone of Minkowski space-time, we deduce the analog of Coulomb's law for hyperbolic space-time field universally acting between the events of space-time. Collective field that enables interaction of world lines of a pair of particles at rest contains a standard 3-dimensional Coulomb's part and logarithmic addendum. We've found that the Coulomb's part depends on a fine balance between causal and geometric space-time characteristics (the two regularizations concordance).
Quantum singularity of Levi-Civita spacetimes
Konkowski, D A; Wieland, C
2004-01-01
Quantum singularities in general relativistic spacetimes are determined by the behavior of quantum test particles. A static spacetime is quantum mechanically singular if the spatial portion of the wave operator is not essentially self-adjoint. Here Weyl's limit point-limit circle criterion is used to determine whether a wave operator is essentially self-adjoint. This test is then applied to scalar wave packets in Levi-Civita spacetimes to help elucidate the physical properties of the spacetimes in terms of their metric parameters.
Simulations of black holes in compactified spacetimes
Zilhao, Miguel; Herdeiro, Carlos [Centro de Fisica do Porto, Departamento de Fisica e Astronomia, Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto (Portugal); Cardoso, Vitor; Nerozzi, Andrea; Sperhake, Ulrich; Witek, Helvi [Centro Multidisciplinar de Astrofisica, Deptartamento de Fisica, Instituto Superior Tecnico, Universidade Tecnica de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa (Portugal); Gualtieri, Leonardo, E-mail: mzilhao@fc.up.pt [Dipartimento di Fisica, Universita di Roma ' Sapienza' and Sezione INFN Roma1, P.A. Moro 5, 00185, Roma (Italy)
2011-09-22
From the gauge/gravity duality to braneworld scenarios, black holes in compactified spacetimes play an important role in fundamental physics. Our current understanding of black hole solutions and their dynamics in such spacetimes is rather poor because analytical tools are capable of handling a limited class of idealized scenarios, only. Breakthroughs in numerical relativity in recent years, however, have opened up the study of such spacetimes to a computational treatment which facilitates accurate studies of a wider class of configurations. We here report on recent efforts of our group to perform numerical simulations of black holes in cylindrical spacetimes.
Quantum Estimation of Parameters of Classical Spacetimes
Downes, T G; Knill, E; Milburn, G J; Caves, C M
2016-01-01
We describe a quantum limit to measurement of classical spacetimes. Specifically, we formulate a quantum Cramer-Rao lower bound for estimating the single parameter in any one-parameter family of spacetime metrics. We employ the locally covariant formulation of quantum field theory in curved spacetime, which allows for a manifestly background-independent derivation. The result is an uncertainty relation that applies to all globally hyperbolic spacetimes. Among other examples, we apply our method to detection of gravitational waves using the electromagnetic field as a probe, as in laser-interferometric gravitational-wave detectors. Other applications are discussed, from terrestrial gravimetry to cosmology.
Predictions of noncommutative space-time
Viet, Nguyen Ai
1994-01-01
An unified structure of noncommutative space-time for both gravity and particle physics is presented. This gives possibilities of testing the idea of noncommutative space-time at the currently available energy scale. There are several arguments indicating that noncommutative space-time is visible already at the electroweak scale. This noncommutative space-time predicts the top quark mass m_t \\sim 172 GeV, the Higgs mass M_H \\sim 241 GeV and the existence of a vector meson and a scalar, which ...
Generalised hyperbolicity in conical space-times
Vickers, J A
2000-01-01
Solutions of the wave equation in a space-time containing a thin cosmic string are examined in the context of non-linear generalised functions. Existence and uniqueness of solutions to the wave equation in the Colombeau algebra G is established for a conical space-time and this solution is shown to be associated to a distributional solution. A concept of generalised hyperbolicity, based on test fields, can be defined for such singular space-times and it is shown that a conical space-time is G-hyperbolic.
Scalar Resonances in Axially Symmetric Spacetimes
Ranea-Sandoval, Ignacio F
2015-01-01
We study properties of resonant solutions to the scalar wave equation in several axially symmetric spacetimes. We prove that non-axial resonant modes do not exist neither in the Lanczos dust cylinder, the $(2+1)$ extreme BTZ spacetime nor in a class of simple rotating wormhole solutions. Moreover, we find unstable solutions to the wave equation in the Lanczos dust cylinder and in the $r^2 <0$ region of the extreme $(2+1)$ BTZ spacetime, two solutions that possess closed timelike curves. Similarities with previous results obtained for the Kerr spacetime are explored.
What is the spacetime of {\\em physically realizable} spherical collapse?
Wagh, S M; Govinder, K S; Wagh, Sanjay M.; Saraykar, Ravindra V.; Govinder, Keshlan S.
2002-01-01
We argue that a particular spacetime, a spherically symmetric spacetime with hyper-surface orthogonal, radial, homothetic Killing vector, is a physically meaningful spacetime that describes the problem of spherical gravitational collapse in its full "physical" generality.
On spacetime structure and electrodynamics
Ni, Wei-Tou
2016-10-01
Electrodynamics is the most tested fundamental physical theory. Relativity arose from the completion of Maxwell-Lorentz electrodynamics. Introducing the metric gij as gravitational potential in 1913, versed in general (coordinate-)covariant formalism in 1914 and shortly after the completion of general relativity, Einstein put the Maxwell equations in general covariant form with only the constitutive relation between the excitation and the field dependent on and connected by the metric in 1916. Further clarification and developments by Weyl in 1918, Murnaghan in 1921, Kottler in 1922 and Cartan in 1923 together with the corresponding developments in electrodynamics of continuous media by Bateman in 1910, Tamm in 1924, Laue in 1952 and Post in 1962 established the premetric formalism of electrodynamics. Since almost all phenomena electrodynamics deal with have energy scales much lower than the Higgs mass energy and intermediate boson energy, electrodynamics of continuous media should be applicable and the constitutive relation of spacetime/vacuum should be local and linear. What is the key characteristic of the spacetime/vacuum? It is the Weak Equivalence Principle I (WEP I) for photons/wave packets of light which states that the spacetime trajectory of light in a gravitational field depends only on its initial position and direction of propagation, and does not depend on its frequency (energy) and polarization, i.e. nonbirefringence of light propagation in spacetime/vacuum. With this principle it is proved by the author in 1981 in the weak field limit, and by Lammerzahl and Hehl in 2004 together with Favaro and Bergamin in 2011 without assuming the weak-field condition that the constitutive tensor must be of the core metric form with only two additional degrees of freedom — the pseudoscalar (Abelian axion or EM axion) degree of freedom and the scalar (dilaton) degree of freedom (i.e. metric with axion and dilaton). In this paper, we review this connection and the
Unstable Fields in Kerr Spacetimes
Dotti, Gustavo; Ranea-Sandoval, Ignacio F
2011-01-01
We present a generalization of previous results regarding the stability under gravitational perturbations of nakedly singular super extreme Kerr spacetime and Kerr black hole interior beyond the Cauchy horizon. To do so we study solutions to the radial and angular Teukolsky's equations with different spin weights, particulary $s=\\pm 1$ representing electromagnetic perturbations, $s=\\pm 1/2$ representing a perturbation by a Dirac field and $s=0$ representing perturbations by a scalar field. By analizing the properties of radial and angular eigenvalues we prove the existence of an infinite family of unstable modes.
Chiral Anomaly in Contorted Spacetimes
Mielke, E W
1999-01-01
The Dirac equation in Riemann-Cartan spacetimes with torsion is reconsidered. As is well-known, only the axial covector torsion $A$, a one-form, couples to massive Dirac fields. Using diagrammatic techniques, we show that besides the familiar Riemannian term only the Pontrjagin type four-form $dA\\wedge dA$ does arise additionally in the chiral anomaly, but not the Nieh-Yan term $d ^* A$, as has been claimed recently. Implications for cosmic strings in Einstein-Cartan theory as well as for Ashtekar's canonical approach to quantum gravity are discussed.
Time Evolution in Dynamical Spacetimes
Tiemblo, A
1996-01-01
We present a gauge--theoretical derivation of the notion of time, suitable to describe the Hamiltonian time evolution of gravitational systems. It is based on a nonlinear coset realization of the Poincaré group, implying the time component of the coframe to be invariant, and thus to represent a metric time. The unitary gauge fixing of the boosts gives rise to the foliation of spacetime along the time direction. The three supressed degrees of freedom correspond to Goldstone--like fields, whereas the remaining time component is a Higgs--like boson.
Saw, Vee-Liem
2016-01-01
We derive the asymptotic solutions for vacuum spacetimes with non-zero cosmological constant $\\Lambda$, using the Newman-Penrose formalism. Our approach is based exclusively on the physical spacetime, i.e. no reference of conformal rescaling nor conformal spacetime is made, at least not explicitly. By investigating the Schwarzschild-de Sitter spacetime in spherical coordinates, we subsequently stipulate the fall-offs of the null tetrad and spin coefficients for asymptotically de Sitter spacetimes such that the terms which would give rise to the Bondi mass-loss due to energy carried by gravitational radiation (i.e. involving $\\sigma^o$) must be non-zero. After solving the vacuum Newman-Penrose equations asymptotically, we obtain the Bondi mass-loss formula by integrating the Bianchi identity involving $D'\\Psi_2$ over a compact 2-surface on $\\mathcal{I}$. Whilst our original intention was to study asymptotically de Sitter spacetimes, the use of spherical coordinates implies that this readily applies for $\\Lambd...
The motion of point particles in curved spacetime
Poisson, Eric; Vega, Ian
2011-01-01
This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The field's action on the particle is difficult to calculate because of its singular nature: the field diverges at the position of the particle. But it is possible to isolate the field's singular part and show that it exerts no force on the particle. What remains after subtraction is a smooth field that is fully responsible for the self-force. The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime are developed here from scratch. The review...
Spherically symmetric brane spacetime with bulk f(R) gravity
Chakraborty, Sumanta [IUCAA, Ganeshkhind, Pune University Campus, Post Bag 4, Pune (India); SenGupta, Soumitra [Indian Association for the Cultivation of Science, Department of Theoretical Physics, Kolkata (India)
2015-01-01
Introducing f(R) term in the five-dimensional bulk action we derive effective Einstein's equation on the brane using Gauss-Codazzi equation. This effective equation is then solved for different conditions on dark radiation and dark pressure to obtain various spherically symmetric solutions. Some of these static spherically symmetric solutions correspond to black hole solutions, with parameters induced from the bulk. Specially, the dark pressure and dark radiation terms (electric part of Weyl curvature) affect the brane spherically symmetric solutions significantly. We have solved for one parameter group of conformal motions where the dark radiation and dark pressure terms are exactly obtained exploiting the corresponding Lie symmetry. Various thermodynamic features of these spherically symmetric space-times are studied, showing existence of second order phase transition. This phenomenon has its origin in the higher curvature term with f(R) gravity in the bulk. (orig.)
Quantum singularities in static and conformally static space-times
Konkowski, D A; 10.1142/S0217751X11054334
2011-01-01
The definition of quantum singularity is extended from static space-times to conformally static space-times. After the usual definitions of classical and quantum singularities are reviewed, examples of quantum singularities in static space-times are given. These include asymptotically power-law space-times, space-times with diverging higher-order differential invariants, and a space-time with a 2-sphere singularity. The theory behind quantum singularities in conformally static space-times is followed by an example, a Friedmann-Robertson-Walker space-time with cosmic string. The paper concludes by discussing areas of future research.
Quantum Field Theory in de Sitter spacetime
So, Ashaq Hussain; Sibuea, Marlina Rosalinda; Akhoon, Shabir Ahmad; Khanday, Bilal Nisar; Majeed, Sajad Ul; Rather, Asloob Ahmad; Nahvi, Ishaq
2013-01-01
In this paper we will analyse quantum ?eld theory on de Sitter space- time. We will ?rst analyse a general scalar and vector ?eld theory on de Sitter spacetime. This is done by ?rst calculating these propagators on four-Sphere and then analytically continuing it to de Sitter spacetime.
Hamilton-Jacobi renormalization for Lifshitz spacetime
Baggio, M.; de Boer, J.; Holsheimer, K.
2012-01-01
Just like AdS spacetimes, Lifshitz spacetimes require counterterms in order to make the on-shell value of the bulk action finite. We study these counterterms using the Hamilton-Jacobi method. Rather than imposing boundary conditions from the start, we will derive suitable boundary conditions by
An analytic regularisation scheme on curved spacetimes with applications to cosmological spacetimes
Géré, Antoine; Pinamonti, Nicola
2015-01-01
We develop a renormalisation scheme for time--ordered products in interacting field theories on curved spacetimes which consists of an analytic regularisation of Feynman amplitudes and a minimal subtraction of the resulting pole parts. This scheme is directly applicable to spacetimes with Lorentzian signature, manifestly generally covariant, invariant under any spacetime isometries present and constructed to all orders in perturbation theory. Moreover, the scheme captures correctly the non--geometric state--dependent contribution of Feynman amplitudes and it is well--suited for practical computations. To illustrate this last point, we compute explicit examples on a generic curved spacetime, and demonstrate how momentum space computations in cosmological spacetimes can be performed in our scheme. In this work, we discuss only scalar fields in four spacetime dimensions, but we argue that the renormalisation scheme can be directly generalised to other spacetime dimensions and field theories with higher spin, as ...
Geodesic congruences in warped spacetimes
Ghosh, Suman; Kar, Sayan
2010-01-01
In this article, we explore the kinematics of timelike geodesic congruences in warped five dimensional bulk spacetimes, with and without thick or thin branes. We begin our investigations with the simplest case, namely geodesic flows in the Randall--Sundrum AdS (Anti de Sitter) geometry without and with branes. Analytical expressions for the expansion scalar are obtained and the effect of including one or more thin branes (i.e. a background which is a slice of AdS spacetime) on its evolution, is pointed out. Subsequently, we move on to studying such congruences in more general warped bulk geometries with a cosmological thick brane and a time-dependent extra dimensional scale. Using the analytical expressions for the velocity field components, we interpret the expansion, shear and rotation (ESR) along the flows. The evolution of a cross-sectional area orthogonal to the congruence, as seen from a local observer's point of view, is also shown graphically. Finally, the Raychaudhuri and geodesic equations in the ba...
Cosmic Censorship for Gowdy Spacetimes.
Ringström, Hans
2010-01-01
Due to the complexity of Einstein's equations, it is often natural to study a question of interest in the framework of a restricted class of solutions. One way to impose a restriction is to consider solutions satisfying a given symmetry condition. There are many possible choices, but the present article is concerned with one particular choice, which we shall refer to as Gowdy symmetry. We begin by explaining the origin and meaning of this symmetry type, which has been used as a simplifying assumption in various contexts, some of which we shall mention. Nevertheless, the subject of interest here is strong cosmic censorship. Consequently, after having described what the Gowdy class of spacetimes is, we describe, as seen from the perspective of a mathematician, what is meant by strong cosmic censorship. The existing results on cosmic censorship are based on a detailed analysis of the asymptotic behavior of solutions. This analysis is in part motivated by conjectures, such as the BKL conjecture, which we shall therefore briefly describe. However, the emphasis of the article is on the mathematical analysis of the asymptotics, due to its central importance in the proof and in the hope that it might be of relevance more generally. The article ends with a description of the results that have been obtained concerning strong cosmic censorship in the class of Gowdy spacetimes.
Dark Energy and Spacetime Symmetry
Irina Dymnikova
2017-03-01
Full Text Available The Petrov classification of stress-energy tensors provides a model-independent definition of a vacuum by the algebraic structure of its stress-energy tensor and implies the existence of vacua whose symmetry is reduced as compared with the maximally symmetric de Sitter vacuum associated with the Einstein cosmological term. This allows to describe a vacuum in general setting by dynamical vacuum dark fluid, presented by a variable cosmological term with the reduced symmetry which makes vacuum fluid essentially anisotropic and allows it to be evolving and clustering. The relevant solutions to the Einstein equations describe regular cosmological models with time-evolving and spatially inhomogeneous vacuum dark energy, and compact vacuum objects generically related to a dark energy: regular black holes, their remnants and self-gravitating vacuum solitons with de Sitter vacuum interiors—which can be responsible for observational effects typically related to a dark matter. The mass of objects with de Sitter interior is generically related to vacuum dark energy and to breaking of space-time symmetry. In the cosmological context spacetime symmetry provides a mechanism for relaxing cosmological constant to a needed non-zero value.
The Space-Time CE/SE Method for Solving Maxwell's Equations in Time-Domain
Wang, X. Y.; Chen, C. L.; Liu, Yen
2002-01-01
An innovative finite-volume-type numerical method named as the space-time conservation element and solution element (CE/SE) method is applied to solve time-dependent Maxwell's equations in this paper. Test problems of electromagnetics scattering and antenna radiation are solved for validations. Numerical results are presented and compared with the analytical solutions, showing very good agreements.
Wave Propagation in Stochastic Spacetimes Localization, Amplification and Particle Creation
Hu, B L
1998-01-01
Here we study novel effects associated with electromagnetic wave propagation in a Robertson-Walker universe and the Schwarzschild spacetime with a small amount of metric stochasticity. We find that localization of electromagnetic waves occurs in a Robertson-Walker universe with time-independent metric stochasticity, while time-dependent metric stochasticity induces exponential instability in the particle production rate. For the Schwarzschild metric, time-independent randomness can decrease the total luminosity of Hawking radiation due to multiple scattering of waves outside the black hole and gives rise to event horizon fluctuations and thus fluctuations in the Hawking temperature.
Separable geodesic action slicing in stationary spacetimes
Bini, Donato; Jantzen, Robert T
2014-01-01
A simple observation about the action for geodesics in a stationary spacetime with separable geodesic equations leads to a natural class of slicings of that spacetime whose orthogonal geodesic trajectories represent freely falling observers. The time coordinate function can then be taken to be the observer proper time, leading to a unit lapse function. This explains some of the properties of the original Painlev\\'e-Gullstrand coordinates on the Schwarzschild spacetime and their generalization to the Kerr-Newman family of spacetimes, reproducible also locally for the G\\"odel spacetime. For the static spherically symmetric case the slicing can be chosen to be intrinsically flat with spherically symmetric geodesic observers, leaving all the gravitational field information in the shift vector field.
Minkowski Spacetime A Hundred Years Later
Petkov, Vesselin
2009-01-01
This volume is dedicated to the one hundredth anniversary of the publication of Hermann Minkowski's paper "Space and Time" in 1909. His work on the spacetime representation of special relativity had a huge impact on the twentieth century physics to the extent that modern physics would be impossible without the notion of spacetime. While there is consensus on the mathematical significance of spacetime in theoretical physics, for a hundred years there has been no consensus on the nature of spacetime itself. We owe Minkowski a clear answer to the question of the nature of spacetime -- whether it is only a mathematical space or represents a real four-dimensional world. A century after its publication the original Minkowski paper still represents an enrichment to the physicists, especially the relativists, who read it with the intent to fully investigate the depth of Minkowski's ideas on space and time and the physical meaning of special relativity. The volume begins with an excellent retranslation of Minkowski's ...
Evolving spacetimes with purely radial tension
B. Nasre Esfahani
2000-12-01
Full Text Available In this study time-dependent and spherically symmetric solutions of the Einstein field equations in an anisotropic background with a purely radial tension are presented. There exist three classes of solutions,1 An open spacetime with a wormhole at its center. 2 A conical spacetime. 3 A closed spacetime. These inhomogeneous solutions are reduced to FRW spacetimes in matter-dominated era, asymptotically. Therefore, they can be used to describe local inhomogeneities that are not considered in the standard model. For the wormhole solution. it is explicity shown that the considered matter is non-exotic, that is, it does not violate the energy conditions. Also, static solutions are studied. There is only one static solution,a conical spacetime. In this case, the matter satisfies the energy condition critically.
Partially massless graviton on beyond Einstein spacetimes
Bernard, Laura; Deffayet, Cédric; Hinterbichler, Kurt; von Strauss, Mikael
2017-06-01
We show that a partially massless graviton can propagate on a large set of spacetimes which are not Einstein spacetimes. Starting from a recently constructed theory for a massive graviton that propagates the correct number of degrees of freedom on an arbitrary spacetime, we first give the full explicit form of the scalar constraint responsible for the absence of a sixth degree of freedom. We then spell out generic conditions for the constraint to be identically satisfied, so that there is a scalar gauge symmetry which makes the graviton partially massless. These simplify if one assumes that spacetime is Ricci symmetric. Under this assumption, we find explicit non-Einstein spacetimes (some, but not all, with vanishing Bach tensors) allowing for the propagation of a partially massless graviton. These include in particular the Einstein static Universe.
Traversable acausal retrograde domains in spacetime
Tippett, Benjamin K.; Tsang, David
2017-05-01
In this paper we present geometry which has been designed to fit a layperson’s description of a ‘time machine’. It is a box which allows those within it to travel backwards and forwards through time and space, as interpreted by an external observer. Timelike observers travel within the interior of a ‘bubble’ of geometry which moves along a circular, acausal trajectory through spacetime. If certain timelike observers inside the bubble maintain a persistent acceleration, their worldlines will close. Our analysis includes a description of the causal structure of our spacetime, as well as a discussion of its physicality. The inclusion of such a bubble in a spacetime will render the background spacetime non-orientable, generating additional consistency constraints for formulations of the initial value problem. The spacetime geometry is geodesically incomplete, contains naked singularities, and requires exotic matter.
Shi, Shuai; Zhou, Zhi-Yuan; Li, Yan; Zhang, Wei; Shi, Bao-Sen; Guo, Guang-Can
2016-01-01
Light with phase front carrying an orbital angular momentum (OAM) is useful in many fields, such as optical tweezers, astronomy. In optical communication, light encoded information in its OAM degrees of freedom enables networks to carry significantly more information and increase their capacity significantly. However, light with OAM has a difficulty in propagating in commercial optical fibers, while light in Gaussian mode encoded with time-bin is most suitable for transmission in fiber. Therefore it is crucially important to build up a bridge for interfacing lights with OAM and time-bin. Here, we report the realization of a photonic space-time transcoder, by which light with an arbitrary OAM superposition is experimentally converted into a time-bin Gaussian pulse and vice versa in principle. Furthermore, we clearly demonstrate that the coherence is conserved very well and there is no crosstalk between orthogonal modes. Such a photonic device is simple and theoretically can be built up in a scalable architectu...
Newtonian gravity on quantum spacetime
Majid Shahn
2014-04-01
Full Text Available The bicrossproduct model λ-Minkowski (or ‘κ-Minkowski’ quantum space-time has an anomaly for the action of the Poincaré quantum group which was resolved by an extra cotangent direction θ’ not visible classically. We show that gauging a coefficient of θ′ introduces gravity into the model. We solve and analyse the model nonrelativisticaly in a 1/r potential, finding an induced constant term in the effective potential energy and a weakening and separation of the effective gravitational and inertial masses as the test particle Klein-Gordon mass increases. The present work is intended as a proof of concept but the approach could be relevant to an understanding of dark energy and possibly to macroscopic quantum systems.
The Motion of Point Particles in Curved Spacetime
Poisson, Eric; Pound, Adam; Vega, Ian
2011-09-01
This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The self-force contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. The work done by the self-force matches the energy radiated away by the particle. The field's action on the particle is difficult to calculate because of its singular nature: the field diverges at the position of the particle. But it is possible to isolate the field's singular part and show that it exerts no force on the particle — its only effect is to contribute to the particle's inertia. What remains after subtraction is a regular field that is fully responsible for the self-force. Because this field satisfies a homogeneous wave equation, it can be thought of as a free field that interacts with the particle; it is this interaction that gives rise to the self-force. The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime are developed here from scratch. The review begins with a discussion of the basic theory of bitensors (Part I). It then applies the theory to the construction of convenient coordinate systems to chart a neighbourhood of the particle's word line (Part II). It continues with a thorough discussion of Green's functions in curved spacetime (Part III). The review presents a detailed derivation of each of the three equations of motion (Part IV). Because the notion of a point mass is problematic in general relativity, the review concludes (Part V) with an
The Motion of Point Particles in Curved Spacetime.
Poisson, Eric; Pound, Adam; Vega, Ian
2011-01-01
This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The self-force contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. The work done by the self-force matches the energy radiated away by the particle. The field's action on the particle is difficult to calculate because of its singular nature: the field diverges at the position of the particle. But it is possible to isolate the field's singular part and show that it exerts no force on the particle - its only effect is to contribute to the particle's inertia. What remains after subtraction is a regular field that is fully responsible for the self-force. Because this field satisfies a homogeneous wave equation, it can be thought of as a free field that interacts with the particle; it is this interaction that gives rise to the self-force. The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime are developed here from scratch. The review begins with a discussion of the basic theory of bitensors (Part I). It then applies the theory to the construction of convenient coordinate systems to chart a neighbourhood of the particle's word line (Part II). It continues with a thorough discussion of Green's functions in curved spacetime (Part III). The review presents a detailed derivation of each of the three equations of motion (Part IV). Because the notion of a point mass is problematic in general relativity, the review concludes (Part V) with an
The Motion of Point Particles in Curved Spacetime
Eric Poisson
2011-09-01
Full Text Available This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The self-force contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. The work done by the self-force matches the energy radiated away by the particle. The field's action on the particle is difficult to calculate because of its singular nature: the field diverges at the position of the particle. But it is possible to isolate the field's singular part and show that it exerts no force on the particle -- its only effect is to contribute to the particle's inertia. What remains after subtraction is a regular field that is fully responsible for the self-force. Because this field satisfies a homogeneous wave equation, it can be thought of as a free field that interacts with the particle; it is this interaction that gives rise to the self-force. The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime are developed here from scratch. The review begins with a discussion of the basic theory of bitensors (Part I. It then applies the theory to the construction of convenient coordinate systems to chart a neighbourhood of the particle's word line (Part II. It continues with a thorough discussion of Green's functions in curved spacetime (Part III. The review presents a detailed derivation of each of the three equations of motion (Part IV. Because the notion of a point mass is problematic in general relativity, the review concludes (Part V
Gravity induced from quantum spacetime
Beggs, Edwin J.; Majid, Shahn
2014-02-01
We show that tensoriality constraints in noncommutative Riemannian geometry in the two-dimensional bicrossproduct model quantum spacetime algebra [x, t] = λx drastically reduce the moduli of possible metrics g up to normalization to a single real parameter, which we interpret as a time in the past from which all timelike geodesics emerge and a corresponding time in the future at which they all converge. Our analysis also implies a reduction of moduli in n-dimensions and we study a suggested spherically symmetric classical geometry in n = 4 in detail, identifying two one-parameter subcases where the Einstein tensor matches that of a perfect fluid for (a) positive pressure, zero density and (b) negative pressure and positive density with ratio w_Q=-{1\\over 2}. The classical geometry is conformally flat and its geodesics motivate new coordinates which we extend to the quantum case as a new description of the quantum spacetime model as a quadratic algebra. The noncommutative Riemannian geometry is fully solved for n = 2 and includes the quantum Levi-Civita connection and a second, nonperturbative, Levi-Civita connection which blows up as λ → 0. We also propose a ‘quantum Einstein tensor’ which is identically zero for the main part of the moduli space of connections (as classically in 2D). However, when the quantum Ricci tensor and metric are viewed as deformations of their classical counterparts there would be an O(λ2) correction to the classical Einstein tensor and an O(λ) correction to the classical metric.
Tensorial spacetime geometries carrying predictive, interpretable and quantizable matter dynamics
Rivera Hernandez, Sergio
2012-02-15
Which tensor fields G on a smooth manifold M can serve as a spacetime structure? In the first part of this thesis, it is found that only a severely restricted class of tensor fields can provide classical spacetime geometries, namely those that can carry predictive, interpretable and quantizable matter dynamics. The obvious dependence of this characterization of admissible tensorial spacetime geometries on specific matter is not a weakness, but rather presents an insight: it was Maxwell theory that justified Einstein to promote Lorentzian manifolds to the status of a spacetime geometry. Any matter that does not mimick the structure of Maxwell theory, will force us to choose another geometry on which the matter dynamics of interest are predictive, interpretable and quantizable. These three physical conditions on matter impose three corresponding algebraic conditions on the totally symmetric contravariant coefficient tensor field P that determines the principal symbol of the matter field equations in terms of the geometric tensor G: the tensor field P must be hyperbolic, time-orientable and energy-distinguishing. Remarkably, these physically necessary conditions on the geometry are mathematically already sufficient to realize all kinematical constructions familiar from Lorentzian geometry, for precisely the same structural reasons. This we were able to show employing a subtle interplay of convex analysis, the theory of partial differential equations and real algebraic geometry. In the second part of this thesis, we then explore general properties of any hyperbolic, time-orientable and energy-distinguishing tensorial geometry. Physically most important are the construction of freely falling non-rotating laboratories, the appearance of admissible modified dispersion relations to particular observers, and the identification of a mechanism that explains why massive particles that are faster than some massless particles can radiate off energy until they are slower than all
Condensation Energy of a Spacetime Condensate
de Matos, Clovis Jacinto
2010-01-01
Starting from an analogy between the Planck-Einstein scale and the dual length scales in Ginzburg-Landau theory of superconductivity, and assuming that space-time is a condensate of neutral fermionic particles with Planck mass, we derive the baryonic mass of the universe. In that theoretical framework baryonic matter appears to be associated with the condensation energy gained by spacetime in the transition from its normal (symetric) to its (less symetric) superconducting-like phase. It is shown however that the critical transition temperature cannot be the Planck temperature. Thus leaving open the enigma of the microscopic description of spacetime at quantum level.
Local spacetime effects on gyroscope systems
Wohlfarth, Mattias N R
2012-01-01
We give a precise theoretical description of initially aligned sets of orthogonal gyroscopes which are transported along different paths from some initial point to the same final point in spacetime. These gyroscope systems can be used to synchronize separated observers' spatial frames by free fall along timelike geodesics. We find that initially aligned gyroscope systems, or spatial frames, lose their synchronization due to the curvature of spacetime and their relative motion. On the basis of our results we propose a simple experiment which enables observers to determine locally whether their spacetime is described by a rotating Kerr or a non-rotating Schwarzschild metric.
Local spacetime effects on gyroscope systems
Wohlfarth, Mattias N. R.; Pfeifer, Christian
2013-01-01
We give a precise theoretical description of initially aligned sets of orthogonal gyroscopes which are transported along different paths from some initial point to the same final point in spacetime. These gyroscope systems can be used to synchronize separated observers’ spatial frames by free fall along timelike geodesics. We find that initially aligned gyroscope systems, or spatial frames, lose their synchronization due to the curvature of spacetime and their relative motion. On the basis of our results we propose a simple experiment that enables observers to determine locally whether their spacetime is described by a rotating Kerr or a nonrotating Schwarzschild metric.
Space-time anisotropy: theoretical issues and the possibility of an observational test
, Sergey; Brinzei, Nicoleta
2008-01-01
The specific astrophysical data collected during the last decade causes the need for the modification of the expression for the Einstein-Hilbert action, and several attempts sufficing this need are known. The modification suggested in this paper stems from the possible anisotropy of space-time and this means the natural change of the simplest scalar in the least action principle. To provide the testable support to this idea, the optic-metrical parametric resonance is regarded - an experiment on the galactic scale based on the interaction between the electromagnetic radiation of cosmic masers and periodical gravitational waves emitted by close double systems or pulsars. Since the effect depends on the space-time metric, the possible anisotropy could reveal itself through observations. To give the corresponding theory predicting the corrections to the expected results of the experiment, the specific mathematical formalism of Finsler geometry was chosen. It was found that in case the anisotropy of the space-time...
An observational criterion to look for an inspiral in a non-Kerr spacetime
Apostolatos, Theocharis A; Lukes-Gerakopoulos, Georgios; Deligiannis, John [Section of Astrophysics, Astronomy, and Mechanics, Department of Physics, University of Athens, Panepistimiopolis Zografos GR-15783, Athens (Greece); Contopoulos, George, E-mail: tapostol@cc.uoa.g [Academy of Athens, Research Center for Astronomy, Soranou Efesiou 4, GR-11527, Athens (Greece)
2009-10-01
In this short article we present a useful observational tool for gravitational wave detectors. More specifically, if we are looking for extreme-mass-ratio inspiraling objects in a non-Kerr spacetime, we could exploit the consequences of the KAM and the Poincare-Birkhoff theorem which predicts plateaus in the ratio of frequencies f{sub {rho}/}f{sub z}, that are related to a generic geodesic orbit in such a spacetime, as a function of the initial conditions of the orbit itself. While both these frequencies are changing under radiation reaction, their ratio is expected to stay stationary if it passes through such a plateau. Therefore, if detectors are able to discern the fundamental frequencies due to {rho} and z oscillations of the orbit, they could in principle detect the non-Kerr-ness of the spacetime involved, just by monitoring the ratio of these two frequencies.
Stringy Space-Time Foam and High-Energy Cosmic Photons
Mavromatos, Nick E
2011-01-01
In this review, I discuss briefly stringent tests of Lorentz-violating quantum space-time foam models inspired from String/Brane theories, provided by studies of high energy Photons from intense celestial sources, such as Active Galactic Nuclei or Gamma Ray Bursts. The theoretical models predict modifications to the radiation dispersion relations, which are quadratically suppressed by the string mass scale, and time delays in the arrival times of photons (assumed to be emitted more or less simultaneously from the source), which are proportional to the photon energy, so that the more energetic photons arrive later. Although the astrophysics at the source of these energetic photons is still not understood, and such non simultaneous arrivals, that have been observed recently, might well be due to non simultaneous emission as a result of conventional physics effects, nevertheless, rather surprisingly, the observed time delays can also fit excellently the stringy space-time foam scenarios, provided the space-time ...
Singularity free gravitational collapse in an effective dynamical quantum spacetime
Torres, R., E-mail: ramon.torres-herrera@upc.edu; Fayos, F., E-mail: f.fayos@upc.edu
2014-06-02
We model the gravitational collapse of heavy massive shells including its main quantum corrections. Among these corrections, quantum improvements coming from Quantum Einstein Gravity are taken into account, which provides us with an effective quantum spacetime. Likewise, we consider dynamical Hawking radiation by modeling its back-reaction once the horizons have been generated. Our results point towards a picture of gravitational collapse in which the collapsing shell reaches a minimum non-zero radius (whose value depends on the shell initial conditions) with its mass only slightly reduced. Then, there is always a rebound after which most (or all) of the mass evaporates in the form of Hawking radiation. Since the mass never concentrates in a single point, no singularity appears.
The bizarre anti-de Sitter spacetime
Sokołowski, Leszek M.
2016-08-01
Anti-de Sitter spacetime is important in general relativity and modern field theory. We review its geometrical features and properties of light signals and free particles moving in it. By applying only the elementary tools of tensor calculus, we derive ab initio of all these properties and show that they are really weird. One finds superluminal velocities of light and particles, infinite particle energy necessary to escape at infinite distance and spacetime regions inaccessible by a free fall, though reachable by an accelerated spaceship. Radial timelike geodesics are identical to the circular ones and actually all timelike geodesics are identical to one circle in a fictitious five-dimensional space. Employing the latter space, one is able to explain these bizarre features of anti-de Sitter spacetime; in this sense the spacetime is not self-contained. This is not a physical world.
B^F Theory and Flat Spacetimes
Waelbroeck, Henri
2009-01-01
We propose a reduced constrained Hamiltonian formalism for the exactly soluble $B \\wedge F$ theory of flat connections and closed two-forms over manifolds with topology $\\Sigma^3 \\times (0,1)$. The reduced phase space variables are the holonomies of a flat connection for loops which form a basis of the first homotopy group $\\pi_1(\\Sigma^3)$, and elements of the second cohomology group of $\\Sigma^3$ with value in the Lie algebra $L(G)$. When $G=SO(3,1)$, and if the two-form can be expressed as $B= e\\wedge e$, for some vierbein field $e$, then the variables represent a flat spacetime. This is not always possible: We show that the solutions of the theory generally represent spacetimes with ``global torsion''. We describe the dynamical evolution of spacetimes with and without global torsion, and classify the flat spacetimes which admit a locally homogeneous foliation, following Thurston's classification of geometric structures.
Cosmic Inflation from Emergent Spacetime Picture
Yang, Hyun Seok
2016-01-01
We argue that the emergent spacetime picture admits a background-independent formulation of cosmic inflation. The inflation in this picture corresponds to the dynamical emergence of spacetime while the conventional inflation is simply an (exponential) expansion of a preexisting spacetime owing to the vacuum energy carried by an inflaton field. We show that the cosmic inflation arises as a time-dependent solution of the matrix quantum mechanics describing the dynamical process of Planck energy condensate in vacuum without introducing any inflaton field as well as an {\\it ad hoc} inflation potential. Thus the emergent spacetime picture realizes a background-independent description of the inflationary universe which has a sufficiently elegant and explanatory power to defend the integrity of physics against the multiverse hypothesis.
Field Theory on Curved Noncommutative Spacetimes
Alexander Schenkel
2010-08-01
Full Text Available We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005, 3511 and Classical Quantum Gravity 23 (2006, 1883], we describe noncommutative spacetimes by using (Abelian Drinfel'd twists and the associated *-products and *-differential geometry. In particular, we allow for position dependent noncommutativity and do not restrict ourselves to the Moyal-Weyl deformation. We construct action functionals for real scalar fields on noncommutative curved spacetimes, and derive the corresponding deformed wave equations. We provide explicit examples of deformed Klein-Gordon operators for noncommutative Minkowski, de Sitter, Schwarzschild and Randall-Sundrum spacetimes, which solve the noncommutative Einstein equations. We study the construction of deformed Green's functions and provide a diagrammatic approach for their perturbative calculation. The leading noncommutative corrections to the Green's functions for our examples are derived.
Riemann curvature of a boosted spacetime geometry
Battista, Emmanuele; Scudellaro, Paolo; Tramontano, Francesco
2014-01-01
The ultrarelativistic boosting procedure had been applied in the literature to map the metric of Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface. This paper evaluates the Riemann curvature tensor of the boosted Schwarzschild-de Sitter metric by means of numerical calculations, which make it possible to reach the ultrarelativistic regime gradually by letting the boost velocity approach the speed of light. Thus, for the first time in the literature, the singular limit of curvature through Dirac's delta distribution and its derivatives is numerically evaluated for this class of spacetimes. Eventually, the analysis of the Kteschmann invariant and the geodesic equation show that the spacetime possesses a scalar curvature singularity within a 3-sphere and it is possible to define what we here call boosted horizon, a sort of elastic wall where all particles are surprisingly pushed away, as numerical analysis demonstrates. Thi...
Field, J H
2016-01-01
Space-time intervals corresponding to different events on the worldline of any ponderable object (for example a clock) are time-like. In consequence, in the analysis of any space-time experiment involving clocks only the region for $c\\Delta t \\ge 0$ between the line $\\Delta x = 0$ and the light cone projection $c\\Delta t = \\Delta x$ of the $c\\Delta t$ versus $\\Delta x$ Minkowski plot is physically relevant. This breaks the manifest space-time symmetry of the plot. A further consequence is the unphysical nature of the `relativity of simultaneity' and `length contraction' effects of conventional special relativity theory. The only modification of space-time transformation laws in passing from Galilean to special relativity is then the replacement of universal Newtonian time by a universal (position independent) time dilation effect for moving clocks.
Relative Locality in Curved Space-time
Kowalski-Glikman, Jerzy
2013-01-01
In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are presents. So far aspects of nonlinearities in momentum space have been studied only for flat or constantly expanding (De Sitter) spacetimes, relying on the their maximally symmetric nature. The extension of curved momentum space frameworks to arbitrary spacetime geometries could be relevant for the opportunities to test Planck-scale curvature/deformation of particles momentum space. As a first example of this construction we describe the particle with kappa-Poincar\\'e momentum space on a circular orbit in Schwarzschild spacetime, where the contributes of momentum space curvature turn out to be negligible. The analysis of this problem relies crucially on the solution of the soccer ball problem.
Pseudo-Z symmetric space-times
Mantica, Carlo Alberto, E-mail: carloalberto.mantica@libero.it [Physics Department, Università degli Studi di Milano, Via Celoria 16, 20133 Milano (Italy); Suh, Young Jin, E-mail: yjsuh@knu.ac.kr [Department of Mathematics, Kyungpook National University, Taegu 702-701 (Korea, Republic of)
2014-04-15
In this paper, we investigate Pseudo-Z symmetric space-time manifolds. First, we deal with elementary properties showing that the associated form A{sub k} is closed: in the case the Ricci tensor results to be Weyl compatible. This notion was recently introduced by one of the present authors. The consequences of the Weyl compatibility on the magnetic part of the Weyl tensor are pointed out. This determines the Petrov types of such space times. Finally, we investigate some interesting properties of (PZS){sub 4} space-time; in particular, we take into consideration perfect fluid and scalar field space-time, and interesting properties are pointed out, including the Petrov classification. In the case of scalar field space-time, it is shown that the scalar field satisfies a generalized eikonal equation. Further, it is shown that the integral curves of the gradient field are geodesics. A classical method to find a general integral is presented.
Space-time crystals of trapped ions.
Li, Tongcang; Gong, Zhe-Xuan; Yin, Zhang-Qi; Quan, H T; Yin, Xiaobo; Zhang, Peng; Duan, L-M; Zhang, Xiang
2012-10-19
Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these space-time crystals are robust for direct experimental observation. We also study the effects of finite temperatures on the persistent rotation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter.
Maximal Hypersurfaces in Spacetimes with Translational Symmetry
Bulawa, Andrew
2016-01-01
We consider four-dimensional vacuum spacetimes which admit a free isometric spacelike R-action. Taking a quotient with respect to the R-action produces a three-dimensional quotient spacetime. We establish several results regarding maximal hypersurfaces (spacelike hypersurfaces of zero mean curvature) in quotient spacetimes. First, we show that complete noncompact maximal hypersurfaces must either be flat cylinders S^1 x R or conformal to the Euclidean plane. Second, we establish a positive mass theorem for certain maximal hypersurfaces. Finally, while it is meaningful to use a bounded lapse when adopting the maximal hypersurface gauge condition in the four-dimensional (asymptotically flat) setting, it is shown here that nontrivial quotient spacetimes admit the maximal hypersurface gauge only with an unbounded lapse.
The bizarre anti-de Sitter spacetime
Sokolowski, Leszek M
2016-01-01
Anti--de Sitter spacetime is important in general relativity and modern field theory. We review its geometrical features and properties of light signals and free particles moving in it. Applying only elementary tools of tensor calculus we derive \\textit{ab initio\\/} all these properties and show that they are really weird. One finds superluminal velocities of light and particles, infinite particle energy necessary to escape at infinite distance and spacetime regions inaccessible by a free fall, though reachable by an accelerated spaceship. Radial timelike geodesics are identical to the circular ones and actually all timelike geodesics are identical to one circle in a fictitious five--dimensional space. Employing the latter space one is able to explain these bizarre features of anti--de Sitter spacetime; in this sense the spacetime is not self--contained. This is not a physical world.
Double conformal space-time algebra
Easter, Robert Benjamin; Hitzer, Eckhard
2017-01-01
The Double Conformal Space-Time Algebra (DCSTA) is a high-dimensional 12D Geometric Algebra G 4,8that extends the concepts introduced with the Double Conformal / Darboux Cyclide Geometric Algebra (DCGA) G 8,2 with entities for Darboux cyclides (incl. parabolic and Dupin cyclides, general quadrics, and ring torus) in spacetime with a new boost operator. The base algebra in which spacetime geometry is modeled is the Space-Time Algebra (STA) G 1,3. Two Conformal Space-Time subalgebras (CSTA) G 2,4 provide spacetime entities for points, flats (incl. worldlines), and hyperbolics, and a complete set of versors for their spacetime transformations that includes rotation, translation, isotropic dilation, hyperbolic rotation (boost), planar reflection, and (pseudo)spherical inversion in rounds or hyperbolics. The DCSTA G 4,8 is a doubling product of two G 2,4 CSTA subalgebras that inherits doubled CSTA entities and versors from CSTA and adds new bivector entities for (pseudo)quadrics and Darboux (pseudo)cyclides in spacetime that are also transformed by the doubled versors. The "pseudo" surface entities are spacetime hyperbolics or other surface entities using the time axis as a pseudospatial dimension. The (pseudo)cyclides are the inversions of (pseudo)quadrics in rounds or hyperbolics. An operation for the directed non-uniform scaling (anisotropic dilation) of the bivector general quadric entities is defined using the boost operator and a spatial projection. DCSTA allows general quadric surfaces to be transformed in spacetime by the same complete set of doubled CSTA versor (i.e., DCSTA versor) operations that are also valid on the doubled CSTA point entity (i.e., DCSTA point) and the other doubled CSTA entities. The new DCSTA bivector entities are formed by extracting values from the DCSTA point entity using specifically defined inner product extraction operators. Quadric surface entities can be boosted into moving surfaces with constant velocities that display the length
Twin Paradox in de Sitter Spacetime
Boblest, Sebastian; Wunner, Günter
2010-01-01
The "twin paradox" of special relativity offers the possibility to make interstellar flights within a lifetime. For very long journeys with velocities close to the speed of light, however, we have to take into account the expansion of the universe. Inspired by the work of Rindler on hyperbolic motion in curved spacetime, we study the worldline of a uniformly accelerated observer in de Sitter spacetime and the communication between the traveling observer and an observer at rest.
Space-Time Disarray and Visual Awareness
Jan Koenderink
2012-04-01
Full Text Available Local space-time scrambling of optical data leads to violent jerks and dislocations. On masking these, visual awareness of the scene becomes cohesive, with dislocations discounted as amodally occluding foreground. Such cohesive space-time of awareness is technically illusory because ground truth is jumbled whereas awareness is coherent. Apparently the visual field is a construction rather than a (veridical perception.
Free of centrifugal acceleration spacetime - Geodesics
Culetu, Hristu
2013-01-01
A static spacetime with no centrifugal repulsion, previously studied by Dadhich, is investigate in this paper. The source of curvature is considered to be an anisotropic fluid with $\\rho = -p_{r}$ and constant angular pressures. The positive parameter from the line-element is interpreted as the invariant acceleration of a static observer. We found that the Tolman-Komar gravitational energy is finite everywhere. The timelike and null geodesics of the spacetime are examined.
Exact Philosophy of Space-Time
Vucetich, Héctor
2011-01-01
Starting from Bunge's (1977) scientific ontology, we expose a materialistic relational theory of space-time, that carries out the program initiated by Leibniz, and provides a protophysical basis consistent with any rigorous formulation of General Relativity. Space-time is constructed from general concepts which are common to any consistent scientific theory and they are interpreted as emergent properties of the greatest assembly of things, namely, the world.
Strong cosmic censorship and Misner spacetime
Denaro, Pedro
2015-01-01
Misner spacetime is among the simplest solutions of Einstein's equation that exhibits a Cauchy horizon with a smooth extension beyond it. Besides violating strong cosmic censorship, this extension contains closed timelike curves. We analyze the stability of the Cauchy horizon, and prove that neighboring spacetimes in one parameter families of solutions through Misner's in pure gravity, gravity coupled to a scalar field, or Einstein-Maxwell theory, end at the Cauchy horizon developing a curvature singularity.
String cosmology and the dimension of spacetime
Cleaver, G B; Gerald B Cleaver; Philip J Rosenthal
1994-01-01
The implications of string theory for understanding the dimension of uncompactified spacetime are investigated. Using recent ideas in string cosmology, a new model is proposed to explain why three spatial dimensions grew large. Unlike the original work of Brandenberger and Vafa, this paradigm uses the theory of random walks. A computer model is developed to test the implications of this new approach. It is found that a four-dimensional spacetime can be explained by the proper choice of initial conditions.
String Cosmology and the Dimension of Spacetime
Cleaver, Gerald B.; Rosenthal, Philip J.
1994-01-01
The implications of string theory for understanding the dimension of uncompactified spacetime are investigated. Using recent ideas in string cosmology, a new model is proposed to explain why three spatial dimensions grew large. Unlike the original work of Brandenberger and Vafa, this paradigm uses the theory of random walks. A computer model is developed to test the implications of this new approach. It is found that a four-dimensional spacetime can be explained by the proper choice of initia...
Space-time as strongly bent plate
Kokarev, S S
1999-01-01
Futher development is made of a consept of space-time as multidimensional elastic plate, proposed earlier in [20,21]. General equilibrium equations, including 4-dimensional tangent stress tensor - energy-momentum tensor of matter - are derived. Comparative analysis of multidimensional elasticity theory (MET) and GR is given. Variational principle, boundary conditions, energy-momentum tensor, matter and space-time signature are reviewed within the context of MET.
Navigation in Curved Space-Time
Bahder, T B
2001-01-01
A covariant and invariant theory of navigation in curved space-time with respect to electromagnetic beacons is written in terms of J. L. Synge's two-point invariant world function. Explicit equations are given for navigation in space-time in the vicinity of the Earth in Schwarzschild coordinates and in rotating coordinates. The restricted problem of determining an observer's coordinate time when their spatial position is known is also considered.
Space-time singularities in Weyl manifolds
Lobo, I.P. [CAPES Foundation, Ministry of Education of Brazil, Brasilia (Brazil); Sapienza Universita di Roma, Dipartimento di Fisica, Rome (Italy); Barreto, A.B.; Romero, C. [Universidade Federal da Paraiba, Departamento de Fisica, C. Postal 5008, Joao Pessoa, PB (Brazil)
2015-09-15
We extend one of the Hawking-Penrose singularity theorems in general relativity to the case of some scalar-tensor gravity theories in which the scalar field has a geometrical character and space-time has the mathematical structure of a Weyl integrable space-time. We adopt an invariant formalism, so that the extended version of the theorem does not depend on a particular frame. (orig.)
A Spacetime Map of the Universe
Gowan, J A
1999-01-01
A geometric spacetime map of the universe is presented challanging certain assumptions of the Hubble model of cosmic expansion. The earth-observer is situated on the edge of spacetime, looking backward in time through ever- smaller universes toward the Big Bang. Implications for the Hubble expansion model, the cosmological horizon problem, and the red shift are discussed. Flat as well as gravitationally curved models are considered.
Dynamical Space-Time and Gravitational Waves
van Holten, J W
2016-01-01
According to General Relativity gravity is the result of the interaction between matter and space-time geometry. In this interaction space-time geometry itself is dynamical: it can store and transport energy and momentum in the form of gravitational waves. We give an introductory account of this phenomenon and discuss how the observation of gravitational waves may open up a fundamentally new window on the universe.
Curvature of spacetime: A simple student activity
Wood, Monika; Smith, Warren; Jackson, Matthew
2016-12-01
The following is a description of an inexpensive and simple student experiment for measuring the differences between the three types of spacetime topology—Euclidean (flat), Riemann (spherical), and Lobachevskian (saddle) curvatures. It makes use of commonly available tools and materials, and requires only a small amount of construction. The experiment applies to astronomical topics such as gravity, spacetime, general relativity, as well as geometry and mathematics.
Electrodynamics and spacetime geometry: Astrophysical applications
Cabral, Francisco; Lobo, Francisco S. N.
2017-07-01
After a brief review of the foundations of (pre-metric) electromagnetism, we explore some physical consequences of electrodynamics in curved spacetime. In general, new electromagnetic couplings and related phenomena are induced by the spacetime curvature. The applications of astrophysical interest considered here correspond essentially to the following geometries: the Schwarzschild spacetime and the spacetime around a rotating spherical mass in the weak field and slow rotation regime. In the latter, we use the Parameterised Post-Newtonian (PPN) formalism. We also explore the hypothesis that the electric and magnetic properties of vacuum reflect the spacetime isometries. Therefore, the permittivity and permeability tensors should not be considered homogeneous and isotropic a priori. For spherical geometries we consider the effect of relaxing the homogeneity assumption in the constitutive relations between the fields and excitations. This affects the generalized Gauss and Maxwell-Ampère laws, where the electric permittivity and magnetic permeability in vacuum depend on the radial coordinate in accordance with the local isometries of space. For the axially symmetric geometries we relax both the assumptions of homogeneity and isotropy. We explore simple solutions and discuss the physical implications related to different phenomena, such as the decay of electromagnetic fields in the presence of gravity, magnetic terms in Gauss law due to the gravitomagnetism of the spacetime around rotating objects, a frame-dragging effect on electric fields and the possibility of a spatial (radial) variability of the velocity of light in vacuum around spherical astrophysical objects for strong gravitational fields.
Circular geodesic of Bardeen and Ayon-Beato-Garcia regular black-hole and no-horizon spacetimes
Stuchlík, Zdeněk; Schee, Jan
2015-12-01
In this paper, we study circular geodesic motion of test particles and photons in the Bardeen and Ayon-Beato-Garcia (ABG) geometry describing spherically symmetric regular black-hole or no-horizon spacetimes. While the Bardeen geometry is not exact solution of Einstein's equations, the ABG spacetime is related to self-gravitating charged sources governed by Einstein's gravity and nonlinear electrodynamics. They both are characterized by the mass parameter m and the charge parameter g. We demonstrate that in similarity to the Reissner-Nordstrom (RN) naked singularity spacetimes an antigravity static sphere should exist in all the no-horizon Bardeen and ABG solutions that can be surrounded by a Keplerian accretion disc. However, contrary to the RN naked singularity spacetimes, the ABG no-horizon spacetimes with parameter g/m > 2 can contain also an additional inner Keplerian disc hidden under the static antigravity sphere. Properties of the geodesic structure are reflected by simple observationally relevant optical phenomena. We give silhouette of the regular black-hole and no-horizon spacetimes, and profiled spectral lines generated by Keplerian rings radiating at a fixed frequency and located in strong gravity region at or nearby the marginally stable circular geodesics. We demonstrate that the profiled spectral lines related to the regular black-holes are qualitatively similar to those of the Schwarzschild black-holes, giving only small quantitative differences. On the other hand, the regular no-horizon spacetimes give clear qualitative signatures of their presence while compared to the Schwarschild spacetimes. Moreover, it is possible to distinguish the Bardeen and ABG no-horizon spacetimes, if the inclination angle to the observer is known.
Supergravity with Doubled Spacetime Structure
Ma, Chen-Te
2016-01-01
Double Field Theory (DFT) is a low-energy effective theory of a manifestly $O(D,D)$ invariant formulation of the closed string theory when the toroidally compact dimensions are present. The theory is based on a doubled spacetime structure and, in order to preserve the gauge symmetry provided by the invariance under generalized diffeomorphisms, a constraint has to be imposed on fields and gauge parameters. In this paper, we propose a DFT-inspired Supergravity by using a suitable {\\em star product} with the aim of studying the corresponding algebraic structure. We get a consistent DFT in which also an orthogonality condition of momenta is necessary for having a closed gauge algebra. In constructing this theory, we start from the simplest case of doubling one spatial dimension where the action is uniquely determined, without any ambiguities, by the gauge symmetry. Then, the extension to the generic $O(D, D)$ case is studied and it results to be consistent with the closed string field theory.
Cosmology in Conformally Flat Spacetime
Endean, Geoffrey
1997-04-01
A possible solution to cosmological age and redshift-distance difficulties has recently been proposed by applying the appropriate conformally flat spacetime (CFS) coordinates to the standard solution of the field equations in a standard dust model closed universe. Here it is shown that CFS time correctly measures the true age of the universe, thus answering a major theoretical objection to the proposal. It is also shown that the CFS interpretation leads to a strong Copernican principle and is in all other respects wholly self-consistent. The deceleration parameter q0 is related to t0, the present age of the universe divided by L, the scale length of its curvature (an absolute constant). The values of q0 and L are approximately 5/6 and 9.2 × 109 yr, respectively. It is shown that the universe started everywhere simultaneously, with no recession velocity until the effects of its closed topology became significant. Conclusions to the contrary in standard theory (the big bang) stem from a different definition of recession velocity. The theoretical present cosmological mass density is quantified as 4.4 × 10-27 kg m-3 approximately, thus greatly reducing, in a closed universe, the observational requirement to find hidden mass. It is also shown that the prediction of standard theory, for a closed universe, of collapse toward a big crunch termination, will not in fact take place.
Quantum gravity from noncommutative spacetime
Lee, Jungjai [Daejin University, Pocheon (Korea, Republic of); Yang, Hyunseok [Korea Institute for Advanced Study, Seoul (Korea, Republic of)
2014-12-15
We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative *-algebra) of quantum gravity.
Spacetime Metrology with LISA Pathfinder
Congedo, Giuseppe
2012-01-01
LISA is the proposed ESA-NASA gravitational wave detector in the 0.1 mHz - 0.1 Hz band. LISA Pathfinder is the down-scaled version of a single LISA arm. The arm -- named Doppler link -- can be treated as a differential accelerometer, measuring the relative acceleration between test masses. LISA Pathfinder -- the in-flight test of the LISA instrumentation -- is currently in the final implementation and planned to be launched in 2014. It will set stringent constraints on the ability to put test masses in geodesic motion to within the required differential acceleration of 3\\times10^{-14} m s^{-2} Hz^{-1/2} and track their relative motion to within the required differential displacement measurement noise of 9\\times10^{-12} m Hz^{-1/2}, around 1 mHz. Given the scientific objectives, it will carry out -- for the first time with such high accuracy required for gravitational wave detection -- the science of spacetime metrology, in which the Doppler link between two free-falling test masses measures the curvature. Thi...
The Elastodynamics of the Spacetime Continuum as a Framework for Strained Spacetime
Millette P. A.
2013-01-01
Full Text Available We derive the elastodynamics of the spacetime continuum by applying continuum me- chanical results to strained spacetime. Based on this model, a stress-strain relation is derived for the spacetime continuum. From the kinematic relations and the equilibrium dynamic equation of the spacetime continuum, we derive a series of wave equations: the displacement, dilatational, rotational and strain wave equations. Hence energy propa- gates in the spacetime continuum as wave-like deformations which can be decomposed into dilatations and distortions. Dilatations involve an invariant change in volume of the spacetime continuum which is the source of the associated rest-mass energy density of the deformation, while distortions correspond to a change of shape of the space- time continuum without a change in volume and are thus massless. The deformations propagate in the continuum by longitudinal and transverse wave displacements. This is somewhat reminiscent of wave-particle duality, with the transverse mode correspond- ing to the wave aspects and the longitudinal mode corresponding to the particle aspects. A continuity equation for deformations of the spacetime continuum is derived, where the gradient of the massive volume dilatation acts as a source term. The nature of the spacetime continuum volume force and the inhomogeneous wave equations need further investigation.
Spontaneous excitation of a static atom in a thermal bath in cosmic string spacetime
Cai, Huabing; Yu, Hongwei; Zhou, Wenting
2015-10-01
We study the average rate of change of energy for a static atom immersed in a thermal bath of electromagnetic radiation in the cosmic string spacetime and separately calculate the contributions of thermal fluctuations and radiation reaction. We find that the transition rates are crucially dependent on the atom-string distance and polarization of the atom and they in general oscillate as the atom-string distance varies. Moreover, the atomic transition rates in the cosmic string spacetime can be larger or smaller than those in Minkowski spacetime contingent upon the atomic polarization and position. In particular, when located on the string, ground-state atoms can make a transition to excited states only if they are polarizable parallel to the string, whereas ground-state atoms polarizable only perpendicular to the string are stable as if they were in a vacuum, even if they are immersed in a thermal bath. Our results suggest that the influence of a cosmic string is very similar to that of a reflecting boundary in Minkowski spacetime.
Non-coherent space-time code based on full diversity space-time block coding
无
2008-01-01
A non-unitary non-coherent space-time code which is capable of achieving full algebraic diversity is proposed based on full diversity space-time block coding. The error performance is optimized by transforming the non-unitary space-time code into unitary space-time code. By exploiting the desired structure of the proposed code, a grouped generalized likelihood ratio test decoding algorithm is presented to overcome the high complexity of the optimal algorithm. Simulation results show that the proposed code possesses high spectrum efficiency in contrast to the unitary space-time code despite slight loss in the SNR, and besides, the proposed grouped decoding algorithm provides good tradeoff between performance and complexity.
Spacetime-Free Approach to Quantum Theory and Effective Spacetime Structure
Raasakka, Matti
2017-01-01
Motivated by hints of the effective emergent nature of spacetime structure, we formulate a spacetime-free algebraic framework for quantum theory, in which no a priori background geometric structure is required. Such a framework is necessary in order to study the emergence of effective spacetime structure in a consistent manner, without assuming a background geometry from the outset. Instead, the background geometry is conjectured to arise as an effective structure of the algebraic and dynamical relations between observables that are imposed by the background statistics of the system. Namely, we suggest that quantum reference states on an extended observable algebra, the free algebra generated by the observables, may give rise to effective spacetime structures. Accordingly, perturbations of the reference state lead to perturbations of the induced effective spacetime geometry. We initiate the study of these perturbations, and their relation to gravitational phenomena.
Einstein Spacetimes with Constant Weyl Eigenvalues
Barnes, Alan
2014-01-01
Einstein spacetimes (that is vacuum spacetimes possibly with a non-zero cosmological constant {\\Lambda}) with constant non-zero Weyl eigenvalus are considered. For type Petrov II & D this assumption allows one to prove that the non-repeated eigenvalue necessarily has the value 2{\\Lambda}/3 and it turns out that the only possible spacetimes are some Kundt-waves considered by Lewandowski which are type II and a Robinson-Bertotti solution of type D. For Petrov type I the only solution turns out to be a homogeneous pure vacuum solution found long ago by Petrov using group theoretic methods. These results can be summarised by the statement that the only vacuum spacetimes with constant Weyl eigenvalues are either homogeneous or are Kundt space- times. This result is similar to that of Coley et al. who proved their result for general spacetimes under the assumption that all scalar invariants constructed from the curvature tensor and all its derivatives were constant. Some preliminary results are also presented f...
Deformed symmetries in noncommutative and multifractional spacetimes
Calcagni, Gianluca; Ronco, Michele
2017-02-01
We clarify the relation between noncommutative spacetimes and multifractional geometries, two quantum-gravity-related approaches where the fundamental description of spacetime is not given by a classical smooth geometry. Despite their different conceptual premises and mathematical formalisms, both research programs allow for the spacetime dimension to vary with the probed scale. This feature and other similarities led to ask whether there is a duality between these two independent proposals. In the absence of curvature and comparing the symmetries of both position and momentum space, we show that κ -Minkowski spacetime and the commutative multifractional theory with q -derivatives are physically inequivalent but they admit several contact points that allow one to describe certain aspects of κ -Minkowski noncommutative geometry as a multifractional theory and vice versa. Contrary to previous literature, this result holds without assuming any specific measure for κ -Minkowski. More generally, no well-defined ⋆-product can be constructed from the q -theory, although the latter does admit a natural noncommutative extension with a given deformed Poincaré algebra. A similar no-go theorem may be valid for all multiscale theories with factorizable measures. Turning gravity on, we write the algebras of gravitational first-class constraints in the multifractional theories with q - and weighted derivatives and discuss their differences with respect to the deformed algebras of κ -Minkowski spacetime and of loop quantum gravity.
Causality in noncommutative space-time
Neves, M.J.; Abreu, E.M.C. [Universidade Federal Rural do Rio de Janeiro (UFRRJ), Seropedica, RJ (Brazil)
2011-07-01
Full text: Space-time noncommutativity has been investigated in the last years as a real possibility to describe physics at fundamental scale. This subject is associated with many tough issues in physics, i.e., strings, gravity, noncommutative field theories and others. The first formulation for a noncommutative spacetime was proposed by Snyder in 1947, where the object of noncommutativity is considered as a constant matrix that breaks the Lorentz symmetry. His objective was to get rid of the infinities that intoxicate quantum field theory. Unfortunately it was demonstrated not a success. Here we consider an alternative recent formulation known as Doplicher-Fredenhagen-Roberts-Amorim (DFRA) algebra in which the object of noncommutativity is treated as an ordinary coordinate by constructing an extended space-time with 4 + 6 dimensions (x + {phi}) - spacetime. In this way, the Lorentz symmetry is preserved in DFRA algebra. A quantum field theory is constructed in accordance with DFRA Poincare algebra, as well as a Lagrangian density formulation. By means of the Klein-Gordon equation in this (x + {phi}) - spacetime. We analyze the aspects of causality by studying the advanced and retarded Green functions. (author)
The characteristic initial value problem for plane symmetric spacetimes with weak regularity
LeFloch, Philippe G [Laboratoire Jacques-Louis Lions and Centre National de la Recherche Scientifique, Universite Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris (France); Stewart, John M, E-mail: pgLeFloch@gmail.com, E-mail: J.M.Stewart@damtp.cam.ac.uk [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Cambridge CB3 0WA (United Kingdom)
2011-07-21
We investigate the existence and the global causal structure of plane symmetric spacetimes with weak regularity when the matter consists of an irrotational perfect fluid with pressure equal to its mass-energy density. Our theory encompasses the class of W{sup 1,2} regular spacetimes whose metric coefficients have square-integrable first-order derivatives and whose curvature must be understood in the sense of distributions. We formulate the characteristic initial value problem with data posed on two null hypersurfaces intersecting along a two-plane. Relying on Newman-Penrose's formalism and expressing our weak regularity conditions in terms of the Newman-Penrose scalars, we arrive at a fully geometrical formulation in which, along each initial hypersurface, two scalar fields describing the incoming radiation must be prescribed in L{sup 1} and W{sup -1,2}, respectively. To analyze the future boundary of such a spacetime and identify its global causal structure, we introduce a gauge that reduces the Einstein equations to a coupled system of wave equations and ordinary differential equations for well-chosen unknowns. We prove that, within the weak regularity class under consideration and for generic initial data, a true spacetime singularity forms in finite proper time. Our formulation is robust enough so that propagating discontinuities in the curvature or in the matter variables do not prevent us from constructing a spacetime whose curvature generically blows up on the future boundary. Earlier work on the problem studied here was restricted to sufficiently regular and vacuum spacetimes.
Self-quartic interaction for a scalar field in an extended DFR noncommutative space-time
Abreu, Everton M. C.; Neves, M. J.
2014-07-01
The framework of Dopliche-Fredenhagen-Roberts (DFR) for a noncommutative (NC) space-time is considered as an alternative approach to study the NC space-time of the early Universe. Concerning this formalism, the NC constant parameter, θ, is promoted to coordinate of the space-time and consequently we can describe a field theory in a space-time with extra-dimensions. We will see that there is a canonical momentum associated with this new coordinate in which the effects of a new physics can emerge in the propagation of the fields along the extra-dimensions. The Fourier space of this framework is automatically extended by the addition of the new momenta components. The main concept that we would like to emphasize from the outset is that the formalism demonstrated here will not be constructed by introducing a NC parameter in the system, as usual. It will be generated naturally from an already NC space. We will review that when the components of the new momentum are zero, the (extended) DFR approach is reduced to the usual (canonical) NC case, in which θ is an antisymmetric constant matrix. In this work we will study a scalar field action with self-quartic interaction ϕ4⋆ defined in the DFR NC space-time. We will obtain the Feynman rules in the Fourier space for the scalar propagator and vertex of the model. With these rules we are able to build the radiative corrections to one loop order of the model propagator. The consequences of the NC scale, as well as the propagation of the field in extra-dimensions, will be analyzed in the ultraviolet divergences scenario. We will investigate about the actual possibility that this kμν conjugate momentum has the property of healing the combination of IR/UV divergences that emerges in this recently new NC spacetime quantum field theory.
Tautology of quantum mechanics and spacetime
Keller, Jaime
Multivector Clifford algebra allows a series of factorizations of the Laplacian (the spacetime d'Alembert operator), similar to the well known Dirac factorization, generating sets of Diraclike equations. It is shown that a basic set has the symmetry corresponding to the standard electroweak-color model. But in contrast to the usual approach to the standard model the properties for the different fields of the model are consequences of the relative properties of the equations, among themselves and in relation to spacetime, and therefore, they do not need to be postulates of the theory. Spinors are the basis of geometric algebra and in fact, they can be considered the basis of all algebras representable by matrices. Here a unified mathematical approach to spinors and multivectors or superalgebra is constructed in a form, to be useful to study the mathematical description of matter and its interaction fields. Matter fields in turn generate the spacetime geometric superalgebra.
Spacetime approach to force-free magnetospheres
Gralla, Samuel E
2014-01-01
Force-Free Electrodynamics (FFE) describes magnetically dominated relativistic plasma via non-linear equations for the electromagnetic field alone. Such plasma is thought to play a key role in the physics of pulsars and active black holes. Despite its simple covariant formulation, FFE has primarily been studied in 3+1 frameworks, where spacetime is split into space and time. In this article we systematically develop the theory of force-free magnetospheres taking a spacetime perspective. Using a suite of spacetime tools and techniques (notably exterior calculus) we cover 1) the basics of the theory, 2) exact solutions that demonstrate the extraction and transport of the rotational energy of a compact object (in the case of a black hole, the Blandford-Znajek mechanism), 3) the behavior of current sheets, 4) the general theory of stationary, axisymmetric magnetospheres and 5) general properties of pulsar and black hole magnetospheres. We thereby synthesize, clarify and generalize known aspects of the physics of ...
Noncommutative effects of spacetime on holographic superconductors
Ghorai, Debabrata, E-mail: debanuphy123@gmail.com [S.N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata 700098 (India); Gangopadhyay, Sunandan, E-mail: sunandan.gangopadhyay@gmail.com [Department of Physics, West Bengal State University, Barasat (India); Inter University Centre for Astronomy & Astrophysics, Pune (India)
2016-07-10
The Sturm–Liouville eigenvalue method is employed to analytically investigate the properties of holographic superconductors in higher dimensions in the framework of Born–Infeld electrodynamics incorporating the effects of noncommutative spacetime. In the background of pure Einstein gravity in noncommutative spacetime, we obtain the relation between the critical temperature and the charge density. We also obtain the value of the condensation operator and the critical exponent. Our findings suggest that the higher value of noncommutative parameter and Born–Infeld parameter make the condensate harder to form. We also observe that the noncommutative structure of spacetime makes the critical temperature depend on the mass of the black hole and higher value of black hole mass is favourable for the formation of the condensate.
The Lamb shift in de Sitter spacetime
Zhou, Wenting
2010-01-01
We study the Lamb shift of both freely-falling and static two-level atoms in interaction with quantized conformally coupled massless scalar fields in the de Sitter-invariant vacuum. We find that the Lamb shifts of both freely-falling and static atoms are in structural similarity to that of an inertial atom immersed in a thermal bath in a Minkowski spacetime. For the freely-falling atom, the Lamb shift gets a correction as if it was immersed in a thermal bath at the Gibbons-Hawking temperature, thus revealing clearly the intrinsic thermal nature of de Sitter spacetime. For the static atom, the Lamb shift is affected by a combination of the effect of the intrinsic thermal nature of de Sitter spacetime and the Unruh effect associated with the inherent acceleration of the atom.
Scalar fields in black hole spacetimes
Thuestad, Izak; Khanna, Gaurav; Price, Richard H.
2017-07-01
The time evolution of matter fields in black hole exterior spacetimes is a well-studied subject, spanning several decades of research. However, the behavior of fields in the black hole interior spacetime has only relatively recently begun receiving some attention from the research community. In this paper, we numerically study the late-time evolution of scalar fields in both Schwarzschild and Kerr spacetimes, including the black hole interior. We recover the expected late-time power-law "tails" on the exterior (null infinity, timelike infinity, and the horizon). In the interior region, we find an interesting oscillatory behavior that is characterized by the multipole index ℓ of the scalar field. In addition, we also study the extremal Kerr case and find strong indications of an instability developing at the horizon.
STATISTICAL SPACE-TIME ADAPTIVE PROCESSING ALGORITHM
Yang Jie
2010-01-01
For the slowly changed environment-range-dependent non-homogeneity,a new statistical space-time adaptive processing algorithm is proposed,which uses the statistical methods,such as Bayes or likelihood criterion to estimate the approximative covariance matrix in the non-homogeneous condition. According to the statistical characteristics of the space-time snapshot data,via defining the aggregate snapshot data and corresponding events,the conditional probability of the space-time snapshot data which is the effective training data is given,then the weighting coefficients are obtained for the weighting method. The theory analysis indicates that the statistical methods of the Bayes and likelihood criterion for covariance matrix estimation are more reasonable than other methods that estimate the covariance matrix with the use of training data except the detected outliers. The last simulations attest that the proposed algorithms can estimate the covariance in the non-homogeneous condition exactly and have favorable characteristics.
Spacetime Average Density (SAD) Cosmological Measures
Page, Don N
2014-01-01
The measure problem of cosmology is how to obtain normalized probabilities of observations from the quantum state of the universe. This is particularly a problem when eternal inflation leads to a universe of unbounded size so that there are apparently infinitely many realizations or occurrences of observations of each of many different kinds or types, making the ratios ambiguous. There is also the danger of domination by Boltzmann Brains. Here two new Spacetime Average Density (SAD) measures are proposed, Maximal Average Density (MAD) and Biased Average Density (BAD), for getting a finite number of observation occurrences by using properties of the Spacetime Average Density (SAD) of observation occurrences to restrict to finite regions of spacetimes that have a preferred beginning or bounce hypersurface. These measures avoid Boltzmann brain domination and appear to give results consistent with other observations that are problematic for other widely used measures, such as the observation of a positive cosmolo...
Cosmological Spacetimes from Negative Tension Brane Backgrounds
Burgess, C P; Rey, S J; Tasinato, G
2002-01-01
We put forward a viable nonsingular cosmology emerging out of negative-tension branes. The cosmology is based on a general class of solutions in Einstein-dilaton-Maxwell theory, presented in {\\tt hep-th/0106120}. We argue that solutions with hyperbolic or planar symmetry describe gravitational interactions due to a pair of negative-tension $q$-branes. These spacetimes are static near each brane, but become time-dependent and expanding at late times -- in some cases asymptotically approaching flat space. We interpret this expansion as being the spacetime's response to the branes presence. The time-dependent regions provide explicit realizations of cosmological spacetimes having past horizons without naked past singularities, and the past horizons are reminiscent of the S-brane solutions. We prove that the singularities in the static regions are repulsive to timelike geodesics, extract a cosmological `bounce' interpretation, compute the explicit charge and tension of the branes, analyse the classical stability ...
Space-time orientations, electrodynamics, antiparticles
Tulczyjew, W M [Associated with Instituto Nazionale di Fisica Nucleare Sezione di Napoli, Italy Complesso universitario Monte Sant' Angelo Via Cintia, 80126 Naples (Italy)
2007-11-15
Two definitions of orientation in space-time are introduced. One is a standard definition found for examples presented elsewhere. The other is a new definition based on the Minkowski geometry of space-time. Parities of differential forms appearing in electrodynamics are analysed. Parities of differential forms based on the standard concept of orientation are those introduced by de Rham. Parities based on the relativistic concept of orientation are the intrinsic space-time version of parities normally assigned to electromagnetic objects in texts on electrodynamics. Such assignments are made by Jackson [5] and also by Landau and Lifshitz. We present two formulations of the dynamics of charged particles corresponding to the two assignments of parities to electromagnetic objects. One is due to Stueckelberg and Feynman. The other is an attempt to formulate a classical theory corresponding to Dirac's quantum interpretation of antiparticles following the publications listed.
Electrodynamics and spacetime geometry I: Foundations
Cabral, Francisco
2016-01-01
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We briefly review the foundations of electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations which introduce the spacetime metric. We then proceed with the tensor formulation by assuming local, linear, homogeneous and isotropic constitutive relations, and explore the physical, observable consequences of Maxwell's equations in curved spacetime. The field equations, charge conservation and the Lorentz force are explicitly expressed in general (pseudo) Riemanian manifolds. The generalized Gauss and Maxwell-Amp\\`{e}re laws, as well as the wave equations, reveal potentially interesting astrophysical applications. In all cases new ele...
Noncommutative effects of spacetime on holographic superconductors
Debabrata Ghorai
2016-07-01
Full Text Available The Sturm–Liouville eigenvalue method is employed to analytically investigate the properties of holographic superconductors in higher dimensions in the framework of Born–Infeld electrodynamics incorporating the effects of noncommutative spacetime. In the background of pure Einstein gravity in noncommutative spacetime, we obtain the relation between the critical temperature and the charge density. We also obtain the value of the condensation operator and the critical exponent. Our findings suggest that the higher value of noncommutative parameter and Born–Infeld parameter make the condensate harder to form. We also observe that the noncommutative structure of spacetime makes the critical temperature depend on the mass of the black hole and higher value of black hole mass is favourable for the formation of the condensate.
Finite Conformal Quantum Gravity and Nonsingular Spacetimes
Modesto, Leonardo
2016-01-01
We explicitly prove that a class of finite quantum gravitational theories (in odd as well as in even dimension) is actually a range of anomaly-free conformally invariant theories in the spontaneously broken phase of the conformal Weyl symmetry. At classical level we show how the Weyl conformal invariance is likely able to tame the spacetime singularities that plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. This latter statement is rigorously proved by a singularity theorem that applies to a large class of weakly non-local theories. Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free black hole exact solutions conformally equivalent to the Schwarzschild metric. Furthermore, we show that the FRW cosmological solutions and the Belinski, Khalatnikov, Lifshitz (BKL) spacetimes, which exactly solve the classical equations of motion, are conformally equivalent to regular spacetimes. Finally, we prove that the ...
Causal cells: spacetime polytopes with null hyperfaces
Neiman, Yasha
2012-01-01
We consider polyhedra and 4-polytopes in Minkowski spacetime - in particular, null polyhedra with zero volume, and 4-polytopes that have such polyhedra as their hyperfaces. We present the basic properties of several classes of null-faced 4-polytopes: 4-simplices, "tetrahedral diamonds" and 4-parallelotopes. We propose a "most regular" representative of each class. The most-regular parallelotope is of particular interest: its edges, faces and hyperfaces are all congruent, and it features both null hyperplanes and null segments. A tiling of spacetime with copies of this polytope can be viewed alternatively as a lattice with null edges, such that each point is at the intersection of four lightrays in a tetrahedral pattern. We speculate on the relevance of this construct for discretizations of curved spacetime and for quantum gravity.
Deformed symmetries in noncommutative and multifractional spacetimes
Calcagni, Gianluca
2016-01-01
We clarify the relation between noncommutative spacetimes and multifractional geometries where the spacetime dimension changes with the probed scale. In the absence of curvature and comparing the symmetries of both position and momentum space, we show that $\\kappa$-Minkowski spacetime and the commutative multifractional theory with $q$-derivatives are physically inequivalent but they admit several contact points that allow one to describe certain aspects of $\\kappa$-Minkowski noncommutative geometry as a multifractional theory and vice versa. Contrary to previous literature, this result holds without assuming any specific measure for $\\kappa$-Minkowski. More generally, no well-defined $\\star$-product can be constructed from the $q$-theory, although the latter does admit a natural noncommutative extension with a given deformed Poincar\\'e algebra. A similar no-go theorem may be valid for all multiscale theories with factorizable measures. Turning gravity on, we write the algebras of gravitational first-class co...
Passive Lorentz transformations with spacetime algebra
Paiva, C R
2005-01-01
In special relativity spacetime algebra developed by David Hestenes, STA, provides a powerful and insightful approach to an invariant formulation of physics, the spacetime physics, through an elegant and concise manipulation of active Lorentz transformations. Therefore, it should come as an oddity, to say the least, to relate STA with passive Lorentz transformations. Nevertheless, length contraction, time dilation and all that are the bread and butter of most introductory courses on relativistic physics. To overcome the coordinate virus, it is necessary to be able to translate and dissolve passive Lorentz transformations in the fluidity and flexibility of STA, thereby bridging the gap between relativistic physics and proper spacetime physics. That is the aim of this paper.
Anisotropic inflation in the Finsler spacetime
Li, Xin [Chongqing University, Department of Physics, Chongqing (China); Institute of Theoretical Physics, Chinese Academy of Sciences, State Key Laboratory of Theoretical Physics, Beijing (China); Wang, Sai [Institute of Theoretical Physics, Chinese Academy of Sciences, State Key Laboratory of Theoretical Physics, Beijing (China); Chang, Zhe [Institute of Theoretical Physics, Chinese Academy of Sciences, State Key Laboratory of Theoretical Physics, Beijing (China); Institute of High Energy Physics, Chinese Academy of Sciences, Beijing (China)
2015-06-15
We suggest the universe is Finslerian in the stage of inflation. The Finslerian background spacetime breaks rotational symmetry and induces parity violation. The primordial power spectrum is given for the quantum fluctuation of the inflation field. It depends not only on the magnitude of the wavenumber but also on the preferred direction. We derive the gravitational field equations in the perturbed Finslerian background spacetime, and we obtain a conserved quantity outside the Hubble horizon. The angular correlation coefficients are presented in our anisotropic inflation model. The parity violation feature of Finslerian background spacetime requires that the anisotropic effect only appears in the angular correlation coefficients if l' = l + 1. The numerical results of the angular correlation coefficients are given describing the anisotropic effect. (orig.)
On the Existence of Spacetime Structure
Curiel, E
2015-01-01
I examine the debate between substantivalists and relationalists about the ontological character of spacetime and conclude it is not well posed. I argue that the so-called Hole Argument does not bear on the debate, because it provides no clear criterion to distinguish the positions. I propose two such precise criteria and construct separate arguments based on each to yield contrary conclusions, one supportive of something like relationalism and the other of something like substantivalism. The lesson is that one must fix an investigative context in order to make such criteria precise, but different investigative contexts yield inconsistent results. I examine questions of existence about spacetime structures other than the spacetime manifold itself to argue that it is more fruitful to focus on pragmatic issues of physicality, a notion that lends itself to several different explications, all of philosophical interest, none privileged a priori over any of the others. I conclude by suggesting an extension of the l...
Causal structure and electrodynamics on Finsler spacetimes
Pfeifer, Christian; Wohlfarth, Mattias N. R.
2011-08-01
We present a concise new definition of Finsler spacetimes that generalizes Lorentzian metric manifolds and provides consistent backgrounds for physics. Extending standard mathematical constructions known from Finsler spaces, we show that geometric objects like the Cartan nonlinear connection and its curvature are well defined almost everywhere on Finsler spacetimes, including their null structure. This allows us to describe the complete causal structure in terms of timelike and null curves; these are essential to model physical observers and the propagation of light. We prove that the timelike directions form an open convex cone with a null boundary, as is the case in Lorentzian geometry. Moreover, we develop action integrals for physical field theories on Finsler spacetimes, and tools to deduce the corresponding equations of motion. These are applied to construct a theory of electrodynamics that confirms the claimed propagation of light along Finsler null geodesics.
Causal structure and electrodynamics on Finsler spacetimes
Pfeifer, Christian
2011-01-01
We present a concise new definition of Finsler spacetimes that generalize Lorentzian metric manifolds and provide consistent backgrounds for physics. Extending standard mathematical constructions known from Finsler spaces we show that geometric objects like the Cartan non-linear connection and its curvature are well-defined almost everywhere on Finsler spacetimes, also on their null structure. This allows us to describe the complete causal structure in terms of timelike and null curves; these are essential to model physical observers and the propagation of light. We prove that the timelike directions form an open convex cone with null boundary as is the case in Lorentzian geometry. Moreover, we develop action integrals for physical field theories on Finsler spacetimes, and tools to deduce the corresponding equations of motion. These are applied to construct a theory of electrodynamics that confirms the claimed propagation of light along Finsler null geodesics.
On the Decomposition of the Spacetime Metric Tensor and of Tensor Fields in Strained Spacetime
Millette P. A.
2012-10-01
Full Text Available We propose a natural decomposition of the spacetime metric tensor of General Relativ- ity into a background and a dynamical part based on an analysis from first principles of the effect of a test mass on the background metric. We find that the presence of mass results in strains in the spacetime continuum. Those strains correspond to the dy- namical part of the spacetime metric tensor. We then apply the stress-strain relation of Continuum Mechanics to the spacetime continuum to show that rest-mass energy den- sity arises from the volume dilatation of the spacetime continuum. Finally we propose a natural decomposition of tensor fields in strained spacetime, in terms of dilatations and distortions. We show that dilatations correspond to rest-mass energy density, while distortions correspond to massless shear transverse waves. We note that this decom- position in a massive dilatation and a massless transverse wave distortion, where both are present in spacetime continuum deformations, is somewhat reminiscent of wave- particle duality. We note that these results are considered to be local effects in the particular reference frame of the observer. In addition, the applicability of the proposed metric to the Einstein field equations remains open.
Space-Time Approximation with Sparse Grids
Griebel, M; Oeltz, D; Vassilevski, P S
2005-04-14
In this article we introduce approximation spaces for parabolic problems which are based on the tensor product construction of a multiscale basis in space and a multiscale basis in time. Proper truncation then leads to so-called space-time sparse grid spaces. For a uniform discretization of the spatial space of dimension d with O(N{sup d}) degrees of freedom, these spaces involve for d > 1 also only O(N{sup d}) degrees of freedom for the discretization of the whole space-time problem. But they provide the same approximation rate as classical space-time Finite Element spaces which need O(N{sup d+1}) degrees of freedoms. This makes these approximation spaces well suited for conventional parabolic and for time-dependent optimization problems. We analyze the approximation properties and the dimension of these sparse grid space-time spaces for general stable multiscale bases. We then restrict ourselves to an interpolatory multiscale basis, i.e. a hierarchical basis. Here, to be able to handle also complicated spatial domains {Omega}, we construct the hierarchical basis from a given spatial Finite Element basis as follows: First we determine coarse grid points recursively over the levels by the coarsening step of the algebraic multigrid method. Then, we derive interpolatory prolongation operators between the respective coarse and fine grid points by a least squares approach. This way we obtain an algebraic hierarchical basis for the spatial domain which we then use in our space-time sparse grid approach. We give numerical results on the convergence rate of the interpolation error of these spaces for various space-time problems with two spatial dimensions. Also implementational issues, data structures and questions of adaptivity are addressed to some extent.
Black-hole horizons as probes of black-hole dynamics I: post-merger recoil in head-on collisions
Jaramillo, José Luis; Moesta, Philipp; Rezzolla, Luciano
2011-01-01
The understanding of strong-field dynamics near black-hole horizons is a long-standing and challenging problem in general relativity. Recent advances in numerical relativity and in the geometric characterization of black-hole horizons open new avenues into the problem. In this first paper in a series of two, we focus on the analysis of the recoil occurring in the merger of binary black holes, extending the analysis initiated in [1] with Robinson-Trautman spacetimes. More specifically, we probe spacetime dynamics through the correlation of quantities defined at the black-hole horizon and at null infinity. The geometry of these hypersurfaces responds to bulk gravitational fields acting as test screens in a scattering perspective of spacetime dynamics. Within a 3+1 approach we build an effective-curvature vector from the intrinsic geometry of dynamical-horizon sections and correlate its evolution with the flux of Bondi linear momentum at large distances. We employ this setup to study numerically the head-on coll...
The birth of spacetime atoms as the passage of time
Dowker, Fay
2014-01-01
The view that the passage of time is physical finds expression in the classical sequential growth models of Rideout and Sorkin in which a discrete spacetime grows by the partially ordered accretion of new spacetime atoms.
Fermions without Vierbeins in Curved Space-Time
Weldon, H A
2001-01-01
A general formulation of spinor fields in Riemannian space-time is given without using vierbeins. The space-time dependence of the Dirac matrices required by the anticommutation relation {\\gamma_{\\mu},\\gamma_{\
Charged fluid distribution in higher dimensional spheroidal space-time
G P Singh; S Kotambkar
2005-07-01
A general solution of Einstein field equations corresponding to a charged fluid distribution on the background of higher dimensional spheroidal space-time is obtained. The solution generates several known solutions for superdense star having spheroidal space-time geometry.
String theory in curved space-time
Viswanathan, K S
1997-01-01
Intrinsic and extrinsic geometric properties of string world sheets in curved space-time background are explored. In our formulation, the only dynamical degrees of freedom of the string are its immersion coordinates. Classical equation of motion and the space-time energy-momentum tensor of the string are obtained. The equations of motion for the extrinsic curvature action are second order for the scalar mean curvature of the world sheet. 1-loop divergent terms are calculated using the background field method. Asymptotic freedom of the extrinsic curvature coupling is established.
A proposal of foundation of spacetime geometry
Tresguerres, Romualdo
2014-01-01
A common approach to metric-affine, local Poincar\\'e, special-relativistic and Galilei spacetime geometry is developed. Starting from an affine composite bundle, we introduce local reference frames and their evolution along worldlines and we study both, absolute and relative simultaneity postulates, giving rise to alternative concepts of spacetime. In particular, the construction of the Minkowski metric, and its required invariance, allows either to reorganize the original affine bundle as a metric-affine geometry with explicit Lorentz symmetry, or to restrict it to a Poincar\\'e geometry, both of them constituting the background of a wide class of gauge theories of gravity.
Spacetime foam in twistor string theory
Hartnoll, S A; Hartnoll, Sean A.; Policastro, Giuseppe
2004-01-01
We show how a Kahler spacetime foam in four dimensional conformal (super)gravity may be mapped to twistor spaces carrying the D1 brane charge of the B model topological string theory. The spacetime foam is obtained by blowing up an arbitrary number of points in $\\C^2$ and can be interpreted as a sum over gravitational instantons. Some twistor spaces for blowups of $\\C^2$ are known explicitly. In these cases we write down a meromorphic volume form and suggest a relation to a holomorphic superform on a corresponding super Calabi-Yau manifold.
Special relativity derived from spacetime magma.
Greensite, Fred
2014-01-01
We present a derivation of relativistic spacetime largely untethered from specific physical considerations, in constrast to the many physically-based derivations that have appeared in the last few decades. The argument proceeds from the inherent magma (groupoid) existing on the union of spacetime frame components [Formula: see text] and Euclidean [Formula: see text] which is consistent with an "inversion symmetry" constraint from which the Minkowski norm results. In this context, the latter is also characterized as one member of a class of "inverse norms" which play major roles with respect to various unital [Formula: see text]-algebras more generally.
Perturbative spacetimes from Yang-Mills theory
Luna, Andrés; Nicholson, Isobel; Ochirov, Alexander; O'Connell, Donal; Westerberg, Niclas; White, Chris D.
2017-04-12
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
Space-time duality and superduality
Burgess, C P; Kamela, M; Knutt-Wehlau, M E; Page, P; Quevedo, Fernando; Zebarjad, M
1999-01-01
We introduce a new class of duality symmetries amongst quantum field theories. The new class is based upon global space-time symmetries, such as Poincare invariance and supersymmetry, in the same way as the existing duality transformations are based on global internal symmetries. We illustrate these new duality transformations by dualizing several scalar and spin-half field theories in 1 + 1 space-time dimensions, involving non-supersymmetric as well as (1, 1) and (2, 2) supersymmetric models. For (2, 2) models the new duality transformations can interchange chiral and twisted chiral multiplets.
Heterotic String Models in Curved Spacetime
Bars, Itzhak
1992-01-01
We explore the possibility of string theories in only four spacetime dimensions without any additional compactified dimensions. We show that, provided the theory is defined in curved spacetime that has a cosmological interpration, it is possible to construct consistent heterotic string theories based on a few non-compact current algebra cosets. We classify these models. The gauge groups that emerge fall within a remarkably narrow range and include the desirable low energy flavor symmetry of $SU(3)\\times SU(2)\\times U(1)$. The quark and lepton states, which come in color triplets and $SU(2)$ doublets, are expected to emerge in several families.
Pair creation in noncommutative space-time
Hamil, B.; Chetouani, L.
2016-09-01
By taking two interactions, the Volkov plane wave and a constant electromagnetic field, the probability related to the process of pair creation from the vacuum is exactly and analytically determined via the Schwinger method in noncommutative space-time. For the plane wave, it is shown that the probability is simply null and for the electromagnetic wave it is found that the expression of the probability has a similar form to that obtained by Schwinger in a commutative space-time. For a certain critical value of H, the probability is simply equal to 1.
Perturbative spacetimes from Yang-Mills theory
Luna, Andres; Nicholson, Isobel; Ochirov, Alexander; O'Connell, Donal; Westerberg, Niclas; White, Chris D.
2016-01-01
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
Generalised hyperbolicity in spacetimes with singular submanifolds
Sanchez, Yafet Sanchez
2015-01-01
The idea of defining a gravitational singularity as an obstruction to the dynamical evolution of a test field (described by a PDE) rather than the dynamical evolution of a particle (described by a geodesics) is explored. In this paper we obtain general conditions under which the wave equation is well-posed in spacetimes with weak singularities in which the singularity is concentrated in a submanifold. In particular, the results can be applied to spacetimes with shell-crossing singularities, surface layers and generalised cosmic strings.
Inflationary spacetimes are incomplete in past directions.
Borde, Arvind; Guth, Alan H; Vilenkin, Alexander
2003-04-18
Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating--or just expanding sufficiently fast--must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.
Special relativity derived from spacetime magma.
Fred Greensite
Full Text Available We present a derivation of relativistic spacetime largely untethered from specific physical considerations, in constrast to the many physically-based derivations that have appeared in the last few decades. The argument proceeds from the inherent magma (groupoid existing on the union of spacetime frame components [Formula: see text] and Euclidean [Formula: see text] which is consistent with an "inversion symmetry" constraint from which the Minkowski norm results. In this context, the latter is also characterized as one member of a class of "inverse norms" which play major roles with respect to various unital [Formula: see text]-algebras more generally.
Astrophysics of Bertrand Space-times
Dey, Dipanjan; Sarkar, Tapobrata
2013-01-01
We construct a model for galactic dark matter that arises as a solution of Einstein gravity, and is a Bertrand space-time matched with an external Schwarzschild metric. This model can explain galactic rotation curves. Further, we study gravitational lensing in these space-times, and in particular we consider Einstein rings, using the strong lensing formalism of Virbhadra and Ellis. Our results are in good agreement with observational data, and indicate that under certain conditions, gravitational lensing effects from galactic dark matter may be similar to that from Schwarzschild backgrounds.
Tidal forces in Reissner-Nordstroem spacetimes
Crispino, Luis C.B.; Oliveira, Ednilton S. de [Universidade Federal do Para, Faculdade de Fisica, Belem, Para (Brazil); Higuchi, Atsushi; Oliveira, Leandro A. [University of York, Department of Mathematics, York (United Kingdom)
2016-03-15
We analyze the tidal forces produced in the spacetime of Reissner-Nordstroem black holes. We point out that the radial component of the tidal force changes sign just outside the event horizon if the charge-to-mass ratio is close to 1, unlike in Schwarzschild spacetime of uncharged black holes, and that the angular component changes sign between the outer and inner horizons. We solve the geodesic deviation equations for radially falling bodies toward the charged black hole. We find, for example, that the radial component of the geodesic deviation vector starts decreasing inside the event horizon unlike in the Schwarzschild case. (orig.)
Space-time framework of internal measurement
Matsuno, Koichiro
1998-07-01
Measurement internal to material bodies is ubiquitous. The internal observer has its own local space-time framework that enables the observer to distinguish, even to a slightest degree, those material bodies fallen into that framework. Internal measurement proceeding among the internal observers come to negotiate a construction of more encompassing local framework of space and time. The construction takes place through friction among the internal observers. Emergent phenomena are related to an occurrence of enlarging the local space-time framework through the frictional negotiation among the material participants serving as the internal observers. Unless such a negotiation is obtained, the internal observers would have to move around in the local space-time frameworks of their own that are mutually incommensurable. Enhancement of material organization as demonstrated in biological evolutionary processes manifests an inexhaustible negotiation for enlarging the local space-time framework available to the internal observers. In contrast, Newtonian space-time framework, that remains absolute and all encompassing, is an asymptote at which no further emergent phenomena could be expected. It is thus ironical to expect something to emerge within the framework of Newtonian absolute space and time. Instead of being a complex and organized configuration of interaction to appear within the global space-time framework, emergent phenomena are a consequence of negotiation among the local space-time frameworks available to internal measurement. Most indicative of the negotiation of local space-time frameworks is emergence of a conscious self grounding upon the reflexive nature of perceptions, that is, a self-consciousness in short, that certainly goes beyond the Kantian transcendental subject. Accordingly, a synthetic discourse on securing consciousness upon the ground of self-consciousness can be developed, though linguistic exposition of consciousness upon self
Hawking effect of Dirac particles in non-stationary Kerr space-time
黎忠恒; 赵峥
1995-01-01
In the process of dealing with the Hawking effect of Dirac particles in the non-stationary Kerr space-time, a new universal method to define the generalized Tortoise coordinate transformation is given. By means of this coordinate transformation, one can discuss the properties of the dynamical equation of particles near event horizons, and get automatically the temperature of Hawking radiation using the method suggested by Damour and others, and thereby dodge the difficulties in calculating the renormalised energy-momentum tensor.
Numerical Relativity in D dimensional space-times: Collisions of unequal mass black holes
Witek, Helvi; Cardoso, Vitor; Sperhake, Ulrich [CENTRA, Departamento de Fisica, Instituto Superior Tecnico, Universidade Tecnica de Lisboa - UTL, Av. Rovisco Pais 1, 1049 Lisboa (Portugal); Gualtieri, Leonardo [Dipartimento di Fisica, Universita di Roma ' Sapienza' and Sezione INFN Roma1, P.A. Moro 5, 00185, Roma (Italy); Herdeiro, Carlos [Departamento de Fisica da Universidade de Aveiro, Campus de Santiago, 3810-183 Aveiro (Portugal); Zilhao, Miguel, E-mail: helvi.witek@ist.utl.pt [Centro de Fisica do Porto - CFP, Departamento de Fisica e Astronomia, Faculdade de Ciencias da Universidade do Porto - FCUP, Rua do Campo Alegre, 4169-007 Porto (Portugal)
2011-09-22
We present unequal mass head-on collisions of black holes in D = 5 dimensional space-times. We have simulated BH systems with mass ratios q 1,1/2, 1/3, 1/4. We extract the total energy radiated throughout the collision and compute the linear momentum flux and the recoil velocity of the final black hole. The numerical results show very good agreement with point particle calculations when extrapolated to this limit.
Dirac Field in FRW Spacetime: Current and Energy Momentum
Dhungel, P R
2011-01-01
The behaviour of the Dirac field in FRW space-time is investigated. The relevant equations are solved to determine the particle and energy distribution. The angular and radial parts are solved in terms of Jacobi polynomials. The time dependence of the massive field is solved in terms of known function only for the radiation filled flat space. WKB method is used for approximate solution in general Friedmann-Le Maitre space. The negative energy solution is found decay in time as the Universe expands, while the positive energy solution grows. This could be the source of the local particle current. The behaviour of the particle number and energy density are also investigated. It is found that the particles arrange themselves in a number and density distribution pattern that produces a constant Newtonian potential as required for the flat rotation curves of galaxies. Further, density contrast is found to grow with the expansion.
Spacetime quantization effects on 5-dimensional black string evaporation
Li, Xiang-Qian
2016-01-01
Spacetime quantization predicts the existence of minimal length and time-interval. Within 5-dimensional Schwarzschild-like black string background, the tunneling of scalar particles, fermions and massive bosons are first studied together in the same generalized uncertainty principle framework. It is found that, the minimal length and time-interval effect weakens the original Hawking radiation. To $\\mathcal{O}(\\frac{1}{M_f^2})$, the corrected temperatures depend on not only the mass of black string, but also the mass and angular momentum of emitted particles. The temperature correction for massive bosons is four times as big as that for scalar particles and fermions. As a result, the bosons cease to tunnel from the black string before the scalar particles and fermions do. The evaporation remnant is expected in our analysis, however it should be verified by full quantum gravity theory.
Experimenting with Quantum Fields in Curved Spacetime in the Lab
Prémont-Schwarz, Isabeau
2011-01-01
In this paper we will investigate how one can create emergent curved spacetimes by locally tuning the coupling constants of condensed matter systems. In the continuum limit we thus obtain continuous effective quantum fields living on curved spacetimes. In particular, using Stingnet condensates we can obtain effective electromagnetism. We will show for example how we obtain quantum electrodynamics in a blackhole (Schwarzschild) spacetime.
Maxwell-Higgs equation on higher dimensional static curved spacetimes
Mulyanto, Akbar, Fiki Taufik; Gunara, Bobby Eka
2015-09-01
In this paper we consider a class of solutions of Maxwell-Higgs equation in higher dimensional static curved spacetimes called Schwarzchild de-Sitter spacetimes. We obtain the general form of the electric fields and magnetic fields in background Schwarzchild de-Sitter spacetimes. However, determining the interaction between photons with the Higgs scalar fields is needed further studies.
Spacetime Variation of Lorentz-Violation Coefficients at Nonrelativistic Scale
Lane, Charles D
2016-01-01
When the Standard-Model Extension (SME) is applied in curved spacetime, the Lorentz-violation coefficients must depend on spacetime position. This work describes some of the consequences of this spacetime variation. We focus on effects that appear at a nonrelativistic scale and extract sensitivity of completed experiments to derivatives of SME coefficient fields.
Maxwell-Higgs equation on higher dimensional static curved spacetimes
Mulyanto, E-mail: mulyanto37@gmail.com [Theoretical Physics Laboratory, Theoretical High Energy Physics and Instrumentation Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10 Bandung 40132 (Indonesia); Akbar, Fiki Taufik, E-mail: ftakbar@fi.itb.ac.id; Gunara, Bobby Eka, E-mail: bobby@fi.itb.ac.id [Theoretical Physics Laboratory, Theoretical High Energy Physics and Instrumentation Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10 Bandung 40132 (Indonesia); Indonesia Center for Theoretical and Mathematical Physics (ICTMP) (Indonesia)
2015-09-30
In this paper we consider a class of solutions of Maxwell-Higgs equation in higher dimensional static curved spacetimes called Schwarzchild de-Sitter spacetimes. We obtain the general form of the electric fields and magnetic fields in background Schwarzchild de-Sitter spacetimes. However, determining the interaction between photons with the Higgs scalar fields is needed further studies.
Quantum Space-Time and Reference Frames in Gravity and Flat Space-Time
Mayburov, S
2000-01-01
The quantum space-time model which accounts material Reference Frames (RF) quantum effects considered for flat space-time and ADM canonical gravity. As was shown by Aharonov for RF - free material object its c.m. nonrelativistic motion in vacuum described by Schrodinger wave packet evolution which modify space coordinate operator of test particle in this RF and changes its Heisenberg uncertainty relations. In the relativistic case we show that Lorentz transformations between two RFs include the quantum corrections for RFs momentum uncertainty and in general can be formulated as the quantum space-time transformations. As the result for moving RF its Lorentz time boost acquires quantum fluctuations which calculated solving relativistic Heisenberg equations for the quantum clocks models. It permits to calculate RF proper time for the arbitrary RF quantum motion including quantum gravity metrics fluctuations. Space-time structure of canonical Quantum Gravity and its observables evolution for RF proper time discus...
Naka, S.; Toyoda, H.; Takanashi, T.; Umezawa, E.
2014-04-01
In kappa -Minkowski spacetime, the coordinates are Lie algebraic elements such that time and space coordinates do not commute, whereas space coordinates commute with each other. The noncommutativity is proportional to a Planck-length-scale constant kappa ^{-1}, which is a universal constant other than the velocity of light, under the kappa -Poincaré transformation. In this sense, the spacetime has a structure called "doubly special relativity." Such a noncommutative structure is known to be realized by SO(1,4) generators in 4-dimensional de Sitter space. In this paper, we try to construct a noncommutative spacetime having a commutative n-dimensional Minkowski spacetime based on AdS_{n+1} space with SO(2,n) symmetry. We also study an invariant wave equation corresponding to the first Casimir invariant of this symmetry as a nonlocal field equation expected to yield finite loop amplitudes.
Stringy Models of Modified Gravity: Space-time defects and Structure Formation
Mavromatos, Nick E.
2013-01-01
Starting from microscopic models of space-time foam, based on brane universes propagating in bulk space-times populated by D0-brane defects ("D-particles"), we arrive at effective actions used by a low-energy observer on the brane world to describe his/her observations of the Universe. These actions include, apart from the metric tensor field, also scalar (dilaton) and vector fields, the latter describing the interactions of low-energy matter on the brane world with the recoiling point-like space-time defect (D-particle). The vector field is proportional to the recoil velocity of the D-particle and as such it satisfies a certain constraint. The vector breaks locally Lorentz invariance, which however is assumed to be conserved on average in a space-time foam situation, involving the interaction of matter with populations of D-particle defects. In this paper we demonstrate that, already at the end of the radiation era, the (constrained) vector field associated with the recoil of the defects provides the seeds f...
Proper Time in Weyl space-time
Avalos, R; Romero, C
2016-01-01
We discuss the question of whether or not a general Weyl structure is a suitable mathematical model of space-time. This is an issue that has been in debate since Weyl formulated his unified field theory for the first time. We do not present the discussion from the point of view of a particular unification theory, but instead from a more general standpoint, in which the viability of such a structure as a model of space-time is investigated. Our starting point is the well known axiomatic approach to space-time given by Elhers, Pirani and Schild (EPS). In this framework, we carry out an exhaustive analysis of what is required for a consistent definition for proper time and show that such a definition leads to the prediction of the so-called "second clock effect". We take the view that if, based on experience, we were to reject space-time models predicting this effect, this could be incorporated as the last axiom in the EPS approach. Finally, we provide a proof that, in this case, we are led to a Weyl integrable ...
p-form electromagnetism on discrete spacetimes
Wise, Derek K [Department of Mathematics, University of California, Riverside, CA 92521 (United States)
2006-09-07
We investigate p-form electromagnetism-with the Maxwell and Kalb-Ramond fields as lowest-order cases-on discrete spacetimes, including not only the regular lattices commonly used in lattice gauge theory, but also more general examples. After constructing a maximally general model of discrete spacetime suitable for our purpose-a chain complex equipped with an inner product on (p + 1)-cochains-we study both the classical and quantum versions of the theory, with either R or U(1) as gauge group. We find results-such as a 'p-form Bohm-Aharonov effect'-that depend in interesting ways on the cohomology of spacetime. We quantize the theory via the Euclidean path integral formalism, where the natural kernels in the U(1) theory are not Gaussians but theta functions. As a special case of the general theory, we show that p-form electromagnetism in p + 1 dimensions has an exact solution which reduces when p = 1 to the Abelian case of 2D Yang-Mills theory as studied by Migdal and Witten. Our main result describes p-form electromagnetism as a 'chain field theory'-a theory analogous to a topological quantum field theory, but with chain complexes replacing manifolds. This makes precise a notion of time evolution in the context of discrete spacetimes of arbitrary topology.
Wave Equations in Bianchi Space-Times
S. Jamal
2012-01-01
Full Text Available We investigate the wave equation in Bianchi type III space-time. We construct a Lagrangian of the model, calculate and classify the Noether symmetry generators, and construct corresponding conserved forms. A reduction of the underlying equations is performed to obtain invariant solutions.
Communicating with Accelerated Observers in Minkowski Spacetime
FLores, F. J.
2008-01-01
Our goal here is to determine the spatial and temporal constraints on communication between two observers at least one of which moves with constant proper acceleration in two-dimensional Minkowski spacetime. We take as a simplified model of communication one observer bouncing a light signal off another observer. Our derivations use only elementary…
Cosmological constant influence on cosmic string spacetime
Abbassi, Amir H; 10.1103/physRevD.67.103504
2008-01-01
We investigate the line element of spacetime around a linear cosmic string in the presence of a cosmological constant. We obtain the metric and argue that it should be discarded because of asymptotic considerations. Then a time dependent and consistent form of the metric is obtained and its properties are discussed.
Chaos in Kundt Type-Ⅲ Spacetimes
I. Sakalli; M. Halilsoy
2011-01-01
We consider geodesic motion in a particular Kundt type-Ⅲ spacetime in which the Einstein-Yang-Mills equations admit the solutions. On a particular surface as constraint,we project the geodesics into the (x,y) plane and treat the problem as a two-dimensional one.Our numerical study shows that chaotic behavior emerges under reasonable conditions.
Quantum singularity of Levi-Civita spacetimes
Konkowski, Deborah; Helliwell, Thomas; Wieland, Chris; Reese, Cassidi
2004-05-01
Quantum singularities in general relativistic spacetimes are determined by the behavior of quantum test particles. A static spacetime is quantum mechanically singular [G.T. Horowitz and D. Marolf, Phys. Rev. D52, 5670 (1995)] if the spatial portion of the wave operator is not essentially self-adjoint on a C_0^∞ domain in L^2, a Hilbert space of square integrable functions. Here Weyl's limit point-limit circle criterion [M. Reed and B. Simon, Fourier Analysis and Self-Adjointness (New York: Academic Press, 1972)] is used to determine whether a wave operator is essentially self-adjoint. This test is then applied to scalar wave packets in Levi-Civita spacetimes with and without a cosmological constant to help elucidate the physical properties of the spacetimes. This discussion is based in part on a paper by D.A. Konkowski, T.M. Helliwell and C. Wieland [Class. Quantum Grav., 21, 265 (2004)]. Finally, the importance of the underlying Hilbert space is considered through a comparison in this instance of the notion of quantum singularity with the notion of wave singularity [A. Ishibashi and A. Hosoya, Phys. Rev. D60, 104028 (1999)].
The charged McVittie spacetime
Faraoni, Valerio; Prain, Angus
2014-01-01
The two-parameter charged McVittie solution of the Einstein equations is revisited and its apparent horizons are discussed and located numerically (for the extremal case, analytically). According to the parameter values, this spacetime can be interpreted as a black hole, or a spacelike naked singularity, in a spatially homogeneous and isotropic universe.
Energy Gaps in a Spacetime Crystal
Horwitz, L P
2009-01-01
This paper presents an analysis of the band structure of a spacetime potential lattice created by a standing electromagnetic wave. We show that there are energy band gaps. We estimate the effect, and propose a measurement that could confirm the existence of such phenomena.
Energy Distribution in LTB Space-time
Salti, M; Salti, Mustafa; Havare, Ali
2005-01-01
Using general relativity analogs of Bergmann-Thomson, Papapetrou, Landau-Lifshitz and Einstein energy and momentum definitions, we find the energy distribution (due to matter plus fields) in the LTB Space-time. The energy distribution is found well defined and the same in all of these energy-momentum complexes.
Geometry of Minkowski Space-Time
Catoni, Francesco; Cannata, Roberto; Catoni, Vincenzo; Zampetti, Paolo
2011-01-01
This book provides an original introduction to the geometry of Minkowski space-time. A hundred years after the space-time formulation of special relativity by Hermann Minkowski, it is shown that the kinematical consequences of special relativity are merely a manifestation of space-time geometry. The book is written with the intention of providing students (and teachers) of the first years of University courses with a tool which is easy to be applied and allows the solution of any problem of relativistic kinematics at the same time. The book treats in a rigorous way, but using a non-sophisticated mathematics, the Kinematics of Special Relativity. As an example, the famous "Twin Paradox" is completely solved for all kinds of motions. The novelty of the presentation in this book consists in the extensive use of hyperbolic numbers, the simplest extension of complex numbers, for a complete formalization of the kinematics in the Minkowski space-time. Moreover, from this formalization the understanding of gravity co...
Riemann curvature of a boosted spacetime geometry
Battista, Emmanuele; Esposito, Giampiero; Scudellaro, Paolo; Tramontano, Francesco
2016-10-01
The ultrarelativistic boosting procedure had been applied in the literature to map the metric of Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface. This paper evaluates the Riemann curvature tensor of the boosted Schwarzschild-de Sitter metric by means of numerical calculations, which make it possible to reach the ultrarelativistic regime gradually by letting the boost velocity approach the speed of light. Thus, for the first time in the literature, the singular limit of curvature, through Dirac’s δ distribution and its derivatives, is numerically evaluated for this class of spacetimes. Moreover, the analysis of the Kretschmann invariant and the geodesic equation shows that the spacetime possesses a “scalar curvature singularity” within a 3-sphere and it is possible to define what we here call “boosted horizon”, a sort of elastic wall where all particles are surprisingly pushed away, as numerical analysis demonstrates. This seems to suggest that such “boosted geometries” are ruled by a sort of “antigravity effect” since all geodesics seem to refuse to enter the “boosted horizon” and are “reflected” by it, even though their initial conditions are aimed at driving the particles toward the “boosted horizon” itself. Eventually, the equivalence with the coordinate shift method is invoked in order to demonstrate that all δ2 terms appearing in the Riemann curvature tensor give vanishing contribution in distributional sense.
Optics in the Schwarzschild space-time
Cadez, A; Cadez, Andrej; Kostic, Uros
2004-01-01
Light coming from the strong gravity region in the vicinity of a black hole is marked by large Doppler shifts, redshifts and aberration effects. In order to understand these effects it is useful to solve the light propagation problem between any two given points in the curved space of a black hole. Here we describe the complete solution for the Schwarzschild space-time.
The Thermal Entropy Density of Spacetime
Rongjia Yang
2013-01-01
Full Text Available Introducing the notion of thermal entropy density via the first law of thermodynamics and assuming the Einstein equation as an equation of thermal state, we obtain the thermal entropy density of any arbitrary spacetime without assuming a temperature or a horizon. The results confirm that there is a profound connection between gravity and thermodynamics.
Kundt spacetimes minimally coupled to scalar field
Tahamtan, T. [Charles University, Institute of Theoretical Physics, Faculty of Mathematics and Physics, Prague 8 (Czech Republic); Astronomical Institute, Czech Academy of Sciences, Prague (Czech Republic); Svitek, O. [Charles University, Institute of Theoretical Physics, Faculty of Mathematics and Physics, Prague 8 (Czech Republic)
2017-06-15
We derive an exact solution belonging to the Kundt class of spacetimes both with and without a cosmological constant that are minimally coupled to a free massless scalar field. We show the algebraic type of these solutions and give interpretation of the results. Subsequently, we look for solutions additionally containing an electromagnetic field satisfying nonlinear field equations. (orig.)
SPACE-TIME ESTIMATE TO HEAT EQUATION
2007-01-01
In this article, we prove the Strichartz type estimate for the solutions of linear heat equation with initial data in Hardy space H1(Rd). As an application, we obtain the full space-time estimate to the solutions of heat equation with initial data in LP(Rd) for 1＜p＜∞.
Quantum teleportation and Kerr-Newman spacetime
Ge Xian-Hui; Shen You-Gen
2005-01-01
We consider the teleportation in the background of Kerr-Newman spacetime. Because of the Hawking effect, the fidelity of the teleportation is reduced. The results also show the fidelity is closely related to the mass, charge and rotating velocity of the black hole: high fidelity can be reached for massive, slowly rotating Kerr-Newman black holes.
Space-time topology (II) - Causality, the fourth Stiefel-Whitney class and space-time as a boundary
Flagga, MSN; Antonsen, F
We show that stable causality is related to the vanishing of the top Stiefel - Whitney class of a space-time manifold M, and that if M is a stably causal space-time manifold, then it is the boundary of a five-dimensional space-time. We then propose a scheme for making it both a necessary and
Dynamical spacetimes and gravitational radiation in a Fully Constrained Formulation
Cordero-Carrión, Isabel; Ibáñez, José María
2010-01-01
This contribution summarizes the recent work carried out to analyze the behavior of the hyperbolic sector of the Fully Constrained Formulation (FCF) derived in Bonazzola et al. 2004. The numerical experiments presented here allows one to be confident in the performances of the upgraded version of CoCoNuT's code by replacing the Conformally Flat Condition (CFC) approximation of the Einstein equations by the FCF.
Dynamical spacetimes and gravitational radiation in a Fully Constrained Formulation
Cordero-Carrion, Isabel; Ibanez, Jose MarIa [Departamento de Astronomia y Astrofisica, Universidad de Valencia, C/ Dr. Moliner 50, E-46100 Burjassot, Valencia (Spain); Cerda-Duran, Pablo, E-mail: isabel.cordero@uv.e, E-mail: cerda@mpa-garching.mpg.d, E-mail: jose.m.ibanez@uv.e [Max-Planck-Institut fuer Astrophysik, Karl-Schwarzschild-Strasse 1, D-85741 Garching (Germany)
2010-05-01
This contribution summarizes the recent work carried out to analyze the behavior of the hyperbolic sector of the Fully Constrained Formulation (FCF) derived in Bonazzola et al. 2004. The numerical experiments presented here allows one to be confident in the performances of the upgraded version of CoCoNuT's code by replacing the Conformally Flat Condition (CFC) approximation of the Einstein equations by the FCF.
Is classical flat Kasner spacetime flat in quantum gravity?
Singh, Parampreet
2016-01-01
Quantum nature of classical flat Kasner spacetime is studied using effective spacetime description in loop quantum cosmology. We find that even though the spacetime curvature vanishes at the classical level, non-trivial quantum gravitational effects can arise. For the standard loop quantization of Bianchi-I spacetime, which uniquely yields universal bounds on expansion and shear scalars and results in a generic resolution of strong singularities, we find that a flat Kasner metric is not a physical solution of the effective spacetime description, except in a limit. The lack of a flat Kasner metric at the quantum level results from a novel feature of the loop quantum Bianchi-I spacetime: quantum geometry induces non-vanishing spacetime curvature components, making it not Ricci flat even when no matter is present. The non-curvature singularity of the classical flat Kasner spacetime is avoided, and the effective spacetime transits from a flat Kasner spacetime in asymptotic future, to a Minkowski spacetime in asym...
Conformal properties of the extremal Schwarzschild de-Sitter spacetime
Gasperin, Edgar
2015-01-01
The conformal structure of the extremal Schwarzschild de-Sitter spacetime is analysed using the extended conformal Einstein field equations. Initial data for an asymptotic initial value problem for the extremal Schwarzschild de-Sitter spacetime is obtained. Using the insights gained from the analysis of the reference spacetime we consider nonlinear perturbations close to the extremal Schwarzschild de-Sitter spacetime. We show that small enough perturbations of initial data for the extremal Schwarzschild de-Sitter spacetime, away from the singularity, give rise to a solution to the Einstein field equations which exists to the future and has an asymptotic structure similar to that of the extremal Schwarzschild de-Sitter spacetime. Similarly, we obtain an existence and stability result for asymptotic initial data close to that of the extremal Schwarzschild de-Sitter spacetime in the non-singular region.
Geometry of a Quantized Spacetime: The Quantum Potential Approach
Mirza, Babur M.
2014-03-01
Quantum dynamics in a curved spacetime can be studied using a modified Lagrangian approach directly in terms of the spacetime variables [Mirza, B.M., Quantum Dynamics in Black Hole Spacetimes, IC-MSQUARE 2012]. Here we investigate the converse problem of determining the nature of the background spacetime when quantum dynamics of a test particle is known. We employ the quantum potential formalism here to obtain the modifications introduced by the quantum effects to the background spacetime. This leads to a novel geometry for the spacetime in which a test particle modifies the spacetime via interaction through the quantum potential. We present here the case of a Gaussian wave packet, and a localized quantum soliton, representing the test particle, and determine the corresponding geometries that emerge.
Uncertainty relation in Schwarzschild spacetime
Feng, Jun; Zhang, Yao-Zhong; Gould, Mark D.; Fan, Heng
2015-04-01
We explore the entropic uncertainty relation in the curved background outside a Schwarzschild black hole, and find that Hawking radiation introduces a nontrivial modification on the uncertainty bound for particular observer, therefore it could be witnessed by proper uncertainty game experimentally. We first investigate an uncertainty game between a free falling observer and his static partner holding a quantum memory initially entangled with the quantum system to be measured. Due to the information loss from Hawking decoherence, we find an inevitable increase of the uncertainty on the outcome of measurements in the view of static observer, which is dependent on the mass of the black hole, the distance of observer from event horizon, and the mode frequency of quantum memory. To illustrate the generality of this paradigm, we relate the entropic uncertainty bound with other uncertainty probe, e.g., time-energy uncertainty. In an alternative game between two static players, we show that quantum information of qubit can be transferred to quantum memory through a bath of fluctuating quantum fields outside the black hole. For a particular choice of initial state, we show that the Hawking decoherence cannot counteract entanglement generation after the dynamical evolution of system, which triggers an effectively reduced uncertainty bound that violates the intrinsic limit -log2 c. Numerically estimation for a proper choice of initial state shows that our result is comparable with possible real experiments. Finally, a discussion on the black hole firewall paradox in the context of entropic uncertainty relation is given.
Spontaneous excitation of a static atom in a thermal bath in cosmic string spacetime
Cai, Huabing; Zhou, Wenting
2015-01-01
We study the average rate of change of energy for a static atom immersed in a thermal bath of electromagnetic radiation in the cosmic string spacetime and separately calculate the contributions of thermal fluctuations and radiation reaction. We find that the transition rates are crucially dependent on the atom-string distance and polarization of the atom and they in general oscillate as the atom-string distance varies. Moreover, the atomic transition rates in the cosmic string spacetime can be larger or smaller than those in Minkowski spacetime contingent upon the atomic polarization and position. In particular, when located on the string, ground-state atoms can make a transition to excited states only if they are polarizable parallel to the string, whereas ground state atoms polarizable only perpendicular to the string are stable as if they were in a vacuum, even if they are immersed in a thermal bath. Our results suggest that the influence of a cosmic string is very similar to that of a reflecting boundary ...
Differential Space-Time Coded Modulation
CHENZhonglin; ZHUGuangxi
2004-01-01
Relying on amicable orthogonal design, we develop for multiple-antenna systems a General differential space-time block code (GDSTBC), which imposes no restrictions on underlying signal constellation compared with the existing differential space-time designs. This generalization potentially allows the spectral efficiency to be increased by carrying information not only on phases but also on amplitudes. We then derive a Noncoherent decoder (NCD) for fiat Rayleigh fading channels. We show that NCD may recover data symbols with full antenna diversity and linear complexity at high signal-to-noise ratio. Particularly, while three kinds of conventional signal constellations are used in GDSTBC, we derive the simplified versions of NCDs which can effectively reduce the cost of implementation.
Perturbations of spiky strings in flat spacetimes
Bhattacharya, Soumya; Panigrahi, Kamal L
2016-01-01
Perturbations of a class of semiclassical strings known today as spiky strings, are studied using the well-known Jacobi equations for small normal deformations of an embedded timelike surface. It is shown that there exists finite normal perturbations of the spiky string worldsheets embedded in a $2+1$ dimensional flat spacetime. Such perturbations lead to a rounding off the spikes, which, in a way, demonstrates the stable nature of the unperturbed worldsheet. The same features appear for the dual spiky string solution and in the spiky as well as their dual solutions in $3+1$ dimensional flat spacetime. Our results are based on exact solutions of the corresponding Jacobi equations which we obtain and use while constructing the profiles of the perturbed configurations.
Gravitational collapse of generalised Vaidya spacetime
Mkenyeleye, Maombi D; Maharaj, Sunil D
2014-01-01
We study the gravitational collapse of a generalised Vaidya spacetime in the context of the Cosmic Censorship hypothesis. We develop a general mathematical framework to study the conditions on the mass function so that future directed non-spacelike geodesics can terminate at the singularity in the past. Thus our result generalises earlier works on gravitational collapse of the combinations of Type-I and Type-II matter fields. Our analysis shows transparently that there exist classes of generalised Vaidya mass functions for which the collapse terminates with a locally naked central singularity. We calculate the strength of the these singularities to show that they are strong curvature singularities and there can be no extension of spacetime through them.
Insights from Melvin-Kerr-Newman spacetimes
Booth, Ivan; Palomo-Lozano, Alberto; Kunduri, Hari K
2015-01-01
We examine several aspects of black hole physics using the Melvin-Kerr-Newman (MKN) family of spacetimes. Roughly speaking these are black holes immersed in a distorting background magnetic field and unlike the standard Kerr-Newman (KN) family they are not asymptotically flat. Among other properties we see that their angular momentum and charge are bounded by horizon area in exactly the same way as KN and also that they obey the uniqueness theorems for extremal horizons: these properties are in accord with standard theorems but are seen to be satisfied in interesting and non-trivial ways. Horizon geometries are compared to KN horizons with equal area, charge and angular momentum. Finally we calculate the energy of these distorted black holes using the isolated horizon, Komar and recently proposed Gibbons-Pang-Pope procedures. Disagreements between these methods highlight the inherent ambiguities in attempting to define energy and other physical properties for a non-asymptotically flat spacetime.
Test particles in a magnetized conformastatic spacetime
Gutiérrez-Piñeres, Antonio C; Quevedo, Hernando
2016-01-01
A class of exact conformastatic solutions of the Einstein-Maxwell field equations is presented in which the gravitational and electromagnetic potentials are completely determined by a harmonic function. We derive the equations of motion for neutral and charged particles in a spacetime background characterized by this class of solutions. As an example, we focus on the analysis of a particular harmonic function which generates a singularity-free and asymptotically flat spacetime and, therefore, describes the gravitational field of a punctual mass endowed with a magnetic field. In this particular case, we investigate the main physical properties of equatorial circular orbits. We show that due to the electromagnetic interaction, it is possible to have charged test particles which stay at rest with respect to a static observer located at infinity. Additionally, we obtain an analytic expression for the perihelion advance of test particles. Our theoretical predictions are compared with the observational data calibra...
Chiral fermions on 2D curved spacetimes
Loran, Farhang
2016-01-01
The theory of free Majorana-Weyl spinors is the prototype of conformal field theory in two dimensions in which the gravitational anomaly and the Weyl anomaly obstruct extending the flat spacetime results to curved backgrounds. In this paper, we investigate a quantization scheme in which the short distance singularity in the two-point function of chiral fermions on a two dimensional curved spacetime is given by the Green's function corresponding to the classical field equation. We compute the singular term in the Green's function explicitly and observe that the short distance limit is not well-defined in general. We identify constraints on the geometry which are necessary to resolve this problem. On such special backgrounds the theory has locally $c=\\frac{1}{2}$ conformal symmetry.
Entropy in locally-de Sitter spacetimes
Araujo, A
2015-01-01
As quotient spaces, Minkowski and de Sitter are fundamental spacetimes in the sense that they are known "a priori", independently of Einstein equation. They represent different non-gravitational backgrounds for the construction of physical theories. If general relativity is constructed on a de Sitter spacetime, the underlying kinematics will no longer be ruled by Poincar\\'e, but by the de Sitter group. In this case the definition of diffeomorphism changes, producing concomitant changes in the notions of energy and entropy. These changes are explicitly discussed for the case of the Schwarzschild solution, in which the black hole and the de Sitter horizons show up as a unique entangled system. Such entanglement, together with energy conservation, create a constraint between the black hole activity and the evolution of the de Sitter radius, providing a new scenario for the study of cosmology.
Global properties of physically interesting Lorentzian spacetimes
Nawarajan, Deloshan
2016-01-01
Under normal circumstances most members of the general relativity community focus almost exclusively on the local properties of spacetime, such as the locally Euclidean structure of the manifold and the Lorentzian signature of the metric tensor. When combined with the classical Einstein field equations this gives an extremely successful empirical model of classical gravity and classical matter --- at least as long as one does not ask too many awkward questions about global issues, (such as global topology and global causal structure). We feel however that this is a tactical error --- even without invoking full-fledged "quantum gravity" we know that the standard model of particle physics is also an extremely good representation of some parts of empirical reality; and we had better be able to carry over all the good features of the standard model of particle physics --- at least into the realm of semi-classical quantum gravity. Doing so gives us some interesting global features that spacetime should possess: On...
Maximally Symmetric Spacetimes emerging from thermodynamic fluctuations
Bravetti, A; Quevedo, H
2015-01-01
In this work we prove that the maximally symmetric vacuum solutions of General Relativity emerge from the geometric structure of statistical mechanics and thermodynamic fluctuation theory. To present our argument, we begin by showing that the pseudo-Riemannian structure of the Thermodynamic Phase Space is a solution to the vacuum Einstein-Gauss-Bonnet theory of gravity with a cosmological constant. Then, we use the geometry of equilibrium thermodynamics to demonstrate that the maximally symmetric vacuum solutions of Einstein's Field Equations -- Minkowski, de-Sitter and Anti-de-Sitter spacetimes -- correspond to thermodynamic fluctuations. Moreover, we argue that these might be the only possible solutions that can be derived in this manner. Thus, the results presented here are the first concrete examples of spacetimes effectively emerging from the thermodynamic limit over an unspecified microscopic theory without any further assumptions.
Emergent spacetime & quantum entanglement in matrix theory
Sahakian, Vatche; Tawabutr, Yossathorn; Yan, Cynthia
2017-08-01
In the context of the Bank-Fishler-Shenker-Susskind Matrix theory, we analyze a spherical membrane in light-cone M theory along with two asymptotically distant probes. In the appropriate energy regime, we find that the membrane behaves like a smeared Matrix black hole; and the spacetime geometry seen by the probes can become non-commutative even far away from regions of Planckian curvature. This arises from non-linear Matrix interactions where fast matrix modes lift a flat direction in the potential — akin to the Paul trap phenomenon in atomic physics. In the regime where we do have a notion of emergent spacetime, we show that there is non-zero entanglement entropy between supergravity modes on the membrane and the probes. The computation can easily be generalized to other settings, and this can help develop a dictionary between entanglement entropy and local geometry — similar to Ryu-Takayanagi but instead for asymptotically flat backgrounds.
Anisotropic compact stars in Karmarkar spacetime
Singh, Ksh Newton; Govender, M
2016-01-01
We present a new class of solutions to the Einstein field equations for an anisotropic matter distribution in which the interior space-time obeys the Karmarkar condition. The necessary and sufficient condition required for a spherically symmetric space-time to be of class one reduces the gravitational behavior of the model to a single metric function. By assuming a physically viable form for the $g_{rr}$ metric potential we obtain an exact solution of the Einstein field equations which is free from any singularities and satisfies all the physical criteria. We utilize this solution to predict the masses and radii of well-known compact objects such as Cen X-3, PSR J0348+0432, PSRB0943+10 and XTE J1739-285. To be publish in Chinese Physics C (Accepted)
Canonical Quantum Gravity on Noncommutative Spacetime
Kober, Martin
2014-01-01
In this paper canonical quantum gravity on noncommutative space-time is considered. The corresponding generalized classical theory is formulated by using the moyal star product, which enables the representation of the field quantities depending on noncommuting coordinates by generalized quantities depending on usual coordinates. But not only the classical theory has to be generalized in analogy to other field theories. Besides, the necessity arises to replace the commutator between the gravitational field operator and its canonical conjugated quantity by a corresponding generalized expression on noncommutative space-time. Accordingly the transition to the quantum theory has also to be performed in a generalized way and leads to extended representations of the quantum theoretical operators. If the generalized representations of the operators are inserted to the generalized constraints, one obtains the corresponding generalized quantum constraints including the Hamiltonian constraint as dynamical constraint. Af...
Dirac operators on noncommutative curved spacetimes
Schenkel, Alexander
2013-01-01
We study Dirac operators in the framework of twist-deformed noncommutative geometry. The definition of noncommutative Dirac operators is not unique and we focus on three different ones, each generalizing the commutative Dirac operator in a natural way. We show that the three definitions are mutually inequivalent, and that demanding formal self-adjointness with respect to a suitable inner product singles out a preferred choice. A detailed analysis shows that, if the Drinfeld twist contains sufficiently many Killing vector fields, the three operators coincide, which can simplify explicit calculations considerably. We then turn to the construction of quantized Dirac fields on noncommutative curved spacetimes. We show that there exist unique retarded and advanced Green's operators and construct a canonical anti-commutation relation algebra. In the last part we study noncommutative Minkowski and AdS spacetimes as explicit examples.
Anisotropic non-gaussianity with noncommutative spacetime
Nautiyal, Akhilesh
2014-01-20
We study single field inflation in noncommutative spacetime and compute two-point and three-point correlation functions for the curvature perturbation. We find that both power spectrum and bispectrum for comoving curvature perturbation are statistically anisotropic and the bispectrum is also modified by a phase factor depending upon the noncommutative parameters. The non-linearity parameter f{sub NL} is small for small statistical anisotropic corrections to the bispectrum coming from the noncommutative geometry and is consistent with the recent PLANCK bounds. There is a scale dependence of f{sub NL} due to the noncommutative spacetime which is different from the standard single field inflation models and statistically anisotropic vector field inflation models. Deviations from statistical isotropy of CMB, observed by PLANCK can tightly constraint the effects due to noncommutative geometry on power spectrum and bispectrum.
Non-Pauli transitions from spacetime noncommutativity.
Balachandran, A P; Joseph, Anosh; Padmanabhan, Pramod
2010-07-30
The consideration of noncommutative spacetimes in quantum theory can be plausibly advocated from physics at the Planck scale. Typically, this noncommutativity is controlled by fixed "vectors" or "tensors" with numerical entries like θμν for the Moyal spacetime. In approaches enforcing Poincaré invariance, these deform or twist the method of (anti)symmetrization of identical particle state vectors. We argue that the Earth's rotation and movements in the cosmos are "sudden" events to Pauli-forbidden processes. This induces (twisted) bosonic components in state vectors of identical spinorial particles. These components induce non-Pauli transitions. From known limits on such transitions, we infer that the energy scale for noncommutativity is ≳10(24) TeV. This suggests a new energy scale beyond the Planck scale.
On geodesic deviation in Schwarzschild spacetime
Philipp, Dennis; Laemmerzahl, Claus; Deshpande, Kaustubh
2015-01-01
For metrology, geodesy and gravimetry in space, satellite based instruments and measurement techniques are used and the orbits of the satellites as well as possible deviations between nearby ones are of central interest. The measurement of this deviation itself gives insight into the underlying structure of the spacetime geometry, which is curved and therefore described by the theory of general relativity (GR). In the context of GR, the deviation of nearby geodesics can be described by the Jacobi equation that is a result of linearizing the geodesic equation around a known reference geodesic with respect to the deviation vector and the relative velocity. We review the derivation of this Jacobi equation and restrict ourselves to the simple case of the spacetime outside a spherically symmetric mass distribution and circular reference geodesics to find solutions by projecting the Jacobi equation on a parallel propagated tetrad as done by Fuchs. Using his results, we construct solutions of the Jacobi equation for...
Gravitational kinks in two spacetime dimensions
Vasilic, M
1996-01-01
The properties of gravitational kinks are studied within some simple models of two dimensional gravity. In spacetimes of cylindrical topology we prove the existence of kinks of constant curvature with arbitrary kink numbers. In R^1\\times R^1 spacetimes m=1 kink solutions of the equation R=0 are found, whereas |m|>1 flat kinks are proved not to exist. We give a detailed analysis of the behaviour of gravitational kinks under coordinate transformations. Viewed as nonsingular black holes |m|>1 kink solutions are found within a simple dilaton gravity theory. The general form of the potential function is determined from the demand that the theory possesses an arbitrary number of inequivalent kink configurations.
Uncertainty relation in Schwarzschild spacetime
Jun Feng
2015-04-01
Full Text Available We explore the entropic uncertainty relation in the curved background outside a Schwarzschild black hole, and find that Hawking radiation introduces a nontrivial modification on the uncertainty bound for particular observer, therefore it could be witnessed by proper uncertainty game experimentally. We first investigate an uncertainty game between a free falling observer and his static partner holding a quantum memory initially entangled with the quantum system to be measured. Due to the information loss from Hawking decoherence, we find an inevitable increase of the uncertainty on the outcome of measurements in the view of static observer, which is dependent on the mass of the black hole, the distance of observer from event horizon, and the mode frequency of quantum memory. To illustrate the generality of this paradigm, we relate the entropic uncertainty bound with other uncertainty probe, e.g., time–energy uncertainty. In an alternative game between two static players, we show that quantum information of qubit can be transferred to quantum memory through a bath of fluctuating quantum fields outside the black hole. For a particular choice of initial state, we show that the Hawking decoherence cannot counteract entanglement generation after the dynamical evolution of system, which triggers an effectively reduced uncertainty bound that violates the intrinsic limit −log2c. Numerically estimation for a proper choice of initial state shows that our result is comparable with possible real experiments. Finally, a discussion on the black hole firewall paradox in the context of entropic uncertainty relation is given.
Common structure-balance between spacetime structure and massenergy structure
Cao, Daqing; Cao, Dayong
2017-01-01
According to Einstein field equation, there is a balance between spacetime structure and massenergy structure. nd the paper consider it as a common structurewhich was brought forward by Daqing Cao in 2011 ecause it is general structure in the universe and everything have the same model of structure in their one system. The Jovian planets is spacetime structure of solar system because they are gas-sphere and they have more density of spacetime (spacetime/massenergy) than the density of massenergy (massenergy/spacetime). The terrestrial planets is massenergy structure of solar system because they are rock-ball and they have more density of massenergy than the density of spacetime. That can explain of that the Jovian planets of big mass is far away from sun. With the idea that the wave is spacetime and the wave effect is spacetime structure, the planets have elliptic orbits and the same direction of their revolution. Because sun is like a massenergy center of the massenergy structure and the terrestrial planets, the paper supposes there is a dark sun-a dark hole who has a spacetime center of spacetime structure and influences on the orbits of the Jovian planets. http://meetings.aps.org/Meeting/APR16/Session/M13.8
Space-Time Crystals of Trapped Ions
2012-10-15
Space-Time Crystals of Trapped Ions Tongcang Li,1 Zhe-Xuan Gong ,2,3 Zhang- Qi Yin,3,4 H. T. Quan,5 Xiaobo Yin,1 Peng Zhang,1 L.-M. Duan,2,3 and Xiang...Z.-X. Gong , G.-D. Lin, and L.-M. Duan, Phys. Rev. Lett. 105, 265703 (2010). [12] K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K
Superstring gravitational wave backgrounds with spacetime supersymmetry
Kiritsis, Elias B; Lüst, Dieter; Kiritsis, E; Kounnas, C; Lüst, D
1994-01-01
We analyse the stringy gravitational wave background based on the current algebra E.sup(c).sub(2). We determine its exact spectrum and construct the modular invariant vacuum energy. The corresponding N=1 extension is also constructed. The algebra is again mapped to free bosons and fermions and we show that this background has N=4 (N=2) unbroken spacetime supersymmetry in the type II (heterotic case).
Cosmological constant influence on cosmic string spacetime
Abbassi, Amir H.; Abbassi, Amir M.; Razmi, H.
2003-05-01
We investigate the line element of spacetime around a linear cosmic string in the presence of a cosmological constant. We obtain a static form of the metric and argue that it should be discarded because of asymptotic considerations. Then a time dependent and consistent form of the metric is obtained and its properties are discussed. This may be considered an example of a preferred frame in physics.
Electromagnetic duality anomaly in curved spacetimes
Agullo, I; Navarro-Salas, J
2016-01-01
The source-free Maxwell action is invariant under electric-magnetic duality rotations in arbitrary spacetimes. This leads to a conserved classical Noether charge. We show that this conservation law is broken at the quantum level in presence of a background classical gravitational field with a non-trivial Chern-Pontryagin invariant, in a parallel way to the chiral anomaly for massless Dirac fermions. Among the physical consequences, the net polarization of the quantum electromagnetic field is not conserved.
On the genericity of spacetime singularities
Pankaj S Joshi
2007-07-01
We consider here the genericity aspects of spacetime singularities that occur in cosmology and in gravitational collapse. The singularity theorems (that predict the occurrence of singularities in general relativity) allow the singularities of gravitational collapse to be either visible to external observers or covered by an event horizon of gravity. It is shown that the visible singularities that develop as final states of spherical collapse are generic. Some consequences of this fact are discussed.
Principle of Spacetime and Black Hole Equivalence
Zhang, Tianxi
2016-06-01
Modelling the universe without relying on a set of hypothetical entities (HEs) to explain observations and overcome problems and difficulties is essential to developing a physical cosmology. The well-known big bang cosmology, widely accepted as the standard model, stands on two fundamentals, which are Einstein’s general relativity (GR) that describes the effect of matter on spacetime and the cosmological principle (CP) of spacetime isotropy and homogeneity. The field equation of GR along with the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric of spacetime derived from CP generates the Friedmann equation (FE) that governs the development and dynamics of the universe. The big bang theory has made impressive successes in explaining the universe, but still has problems and solutions of them rely on an increasing number of HEs such as inflation, dark matter, dark energy, and so on. Recently, the author has developed a new cosmological model called black hole universe, which, instead of making many those hypotheses, only includes a new single postulate (or a new principle) to the cosmology - Principle of Spacetime and Black Hole Equivalence (SBHEP) - to explain all the existing observations of the universe and overcome all the existing problems in conventional cosmologies. This study thoroughly demonstrates how this newly developed black hole universe model, which therefore stands on the three fundamentals (GR, CP, and SBHEP), can fully explain the universe as well as easily conquer the difficulties according to the well-developed physics, thus, neither needing any other hypotheses nor existing any unsolved difficulties. This work was supported by NSF/REU (Grant #: PHY-1263253) at Alabama A & M University.
Characterization of Null Geodesics on Kerr Spacetimes
Paganini, Claudio F; Oancea, Marius A
2016-01-01
We consider null geodesics in the domain of outer communication of a sub-extremal Kerr spacetime. We show, that most fundamental properties of null geodesics can be represented in one plot. In particular one can see immediately that the ergoregion and trapping are separated in phase space. Furthermore we show that from the point of view of any timelike observer outside of a black hole, trapping can be understood as a smooth set of spacelike directions on the observers' celestial sphere.
Vaidya Spacetime for Galileon Gravity's Rainbow
Rudra, Prabir; Ali, Ahmed Farag
2016-01-01
In this paper, we analyze Vaidya spacetime with an energy dependent metric in Galileon gravity's rainbow. This will be done using the rainbow functions which are motivated from the results obtained in loop quantum gravity approach and non-commutative geometry. We will investigate the Gravitational collapse in this Galileon gravity's rainbow. We will discuss the behavior of singularities formed from the gravitational collapse in this rainbow deformed Galileon gravity.
High Energy Effects of Noncommutative Spacetime Geometry
Sidharth, Burra G
2016-01-01
In this paper, we endeavour to obtain a modified form of the Foldy-Wouthuysen and Cini-Toushek transformations by resorting to the noncommutative nature of space-time geometry, starting from the Klein-Gordon equation. Also, we obtain a shift in the energy levels due to noncommutativity and from these results a limit for the Lorentz factor in the ultra-relativistic case has been derived in conformity with observations
A noncommutative model of BTZ spacetime
Maceda, Marco [Universidad Autonoma Metropolitana-Iztapalapa, Departamento de Fisica, A.P. 55-534, Mexico D.F. (Mexico); Macias, Alfredo [Universidad Autonoma Metropolitana-Iztapalapa, Departamento de Fisica, A.P. 55-534, Mexico D.F. (Mexico); CINVESTAV-IPN, Departamento de Fisica, A.P. 14-740, Mexico D.F. (Mexico)
2013-04-15
We analyze a noncommutative model of BTZ spacetime based on deformation of the standard symplectic structure of phase space, i.e., a modification of the standard commutation relations among coordinates and momenta in phase space. We find a BTZ-like solution that is nonperturbative in the non-trivial noncommutative structure. It is shown that the use of deformed commutation relations in the modified non-canonical phase space eliminates the horizons of the standard metric. (orig.)
Wavefronts and Light Cones for Kerr Spacetimes
Frutos-Alfaro, Francisco; Mueller, Thomas; Adis, Daria
2014-01-01
We investigate the light propagation by means of simulations of wavefronts and light cones for Kerr spacetimes. Simulations of this kind give us a new insight to better understand the light propagation in presence of massive rotating black holes. A relevant result is that wavefronts are back scattered with winding around the black hole. To generate these visualizations, an interactive computer program with a graphical user interface, called JWFront, was written in Java.
Isocausal spacetimes may have different causal boundaries
Flores, J L; Herrera, J [Departamento de Algebra, Geometria y Topologia, Facultad de Ciencias, Universidad de Malaga, Campus Teatinos, 29071 Malaga (Spain); Sanchez, M, E-mail: floresj@agt.cie.uma.es, E-mail: jherrera@uma.es, E-mail: sanchezm@ugr.es [Departamento de Geometria y Topologia, Facultad de Ciencias, Universidad de Granada, Avenida Fuentenueva s/n, 18071 Granada (Spain)
2011-09-07
We construct an example which shows that two isocausal spacetimes, in the sense introduced recently in GarcIa-Parrado and Senovilla (2003 Class. Quantum Grav. 20 625-64), may have c-boundaries which are not equal (more precisely, not equivalent, as no bijection between the completions can preserve all the binary relations induced by causality). This example also suggests that isocausality can be useful for the understanding and computation of the c-boundary.
Brane Space-Time and Cosmology
Naboulsi, R
2003-01-01
I reconsider the cosmology of a 3-brane universe imbedded in a five-dimensional anti-de Sitter space AdS5 with a cosmological constant and show that the resulting Friedmann equations for this system are identical to those standard obtained in 4D FRW space-time in the presence of an additional density, playing two roles: the tension of the brane and the gravitino density We discuss some important concequences on hot big bang cosmology.
Wave Scattering by Superluminal Spacetime Slab
Deck-Léger, Zoé-Lise
2016-01-01
Spacetime media offers new opportunities for wave manipulation. Here we study superluminal slabs, and show that the amplitudes of the reflected waves are controlled by the velocity of the medium. In addition, the backward wave continuously scans from the specular to the collinear angle. A diagrammatic method is provided for insight into the deflection angles. A fundamental symmetry between sub- and superluminal scattering is derived from this diagrammatic description.
Gaussian quantum steering and its asymmetry in curved spacetime
Wang, Jieci; Cao, Haixin; Jing, Jiliang; Fan, Heng
2016-06-01
We study Gaussian quantum steering and its asymmetry in the background of a Schwarzschild black hole. We present a Gaussian channel description of quantum state evolution under the influence of Hawking radiation. We find that thermal noise introduced by the Hawking effect will destroy the steerability between an inertial observer Alice and an accelerated observer Bob who hovers outside the event horizon, while it generates steerability between Bob and a hypothetical observer anti-Bob inside the event horizon. Unlike entanglement behaviors in curved spacetime, here the steering from Alice to Bob suffers from a "sudden death" and the steering from anti-Bob to Bob experiences a "sudden birth" with increasing Hawking temperature. We also find that the Gaussian steering is always asymmetric and the maximum steering asymmetry cannot exceed ln 2 , which means the state never evolves to an extremal asymmetry state. Furthermore, we obtain the parameter settings that maximize steering asymmetry and find that (i) s =arccosh cosh/2r 1 -sinh2r is the critical point of steering asymmetry and (ii) the attainment of maximal steering asymmetry indicates the transition between one-way steerability and both-way steerability for the two-mode Gaussian state under the influence of Hawking radiation.
Space-time and physical fields inside a black hole
Doroshkevich, A.G.; Novikov, I.D.
1978-01-01
Physical fields and the perturbations of the space-time metric inside a slowly rotating and weakly charged black hole are investigated. It is shown that in the Schwarzschild coordinates r and t for r
Iovane, G. [Dipartimento di Ingegneria dell' Informazione e Matematica Applicata, Universita di Salerno, Via Ponte Don Melillo, 84084 Fisicano (Saudi Arabia) (Italy)]. E-mail: iovane@diima.unisa.it
2007-03-15
In this work starting from some earlier results on hypersingular integral equations and analyzing a more realistic model of gravitational waveguides on a Cantorian spacetime we obtain a description of our Universe according to Kaehler manifold in the context of El Naschie's {epsilon} {sup ({infinity})} Cantorian space-time. In particular, we consider filamentary and planar large scale structures as possible refraction channels for electromagnetic radiation coming from cosmological structures. From this vision the Universe appears like a large self-similar adaptive mirrors set. This is made evident through numerical simulations. Consequently, an infinite Universe is just an optical illusion that is produced by mirroring effects connected to the large scale structure of a finite and not so large Universe.
Newtonian analogue of static general relativistic spacetimes: An extension to naked singularities
Ghosh, Shubhrangshu; Bhadra, Arunava
2015-01-01
We formulate a generic Newtonian like analogous potential for static spherically symmetric general relativistic (GR) spacetime, and subsequently derived proper Newtonian like analogous potential corresponding to Janis-Newman-Winicour (JNW) and Reissner-Nordstr\\"{o}m (RN) spacetimes, both exhibiting naked singularities. The derived potentials found to reproduce the entire GR features including the orbital dynamics of the test particle motion and the orbital trajectories, with precise accuracy. The nature of the particle orbital dynamics including their trajectory profiles in JNW and RN geometries show altogether different behavior with distinctive traits as compared to the nature of particle dynamics in Schwarzschild geometry. Exploiting the Newtonian like analogous potentials, we found that the radiative efficiency of a geometrically thin and optically thick Keplerian accretion disk around naked singularities corresponding to both JNW and RN geometries, in general, is always higher than that for Schwarzschild...
A bound on the scale of spacetime noncommutativity from the reheating phase after inflation
Horvat, R
2011-01-01
In an approach to noncommutative gauge theories, where the full noncommutative behavior is delimited by the presence of the UV and IR cutoffs, we consider the possibility of describing a system at a temperature T in a box of size L. Employing a specific form of UV/IR relationship inherent in such an approach of restrictive noncommutativity, we derive, for a given temperature T, an upper bound on the parameter of spacetime noncommutativity Lambda_NC ~ |theta|^{-1/2}. Considering such epochs in the very early universe which are expected to reflect spacetime noncommutativity to a quite degree, like the reheating stage after inflation, or believable pre-inflation radiation-dominated epochs, the best limits on Lambda_NC are obtained. We also demonstrate how the nature and size of the thermal system (for instance, the Hubble distance versus the future event horizon) can affect our bounds.
Exotic solutions in General Relativity: Traversable wormholes and 'warp drive' spacetimes
Lobo, Francisco S N
2007-01-01
The General Theory of Relativity has been an extremely successful theory, with a well established experimental footing, at least for weak gravitational fields. Its predictions range from the existence of black holes, gravitational radiation to the cosmological models, predicting a primordial beginning, namely the big-bang. All these solutions have been obtained by first considering a plausible distribution of matter, and through the Einstein field equation, the spacetime metric of the geometry is determined. However, one may solve the Einstein field equation in the reverse direction, namely, one first considers an interesting and exotic spacetime metric, then finds the matter source responsible for the respective geometry. In this manner, it was found that some of these solutions possess a peculiar property, namely 'exotic matter,' involving a stress-energy tensor that violates the null energy condition. These geometries also allow closed timelike curves, with the respective causality violations. These soluti...
Asymptotics with a positive cosmological constant: II. Linear fields on de Sitter space-time
Ashtekar, Abhay; Kesavan, Aruna
2015-01-01
Linearized gravitational waves in de Sitter space-time are analyzed in detail to obtain guidance for constructing the theory of gravitational radiation in presence of a positive cosmological constant in full, nonlinear general relativity. Specifically: i) In the exact theory, the intrinsic geometry of $\\scri$ is often assumed to be conformally flat in order to reduce the asymptotic symmetry group from $\\Diff$ to the de Sitter group. Our {results show explicitly} that this condition is physically unreasonable; ii) We obtain expressions of energy-momentum and angular momentum fluxes carried by gravitational waves in terms of fields defined at $\\scrip$; iii) We argue that, although energy of linearized gravitational waves can be arbitrarily negative in general, gravitational waves emitted by physically reasonable sources carry positive energy; and, finally iv) We demonstrate that the flux formulas reduce to the familiar ones in Minkowski space-time in spite of the fact that the limit $\\Lambda \\to 0$ is discontin...
A bound on the scale of spacetime noncommutativity from the reheating phase after inflation
Horvat, R., E-mail: horvat@lei3.irb.hr [Institute Ruder Boskovic, Bijenicka 54, 10000 Zagreb (Croatia); Trampetic, J., E-mail: josipt@rex.irb.hr [Institute Ruder Boskovic, Bijenicka 54, 10000 Zagreb (Croatia); Max-Planck-Institut fuer Physik (Werner-Heisenberg-Institut), Foehringer Ring 6, D-80805 Muenchen (Germany)
2012-03-29
In an approach to noncommutative gauge theories, where the full noncommutative behavior is delimited by the presence of the UV and IR cutoffs, we consider the possibility of describing a system at a temperature T in a box of size L. Employing a specific form of UV/IR relationship inherent in such an approach of restrictive noncommutativity, we derive, for a given temperature T, an upper bound on the parameter of spacetime noncommutativity {Lambda}{sub NC}{approx}|{theta}|{sup -1/2}. Considering such epochs in the very early universe which are expected to reflect spacetime noncommutativity to a quite degree, like the reheating stage after inflation, or believable pre-inflation radiation-dominated epochs, the best limits on {Lambda}{sub NC} are obtained. We also demonstrate how the nature and size of the thermal system (for instance, the Hubble distance versus the future event horizon) can affect our bounds.
Mixer-Duplexer-Antenna Leaky-Wave System Based on Periodic Space-Time Modulation
Taravati, Sajjad
2016-01-01
We present a mixer-duplexer-antenna leaky-wave system based on periodic space-time modulation. This system operates as a full transceiver, where the upconversion and downconversion mixing operations are accomplished via space-time transitions, the duplexing operation is induced by the nonreciprocal nature of the structure, and the radiation operation is provided by the leaky-wave nature of the wave. A rigorous electromagnetic solution is derived for the dispersion relation and field distributions. The system is implemented in the form of a spatio-temporally modulated microstrip leaky-wave structure incorporating an array of sub-wavelengthly spaced varactors modulated by a harmonic wave. In addition to the overall mixer-duplexer-antenna operation, frequency beam scanning at fixed input frequency is demonstrated as one of the interesting features of the system. A prototype is realized and demonstrated by full-wave and experimental results.
A Holographic Approach to Spacetime Entanglement
Wien, Jason
2014-01-01
Recently it has been proposed that the Bekenstein-Hawking formula for the entropy of spacetime horizons has a larger significance as the leading contribution to the entanglement entropy of general spacetime regions, in the underlying quantum theory [2]. This `spacetime entanglement conjecture' has a holographic realization that equates the entropy formula evaluated on an arbitrary space-like co-dimension two surface with the differential entropy of a particular family of co-dimension two regions on the boundary. The differential entropy can be thought of as a directional derivative of entanglement entropy along a family of surfaces. This holographic relation was first studied in [3] and extended in [4], and it has been proven to hold in Einstein gravity for bulk surfaces with planar symmetry (as well as for certain higher curvature theories) in [4]. In this essay, we review this proof and provide explicit examples of how to build the appropriate family of boundary intervals for a given bulk curve. Conversely,...
Holographic thermal field theory on curved spacetimes
Marolf, Donald; Rangamani, Mukund; Wiseman, Toby
2014-03-01
The AdS/CFT correspondence relates certain strongly-coupled CFTs with large effective central charge ceff to semi-classical gravitational theories with AdS asymptotics. We describe recent progress in understanding gravity duals for CFTs on non-trivial spacetimes at finite temperature, both in and out of equilibrium. Such gravity methods provide powerful new tools to access the physics of these strongly-coupled theories, which often differs qualitatively from that found at weak coupling. Our discussion begins with basic aspects of AdS/CFT and progresses through thermal CFTs on the Einstein Static Universe and on periodically identified Minkowski spacetime. In the latter context we focus on states describing so-called plasma-balls, which become stable at large ceff. We then proceed to out-of-equilibrium situations associated with dynamical bulk black holes. In particular, the non-compact nature of these bulk black holes allows stationary solutions with non-Killing horizons that describe time-independent flows of CFT plasma. As final a topic we consider CFTs on black hole spacetimes. This discussion provides insight into how the CFT transports heat between general heat sources and sinks of finite size. In certain phases the coupling to small sources can be strongly suppressed, resulting in negligible heat transport despite the presence of a deconfined plasma with sizeable thermal conductivity. We also present a new result, explaining how this so-called droplet behaviour is related to confinement via a change of conformal frame.
Spacetime Deformation-Induced Inertia Effects
Gagik Ter-Kazarian
2012-01-01
Full Text Available We construct a toy model of spacetime deformation-induced inertia effects, in which we prescribe to each and every particle individually a new fundamental constituent of hypothetical 2D, so-called master space (MS, subject to certain rules. The MS, embedded in the background 4D-spacetime, is an indispensable companion to the particle of interest, without relation to every other particle. The MS is not measurable directly, but we argue that a deformation (distortion of local internal properties of MS is the origin of inertia effects that can be observed by us. With this perspective in sight, we construct the alternative relativistic theory of inertia. We go beyond the hypothesis of locality with special emphasis on distortion of MS, which allows to improve essentially the standard metric and other relevant geometrical structures referred to a noninertial frame in Minkowski spacetime for an arbitrary velocities and characteristic acceleration lengths. Despite the totally different and independent physical sources of gravitation and inertia, this approach furnishes justification for the introduction of the weak principle of equivalence (WPE, that is, the universality of free fall. Consequently, we relate the inertia effects to the more general post-Riemannian geometry.
Quantum Dynamics of Lorentzian Spacetime Foam
Redmount, Ian; 10.1103/PhysRevD.49.5199
2009-01-01
A simple spacetime wormhole, which evolves classically from zero throat radius to a maximum value and recontracts, can be regarded as one possible mode of fluctuation in the microscopic ``spacetime foam'' first suggested by Wheeler. The dynamics of a particularly simple version of such a wormhole can be reduced to that of a single quantity, its throat radius; this wormhole thus provides a ``minisuperspace model'' for a structure in Lorentzian-signature foam. The classical equation of motion for the wormhole throat is obtained from the Einstein field equations and a suitable equation of state for the matter at the throat. Analysis of the quantum behavior of the hole then proceeds from an action corresponding to that equation of motion. The action obtained simply by calculating the scalar curvature of the hole spacetime yields a model with features like those of the relativistic free particle. In particular the Hamiltonian is nonlocal, and for the wormhole cannot even be given as a differential operator in clos...
Perturbative Critical Behavior from Spacetime Dependent Couplings
Dong, Xi; Horn, Bart; Silverstein, Eva; Torroba, Gonzalo
2012-08-03
We find novel perturbative fixed points by introducing mildly spacetime-dependent couplings into otherwise marginal terms. In four-dimensional QFT, these are physical analogues of the small-{epsilon} Wilson-Fisher fixed point. Rather than considering 4-{epsilon} dimensions, we stay in four dimensions but introduce couplings whose leading spacetime dependence is of the form {lambda}x{sup {kappa}}{mu}{sup {kappa}}, with a small parameter {kappa} playing a role analogous to {epsilon}. We show, in {phi}{sup 4} theory and in QED and QCD with massless flavors, that this leads to a critical theory under perturbative control over an exponentially wide window of spacetime positions x. The exact fixed point coupling {lambda}{sub *}(x) in our theory is identical to the running coupling of the translationally invariant theory, with the scale replaced by 1/x. Similar statements hold for three-dimensional {phi}{sup 6} theories and two-dimensional sigma models with curved target spaces. We also describe strongly coupled examples using conformal perturbation theory.
Casimir effect in de Sitter spacetime
Saharian, A A
2011-01-01
The vacuum expectation value of the energy-momentum tensor and the Casimir forces are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the geometry of two parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch--Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. The vacuum energy-momentum tensor is non-diagonal, with the off-diagonal component corresponding to the energy flux along the direction normal to the plates. It is shown that the curvature of the background spacetime decisively influences the behavior of the Casimir forces at separations larger than the curvature radius of de Sitter spacetime. In dependence of the curvature coupling parameter and the mass of the field, two different regimes are realized, which exhibit monotonic or oscillatory behavior of the forces. The decay of the Casimir force at large plate separation is shown to be power-law, with independence of the value of the...
Towards a theory of spacetime theories
Schiemann, Gregor; Scholz, Erhard
2017-01-01
This contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories? How do we judge, objectively, which is the “best” theory? Is there even a unique answer to this question? The goal of the workshop, and of this book, is to contribute to the development of a meta-theory of spacetime theories. Such a meta-theory would reveal insights about specific spacetime theories by distilling their essential similarities and differences, deliver a framework for a class of theories that could be helpful as a blueprint to build other meta-theories, and provide a higher level viewpoint for judging which theory most accurately describes nature. But rather than drawing a map in broad strokes, the focus is on particularly rich regions in the “space of spaceti...
Probe Annihilation process on noncommutative spacetime
Chen, Chien Yu; He, Xiao Gang
2008-01-01
If the twist Poincar$\\acute{e}$ transformation is involved on the non-flat spacetime, then Lorentz invariant will not be a best method to describe the QFT anymore. Recently, noncommutative theory is one of the best candidates to modify this perfect symmetry undoubted before, which gives the concept of spacetime is not commutable. In this paper, we will argue the parity violation under the process of $e^{+}e^{-}\\to\\gamma\\gamma$ and also take more detail analysis to express the different behavior of each helicity state on the noncommutable spacetime. The effect is result from the spin-magnetic field production, hence the cross section will induce the different energy distribution on the finial photon luminosity. Meanwhile, we also check the energy momentum conservation on the each coupling constant. Exploring out that electric field just could induce the different energy distribution, no symmetry violated effect will be produced. Which field will produce the longitudinal state on the finial triple photon boson ...
Electrodynamics of Radiating Charges
Øyvind Grøn
2012-01-01
Full Text Available The theory of electrodynamics of radiating charges is reviewed with special emphasis on the role of the Schott energy for the conservation of energy for a charge and its electromagnetic field. It is made clear that the existence of radiation from a charge is not invariant against a transformation between two reference frames that has an accelerated motion relative to each other. The questions whether the existence of radiation from a uniformly accelerated charge with vanishing radiation reaction force is in conflict with the principle of equivalence and whether a freely falling charge radiates are reviewed. It is shown that the resolution of an electromagnetic “perpetuum mobile paradox” associated with a charge moving geodetically along a circular path in the Schwarzschild spacetime requires the so-called tail terms in the equation of motion of a charged particle.
Noether gauge symmetry classes for pp-wave spacetimes
Camci, U
2016-01-01
The Noether gauge symmetries of geodesic Lagrangian for the pp-wave spacetimes are determined in each of the Noether gauge symmetry classes of the pp-wave spacetimes. It is shown that a type N pp-wave spacetime can admit at most three Noether gauge symmetry, and furthermore the number of Noether gauge symmetries turn out to be four, five, six, seven and eight. We found that all conformally flat plane wave spacetimes admit the maximal, i.e. ten, Noether gauge symmetry. Also it is found that if the pp-wave spacetime is non-conformally flat plane wave, then the number of Noether gauge symmetry is nine or ten. By means of the obtained Noether constants the search of the exact solutions of the geodesic equations for the pp-wave spacetimes is considered and we found new exact solutions of the geodesic equations in some special Noether gauge symmetry classes.
Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
Geracie, Michael; Roberts, Matthew M
2015-01-01
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-relativisitic symmetries which supports massive matter fields. In particular, one can not 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-relativis...
Cosmological applications of algebraic quantum field theory in curved spacetimes
Hack, Thomas-Paul
2016-01-01
This book provides a largely self-contained and broadly accessible exposition on two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology; and a fundamental study of the perturbations in inflation. The two central sections of the book dealing with these applications are preceded by sections providing a pedagogical introduction to the subject. Introductory material on the construction of linear QFTs on general curved spacetimes with and without gauge symmetry in the algebraic approach, physically meaningful quantum states on general curved spacetimes, and the backreaction of quantum fields in curved spacetimes via the semiclassical Einstein equation is also given. The reader should have a basic understanding of General Relativity and QFT on Minkowski spacetime, but no background in QFT on curved spacetimes or the algebraic approach to QFT is required.
Cosmological Applications of Algebraic Quantum Field Theory in Curved Spacetimes
Hack, Thomas-Paul
2015-01-01
This monograph provides a largely self--contained and broadly accessible exposition of two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology and a fundamental study of the perturbations in Inflation. The two central sections of the book dealing with these applications are preceded by sections containing a pedagogical introduction to the subject as well as introductory material on the construction of linear QFTs on general curved spacetimes with and without gauge symmetry in the algebraic approach, physically meaningful quantum states on general curved spacetimes, and the backreaction of quantum fields in curved spacetimes via the semiclassical Einstein equation. The target reader should have a basic understanding of General Relativity and QFT on Minkowski spacetime, but does not need to have a background in QFT on curved spacetimes or the algebraic approach to QFT. In particul...
Static- and Stationary-complete Spacetimes: Algebraic and Causal Structures
Harris, Steven G
2014-01-01
This is intended as an analysis of the global properties of static and stationary spacetimes with complete (timelike) Killing field, with particular attention to quotients by group actions. This is presented in terms of algebraic structures which are fairly simple for the static case and more involved for the stationary case; the most important tool, the fundamental cocycle, is a cohomological class for static spacetimes but of somewhat looser structure in the stationary case. In particular: (1) A new measurement, similar to the spacetime interval in Minkowski space, is devised for detecting whether two points are causally related in a stationary spacetime; this proves very useful for analysis. (2) All stationary spacetimes are categorized by how they behave with respect to the fundamental cocycle; this enables a complete characterization of global causality properties. (3) It is shown how these tools determine whether global hyperbolicity of a stationary spacetime is inherited by its quotients. (4) Examples ...
Fine structure constant variation or space-time anisotropy?
Chang, Zhe; Li, Xin
2011-01-01
Recent observations on quasar absorption spectra supply evidences for variation of fine structure constant $\\alpha$. In this paper, we propose another interpretation of the observational data on quasar absorption spectra: a scenario with space-time inhomogeneity and anisotropy but uniform fine structure constant. Maybe the space-time is characterized by Finsler geometry instead of Riemann one. Finsler geometry admits less symmetries than Riemann geometry does. We investigate the Finslerian geodesic equations in Randers space-time (a special Finsler space-time). It is found that the cosmological redshift in this space-time is deviated from the one in general relativity. The modification term to redshift could be generally revealed as a monopole plus dipole function about space-time locations and directions. We suggest that this modification corresponds to the observed spatial monopole and Australian Dipole in quasar absorption spectra.
Geodesic flows and their deformations in Bertrand spacetimes
Kumar, Prashant; Sarkar, Tapobrata
2012-01-01
In this article we will discuss some features of a particular spacetime called Bertrand space-time of Type II (BST-II). This spacetime is associated with multiple real parameters. The various energy conditions and geodesic equations of BST-II are used to find the limits of these parameters which can result in a meaningful and physical space-time. It will be shown that in certain circumstances where the weak and strong energy conditions hold BST-II can be thought of as a physically interesting spacetime. Further, the talk discusses about the ESR parameters in this spacetime. The properties of these parameters are nemerically analyzed keeping an eye on the focussing property of radial timelike and radial null geodesics.
Gravitational Tension, Spacetime Pressure and Black Hole Volume
Armas, Jay; Sanchioni, Marco
2015-01-01
We study the first law of black hole thermodynamics in the presence of surrounding gravitational fields and argue that variations of these fields are naturally incorporated in the first law by defining gravitational tension or gravitational binding energy. We demonstrate that this notion can also be applied in Anti-de Sitter spacetime, in which the surrounding gravitational field is sourced by a cosmological fluid, therefore showing that spacetime volume and gravitational tension encode the same physics as spacetime pressure and black hole volume. We furthermore show that it is possible to introduce a definition of spacetime pressure and black hole volume for any spacetime with characteristic length scales which does not necessarily require a cosmological constant sourcing Einstein equations. However, we show that black hole volume is non-universal in the flat spacetime limit, questioning its significance. We illustrate these ideas by studying the resulting black hole volume of Kaluza-Klein black holes and of...
Moschidis, Georgios
2015-01-01
In [M. Dafermos and I. Rodnianski, A new physical-space approach to decay for the wave equation with applications to black hole spacetimes, in XVIth International Congress on Mathematical Physics, Pavel Exner ed., Prague 2009 pp. 421-433, 2009, arXiv:0910.4957], Dafermos and Rodnianski presented a novel approach to establish uniform decay rates for solutions $\\phi$ to the scalar wave equation $\\square_{g}\\phi=0$ on Minkowski, Schwarzschild and other asymptotically flat backgrounds. This paper generalises the methods and results of the above paper to a broad class of asymptotically flat spacetimes $(\\mathcal{M},g)$, including Kerr spacetimes in the full subextremal range $|a|
A curious spacetime entirely free of centrifugal acceleration
Dadhich, Naresh
2012-01-01
In the Einstein gravity, besides the usual gravitational and centrifugal potential there is an additional attractive term that couples these two together. It is fun to enquire whether the latter could fully counteract the centrifugal repulsion everywhere making the spacetime completely free of the centrifugal acceleration. We present here such a curious spacetime metric and it produces a global monopole like stresses going as $~1/r^2$ in an AdS spacetime.
Hopf-algebra description of noncommutative-spacetime symmetries
2003-01-01
In the study of certain noncommutative versions of Minkowski spacetime there is still a large ambiguity concerning the characterization of their symmetries. Adopting as our case study the kappaMinkowski noncommutative space-time, on which a large literature is already available, we propose a line of analysis of noncommutative-spacetime symmetries that relies on the introduction of a Weyl map (connecting a given function in the noncommutative Minkowski with a corresponding function in commutat...
Quasi-Asimptotically Flat Spacetimes and Their ADM Mass
Nucamendi, U; Nucamendi, Ulises; Sudarsky, Daniel
1996-01-01
We define spacetimes that are asymptotically flat, except for a deficit solid angle $\\alpha$, and present a definition of their ``ADM'' mass, which is finite for this class of spacetimes, and, in particular, coincides with the value of the parameter $M$ of the global monopole spacetime studied by Vilenkin and Barriola . Moreover, we show that the definition is coordinate independent, and explain why it can, in some cases, be negative.
Fuzzy Spacetime with SU(3) Isometry in IIB Matrix Model
Kaneko, H; Tomino, D
2005-01-01
A group of fuzzy spacetime with SU(3) isometry is studied at the two loop level in IIB matrix model. It consists of spacetime from 4 to 6 dimensions, namely from CP2 to SU(3)/U(1)x U(1). The effective action scales in a universal manner in the large N limit as N and N^{4/3} on 4 and 6 dimensional manifolds respectively. The 4 dimensional spacetime CP2 possesses the smallest effective action in this class.
Spacetime-symmetry violations: motivations, phenomenology, and tests
Lehnert, Ralf
2014-01-01
An important open question in fundamental physics concerns the nature of spacetime at distance scales associated with the Planck length. The widespread belief that probing such distances necessitates Planck-energy particles has impeded phenomenological and experimental research in this context. However, it has been realized that various theoretical approaches to underlying physics can accommodate Planck-scale violations of spacetime symmetries. This talk surveys the motivations for spacetime-symmetry research, the SME test framework, and experimental efforts in this field.
Geodesic completeness in a wormhole spacetime with horizons
Olmo, Gonzalo J; Sanchez-Puente, A
2015-01-01
The geometry of a spacetime containing a wormhole generated by a spherically symmetric electric field is investigated in detail. These solutions arise in high-energy extensions of General Relativity formulated within the Palatini approach and coupled to Maxwell electrodynamics. Even though curvature divergences generically arise at the wormhole throat, we find that these spacetimes are geodesically complete. This provides an explicit example where curvature divergences do not imply spacetime singularities.
Causality and Micro-Causality in Curved Spacetime
Hollowood, Timothy J.; Shore, Graham M.
2007-01-01
We consider how causality and micro-causality are realised in QED in curved spacetime. The photon propagator is found to exhibit novel non-analytic behaviour due to vacuum polarization, which invalidates the Kramers-Kronig dispersion relation and calls into question the validity of micro-causality in curved spacetime. This non-analyticity is ultimately related to the generic focusing nature of congruences of geodesics in curved spacetime, as implied by the null energy condition, and the exist...
Radially homothetic spacetime is of Petrov-type D
Wagh, S M; Wagh, Sanjay M; Govinder, Keshlan S
2002-01-01
It is well-known \\cite{mtbh} that {\\em all} black hole solutions of General Relativity are of Petrov-type D. It may thus be expected that the spacetime of {\\em physically realizable} spherical gravitational collapse is also of Petrov-type D. We show that a radially homothetic spacetime, {\\em ie}, a spherically symmetric spacetime with hyper-surface orthogonal, radial, homothetic Killing vector, is of Petrov-type D. As has been argued in \\cite{prl1}, it is a spacetime of {\\em physically realizable} spherical collapse.
Null geodesics in a magnetically charged stringy black hole spacetime
Kuniyal, Ravi Shankar; Uniyal, Rashmi; Nandan, Hemwati; Purohit, K. D.
2016-04-01
We study the null geodesics of a four-dimensional magnetic charged black hole spacetime arising in string theory. The behaviour of effective potential in view of the different values of black hole parameters are analysed in the equatorial plane. The possible orbits for null geodesics are also discussed in view of the different values of the impact parameter. We have also calculated the frequency shift of photons in this spacetime. The results are compared to those obtained for the electrically charged stringy black hole spacetime and the Schwarzschild black hole spacetime in general relativity.
Complete classification of spherically symmetric static spacetimes via Noether symmetries
Ali, Farhad; Ali, Sajid
2013-01-01
In this paper we give a complete classification of spherically symmetric static space-times by their Noether symmetries. The determining equations for Noether symmetries are obtained by using the usual Lagrangian of a general spherically symmetric static spacetime which are integrated for each case. In particular we observe that spherically symmetric static spacetimes are categorized into six distinct classes corresponding to Noether algebra of dimensions 5, 6, 7, 9, 11 and 17. Using Noether`s theorem we also write down the first integrals for each class of such spacetimes corresponding to their Noether symmetries.
Gravitational tension, spacetime pressure and black hole volume
Armas, Jay; Obers, Niels A.; Sanchioni, Marco
2016-09-01
We study the first law of black hole thermodynamics in the presence of surrounding gravitational fields and argue that variations of these fields are naturally incorporated in the first law by defining gravitational tension or gravitational binding energy. We demonstrate that this notion can also be applied in Anti-de Sitter spacetime, in which the surrounding gravitational field is sourced by a cosmological fluid, therefore showing that spacetime volume and gravitational tension encode the same physics as spacetime pressure and black hole volume. We furthermore show that it is possible to introduce a definition of spacetime pressure and black hole volume for any spacetime with characteristic length scales which does not necessarily require a cosmological constant sourcing Einstein equations. However, we show that black hole volume is non-universal in the flat spacetime limit, questioning its significance. We illustrate these ideas by studying the resulting black hole volume of Kaluza-Klein black holes and of a toy model for a black hole binary system in five spacetime dimensions (the black saturn solution) as well as of several novel perturbative black hole solutions. These include the higher-dimensional Kerr-Newman solution in Anti-de Sitter spacetime as well as other black holes in plane wave and Lifshitz spacetimes.
Radiation spectrum of a high-dimensional rotating black hole
无
2010-01-01
This study extends the classical Damour-Ruffini method and discusses Hawking radiation in a (n + 4)-dimensional rotating black hole. Under the condition that the total energy and angular momentum of spacetime are conservative, but angular momentum a = J/M of unit mass of the black hole is variable, taking into consideration the reaction of the radiation of the particle to the spacetime, a new Tortoise coordinate transformation and discuss the black hole radiation spectrum is discussed. The radiation spectrum that satisfies the unitary principle in the general case is derived.
Radiation damping in closed expanding universes
Bernui, Armando
The dynamics of a coupled model (harmonic oscillator-relativistic scalar field) in Conformal Robertson-Walker (k = +1) spacetimes is investigated. The exact radiation-reaction equation of the source-including the retarded radiation terms due to the closed space geometry - is obtained and analyzed. A suitable family of Lyapunov functions is constructed to show that, if the spacetime expands monotonely, then the source's energy damps. A numerical simulation of this equation for expanding Universes, with and without Future Event Horizon, is performed.
Consciousness, the brain, and spacetime geometry.
Hameroff, S
2001-04-01
What is consciousness? Conventional approaches see it as an emergent property of complex interactions among individual neurons; however these approaches fail to address enigmatic features of consciousness. Accordingly, some philosophers have contended that "qualia," or an experiential medium from which consciousness is derived, exists as a fundamental component of reality. Whitehead, for example, described the universe as being composed of "occasions of experience." To examine this possibility scientifically, the very nature of physical reality must be re-examined. We must come to terms with the physics of spacetime--as described by Einstein's general theory of relativity, and its relation to the fundamental theory of matter--as described by quantum theory. Roger Penrose has proposed a new physics of objective reduction: "OR," which appeals to a form of quantum gravity to provide a useful description of fundamental processes at the quantum/classical borderline. Within the OR scheme, we consider that consciousness occurs if an appropriately organized system is able to develop and maintain quantum coherent superposition until a specific "objective" criterion (a threshold related to quantum gravity) is reached; the coherent system then self-reduces (objective reduction: OR). We contend that this type of objective self-collapse introduces non-computability, an essential feature of consciousness which distinguishes our minds from classical computers. Each OR is taken as an instantaneous event--the climax of a self-organizing process in fundamental spacetime--and a candidate for a conscious Whitehead "occasion of experience." How could an OR process occur in the brain, be coupled to neural activities, and account for other features of consciousness? We nominate a quantum computational OR process with the requisite characteristics to be occurring in cytoskeletal micro-tubules within the brain's neurons. In this model, quantum-superposed states develop in microtubule
Quantum dynamics of Lorentzian spacetime foam
Redmount, Ian H.; Suen, Wai-Mo
1994-05-01
A simple spacetime wormhole, which evolves classically from zero throat radius to a maximum value and recontracts, can be regarded as one possible mode of fluctuation in the microscopic ``spacetime foam'' first suggested by Wheeler. The dynamics of a particularly simple version of such a wormhole can be reduced to that of a single quantity, its throat radius; this wormhole thus provides a ``minisuperspace model'' for a mode of Lorentzian-signature foam. The classical equation of motion for the wormhole throat is obtained from the Einstein field equations and a suitable equation of state for the matter at the throat. Analysis of the quantum behavior of the hole then proceeds from an action corresponding to that equation of motion. The action obtained simply by calculating the scalar curvature of the hole spacetime yields a model with features like those of the relativistic free particle. In particular the Hamiltonian is nonlocal, and for the wormhole cannot even be given as a differential operator in closed form. Nonetheless the general solution of the Schrödinger equation for wormhole wave functions, i.e., the wave-function propagator, can be expressed as a path integral. Too complicated to perform exactly, this can yet be evaluated via a WKB approximation. The result indicates that the wormhole, classically stable, is quantum-mechanically unstable: A Feynman-Kac decomposition of the WKB propagator yields no spectrum of bound states. Although an initially localized wormhole wave function may oscillate for many classical expansion and recontraction periods, it must eventually leak to large radius values. The possibility of such a mode unstable against growth, combined with the observed absence of macroscopic wormholes, suggests that stability considerations may place constraints on the nature or even the existence of Planck-scale foamlike structure, at least of Lorentzian signature.
Unravelling Lorentz Covariance and the Spacetime Formalism
Cahill R. T.
2008-10-01
Full Text Available We report the discovery of an exact mapping from Galilean time and space coordinates to Minkowski spacetime coordinates, showing that Lorentz covariance and the space-time construct are consistent with the existence of a dynamical 3-space, and absolute motion. We illustrate this mapping first with the standard theory of sound, as vibrations of a medium, which itself may be undergoing fluid motion, and which is covariant under Galilean coordinate transformations. By introducing a different non-physical class of space and time coordinates it may be cast into a form that is covariant under Lorentz transformations wherein the speed of sound is now the invariant speed. If this latter formalism were taken as fundamental and complete we would be lead to the introduction of a pseudo-Riemannian spacetime description of sound, with a metric characterised by an invariant speed of sound. This analysis is an allegory for the development of 20th century physics, but where the Lorentz covariant Maxwell equations were constructed first, and the Galilean form was later constructed by Hertz, but ignored. It is shown that the Lorentz covariance of the Maxwell equations only occurs because of the use of non-physical space and time coordinates. The use of this class of coordinates has confounded 20th century physics, and resulted in the existence of a allowing dynamical 3-space being overlooked. The discovery of the dynamics of this 3-space has lead to the derivation of an extended gravity theory as a quantum effect, and confirmed by numerous experiments and observations
Lifshitz Space-Times for Schroedinger Holography
Hartong, Jelle; Obers, Niels A
2014-01-01
We show that asymptotically locally Lifshitz space-times are holographically dual to field theories that exhibit Schroedinger invariance. This involves a complete identification of the sources, which describe torsional Newton-Cartan geometry on the boundary and transform under the Schroedinger algebra. We furthermore identify the dual vevs from which we define and construct the boundary energy-momentum tensor and mass current and show that these obey Ward identities that are organized by the Schroedinger algebra. We also point out that even though the energy flux has scaling dimension larger than z+2, it can be expressed in terms of computable vev/source pairs.
Rehabilitating space-times with NUTs
Clément, Gérard, E-mail: gerard.clement@lapth.cnrs.fr [LAPTh, Université Savoie Mont Blanc, CNRS, 9 chemin de Bellevue, BP 110, F-74941, Annecy-le-Vieux cedex (France); Gal' tsov, Dmitri, E-mail: galtsov@phys.msu.ru [Department of Theoretical Physics, Faculty of Physics, Moscow State University, 119899, Moscow (Russian Federation); Guenouche, Mourad, E-mail: guenouche_mourad@umc.edu.dz [Laboratoire de Physique Théorique, Département de Physique, Faculté des Sciences Exactes, Université de Constantine 1 (Algeria); Department of Physics, Faculty of Sciences, Hassiba Benbouali University of Chlef (Algeria)
2015-11-12
We revisit the Taub–NUT solution of the Einstein equations without time periodicity condition, showing that the Misner string is still fully transparent for geodesics. In this case, analytic continuation can be carried out through both horizons leading to a Hausdorff spacetime without a central singularity, and thus geodesically complete. Furthermore, we show that, in spite of the presence of a region containing closed time-like curves, there are no closed causal geodesics. Thus, some longstanding obstructions to accept the Taub–NUT solution as physically relevant are removed.
Lax pairs for deformed Minkowski spacetimes
Kyono, Hideki; Yoshida, Kentaroh
2015-01-01
We proceed to study Yang-Baxter deformations of 4D Minkowski spacetime based on a conformal embedding. We first revisit a Melvin background and argue a Lax pair by adopting a simple replacement law invented in 1509.00173. This argument enables us to deduce a general expression of Lax pair. Then the anticipated Lax pair is shown to work for arbitrary classical $r$-matrices with Poinca\\'e generators. As other examples, we present Lax pairs for pp-wave backgrounds, the Hashimoto-Sethi background, the Spradlin-Takayanagi-Volovich background.
Rehabilitating space-times with NUTs
Clément, Gérard; Guenouche, Mourad
2015-01-01
We revisit the Taub-NUT solution of the Einstein equations without time periodicity condition, showing that the Misner string is still fully transparent for geodesics. In this case, analytic continuation can be carried out through both horizons leading to a Hausdorff spacetime without a central singularity, and thus geodesically complete. Furthermore, we show that, in spite of the presence of a region containing closed time-like curves, there are no closed causal {\\em geodesics}. Thus, some longstanding obstructions to accept the Taub-NUT solution as physically relevant are removed.
Rehabilitating space-times with NUTs
Gérard Clément
2015-11-01
Full Text Available We revisit the Taub–NUT solution of the Einstein equations without time periodicity condition, showing that the Misner string is still fully transparent for geodesics. In this case, analytic continuation can be carried out through both horizons leading to a Hausdorff spacetime without a central singularity, and thus geodesically complete. Furthermore, we show that, in spite of the presence of a region containing closed time-like curves, there are no closed causal geodesics. Thus, some longstanding obstructions to accept the Taub–NUT solution as physically relevant are removed.
Anisotropic strange star with de Sitter spacetime
Kalam, Mehedi; Rahaman, Farook; Ray, Saibal; Hossein, Sk. Monowar; Karar, Indrani; Naskar, Jayanta
2012-12-01
Stars can be treated as self-gravitating fluid. Krori and Barua (J. Phys. A., Math. Gen. 8:508, 1975) gave an analytical solution to that kind of fluids. In this connection, we propose a de Sitter model for an anisotropic strange star with the Krori-Barua spacetime. We incorporate the existence of the cosmological constant on a small scale to study the structure of anisotropic strange stars and come to the conclusion that this doping is very well compatible with the well-known physical features of strange stars.
Charged black holes in colored Lifshitz spacetimes
Zhong-Ying Fan
2015-04-01
Full Text Available We consider Einstein gravities coupled to a cosmological constant and SU(2 Yang–Mills fields in four and five dimensions. We find that the theories admit colored Lifshitz solutions with dynamic exponents z>1. We study the wave equations of the SU(2 scalar triplet in the bulk, and find that the vacuum color modifies the scaling dimensions of the dual operators. We also introduce a Maxwell field and construct exact solutions of electrically-charged black holes that approach the D=4, z=3 and D=5, z=4 colored Lifshitz spacetimes. We derive the thermodynamical first law for general colored and charged Lifshitz black holes.
High-order tail in Kerr spacetime
Casals, Marc; Ottewill, Adrian C
2016-01-01
We investigate the late-time tail of the retarded Green function for the dynamics of a linear field perturbation of Kerr spacetime. We develop an analytical formalism for obtaining the late-time tail up to arbitrary order for general integer spin of the field. We then apply this formalism to obtain the details of the first five orders in the late-time tail of the Green function for the case of a scalar field: to leading order we recover the known power law tail $t^{-2\\ell-3}$, and at third order we obtain a logarithmic correction, $t^{-2\\ell-5}\\ln t$, where $\\ell$ is the field multipole.
Relative-locality effects in Snyder spacetime
Mignemi, S
2016-01-01
When applied to some models of noncommutative geometry, the formalism of relative locality predicts the occurrence of a delay in the time of arrival of massless particle of different energies emitted by a distant observer. In this letter, we show that this is not the case with Snyder spacetime, essentially because the Lorentz invariance is not deformed in this case. This conclusion is in accordance with the findings of doubly special relativity. Distant observers may however measure different times of flight for massive particle.
Late time tails in the Kerr spacetime
Gleiser, Reinaldo J; Pullin, Jorge
2008-01-01
Outside a black hole, perturbation fields die off in time as $1/t^n$. For spherical holes $n=2\\ell+3$ where $\\ell$ is the multipole index. In the nonspherical Kerr spacetime there is no coordinate-independent meaning of "multipole," and a common sense viewpoint is to set $\\ell$ to the lowest radiatiable index, although theoretical studies have led to very different claims. Numerical results, to date, have been controversial. Here we show that expansion for small Kerr spin parameter $a$ leads to very definite numerical results confirming previous theoretical analyses.
Effective Lagrangian in de Sitter Spacetime
Kitamoto, Hiroyuki
2016-01-01
Scale invariant fluctuations of metric are universal feature of quantum gravity in de Sitter spacetime. We construct an effective Lagrangian which summarizes their implications on local physics by integrating super-horizon metric fluctuations. It shows infrared quantum effects are local and render fundamental couplings time dependent. We impose Lorenz invariance on the effective Lagrangian as it is required by the principle of general covariance. We show that such a requirement leads to unique physical predictions by fixing the quantization ambiguities. We explain how the gauge parameter dependence of observables is canceled. In particular the relative evolution speed of the couplings are shown to be gauge invariant.
Tools for the study of dynamical spacetimes
Zhang, Fan
This thesis covers a range of topics in numerical and analytical relativity, centered around introducing tools and methodologies for the study of dynamical spacetimes. The scope of the studies is limited to classical (as opposed to quantum) vacuum spacetimes described by Einstein's general theory of relativity. The numerical works presented here are carried out within the Spectral Einstein Code (SpEC) infrastructure, while analytical calculations extensively utilize Wolfram's Mathematica program. We begin by examining highly dynamical spacetimes such as binary black hole mergers, which can be investigated using numerical simulations. However, there are difficulties in interpreting the output of such simulations. One difficulty stems from the lack of a canonical coordinate system (henceforth referred to as gauge freedom) and tetrad, against which quantities such as Newman-Penrose Psi4 (usually interpreted as the gravitational wave part of curvature) should be measured. We tackle this problem in Chapter 2 by introducing a set of geometrically motivated coordinates that are independent of the simulation gauge choice, as well as a quasi-Kinnersley tetrad, also invariant under gauge changes in addition to being optimally suited to the task of gravitational wave extraction. Another difficulty arises from the need to condense the overwhelming amount of data generated by the numerical simulations. In order to extract physical information in a succinct and transparent manner, one may define a version of gravitational field lines and field strength using spatial projections of the Weyl curvature tensor. Introduction, investigation and utilization of these quantities will constitute the main content in Chapters 3 through 6. For the last two chapters, we turn to the analytical study of a simpler dynamical spacetime, namely a perturbed Kerr black hole. We will introduce in Chapter 7 a new analytical approximation to the quasi-normal mode (QNM) frequencies, and relate various
Generalized Vaidya spacetime for cubic gravity
Ruan, Shan-Ming
2015-01-01
We present a kind of generalized Vaidya solutions of a new cubic gravity in five dimensions whose field equations in spherically spacetime are always second order like the Lovelock gravity. We also study the thermodynamics of its apparent horizon and get its entropy expression and generalized Misner-Sharp energy. Finally we present the first law and second law hold in this gravity. Although all the results are analogue to those in Lovelock gravity, we in fact introduce the contribution of new cubic term in five dimensions where cubic Lovelock term is just zero.
Lax pairs for deformed Minkowski spacetimes
Kyono, Hideki; Sakamoto, Jun-ichi; Yoshida, Kentaroh [Department of Physics, Kyoto University,Kitashirakawa Oiwake-cho, Kyoto 606-8502 (Japan)
2016-01-25
We proceed to study Yang-Baxter deformations of 4D Minkowski spacetime based on a conformal embedding. We first revisit a Melvin background and argue a Lax pair by adopting a simple replacement law invented in 1509.00173. This argument enables us to deduce a general expression of Lax pair. Then the anticipated Lax pair is shown to work for arbitrary classical r-matrices with Poincaré generators. As other examples, we present Lax pairs for pp-wave backgrounds, the Hashimoto-Sethi background, the Spradlin-Takayanagi-Volovich background.
Smarandache Curves in Minkowski Space-time
Turgut, Melih; Yilmaz, Suha
2008-01-01
A regular curve in Minkowski space-time, whose position vector is composed by Frenet frame vectors on another regular curve, is called a Smarandache Curve. In this paper, we define a special case of such curves and call it Smarandache TB2 Curves in the space E41. Moreover, we compute formulas of its Frenet apparatus according to base curve via the method expressed in [3]. By this way, we obtain an another orthonormal frame of E41.
Discreteness of Curved Spacetime from GUP
Ahmad Adel Abutaleb
2013-01-01
Full Text Available Diverse theories of quantum gravity expect modifications of the Heisenberg's uncertainty principle near the Planck scale to a so-called Generalized uncertainty principle (GUP. It was shown by some authors that the GUP gives rise to corrections to the Schrodinger , Klein-Gordon, and Dirac equations. By solving the GUP corrected equations, the authors arrived at quantization not only of energy but also of box length, area, and volume. In this paper, we extend the above results to the case of curved spacetime (Schwarzschild metric. We showed that we arrived at the quantization of space by solving Dirac equation with GUP in this metric.
Relative-locality effects in Snyder spacetime
Mignemi, S.; Samsarov, A.
2017-05-01
Most models of noncommutative geometry and doubly special relativity suggest that the principle of absolute locality should be replaced by the milder notion of relative locality. In particular, they predict the occurrence of a delay in the time of arrival of massless particle of different energies emitted by a distant observer. In this letter, we show that this is not the case with Snyder spacetime, essentially because the Lorentz invariance is not deformed in this case. Distant observers may however measure different times of flight for massive particles.
Noncommutative Space-time from Quantized Twistors
Lukierski, Jerzy
2013-01-01
We consider the relativistic phase space coordinates (x_{\\mu},p_{\\mu}) as composite, described by functions of the primary pair of twistor coordinates. It appears that if twistor coordinates are canonicaly quantized the composite space-time coordinates are becoming noncommutative. We obtain deformed Heisenberg algebra which in order to be closed should be enlarged by the Pauli-Lubanski four-vector components. We further comment on star-product quantization of derived algebraic structures which permit to introduce spin-extended deformed Heisenberg algebra.
Rehabilitating space-times with NUTs
Clément, Gérard; Gal'tsov, Dmitri; Guenouche, Mourad
2015-11-01
We revisit the Taub-NUT solution of the Einstein equations without time periodicity condition, showing that the Misner string is still fully transparent for geodesics. In this case, analytic continuation can be carried out through both horizons leading to a Hausdorff spacetime without a central singularity, and thus geodesically complete. Furthermore, we show that, in spite of the presence of a region containing closed time-like curves, there are no closed causal geodesics. Thus, some longstanding obstructions to accept the Taub-NUT solution as physically relevant are removed.
Causal Stability Conditions for General Relativistic Spacetimes
Howard, E M
2016-01-01
A brief overview of some open questions in general relativity with important consequences for causality theory is presented, aiming to a better understanding of the causal structure of the spacetime. Special attention is accorded to the problem of fundamental causal stability conditions. Several questions are raised and some of the potential consequences of recent results regarding the causality problem in general relativity are presented. A key question is whether causality violating regions are locally allowed. The new concept of almost stable causality is introduced; meanwhile, related conditions and criteria for the stability and almost stability of the causal structure are discussed.
Charged Anisotropic Star on Paraboloidal Spacetime
Ratanpal, B S
2015-01-01
The charged anisotropic star on paraboloidal spacetime is reported by choosing particular form of radial pressure and electric field intensity. The non-singular solution of Einstein-Maxwell system of equation have been derived and it is shown that model satisfy all the physical plausibility conditions. It is observed that in the absence of electric field intensity, model reduces to particular case of uncharged Sharma \\& Ratanpal model. It is also observed that the parameter used in electric field intensity directly effects the mass of the star.
Asymptotically Flat Space-Times and its Hidden Recesses: An Enigma from GR
Newman, Ezra T
2016-01-01
We begin by emphasizing that we are dealing with standard Einstein or Einstein-Maxwell theory - absolutely no new physics has been inserted. The fresh item is that the well-known asymptotically flat solutions of the Einstein-Maxwell theory are transformed to a new coordinate system with surprising and (seemingly) inexplicable results. We begin with the standard description of (Null) Asymptotically Flat Space-Times described in conventional Bondi-coordinates. After transforming the variables (mainly the asymptotic Weyl tensor components) to a very special set of NU (Newman-Unti) coordinates, we find a series of relations totally mimicking standard Newtonian classical mechanics and Maxwell theory. The surprising and troubling aspect of these relations is that the associated motion and radiation does not take place in physical space-time. Instead these relations takes place in an unusual inherited complex four-dimensional manifold referred to as H-Space that has no immediate relationship with space-time. In fact...
Naked Singularities in Spherically Symmetric, Self-Similar Spacetimes
Wagh, S M; Wagh, Sanjay M.; Govinder, Keshlan S.
2001-01-01
We show that all known naked singularities in spherically symmetric self-similar spacetimes arise as a result of singular initial matter distribution. This is a result of the peculiarity of the coordinate transformation that takes these spacetimes into a separable form. Therefore, these examples of naked singularities are of no apparent consequence to astrophysical observations or theories.
Space-time domain decomposition method for scalar conservation laws
Doucoure, S
2012-01-01
The Space-Time Integrated Least-Squares (STILS) method is considered to analyze a space-time domain decomposition algorithm for scalar conservation laws. Continuous and discrete convergence estimates are given. Next using a time-marching finite element formulation, the STILS solution and its domain decomposition form are numerically compared.
Photoelectric Effect for Twist-deformed Space-time
Daszkiewicz, M.
In this article, we investigate the impact of twisted space-time on the photoelectric effect, i.e., we derive the $\\theta$-deformed threshold frequency. In such a way we indicate that the space-time noncommutativity strongly enhances the photoelectric process.
On the spacetime connecting two aeons in conformal cyclic cosmology
Araujo, A; Pereira, J G; Sampson, A C; Savi, L L
2015-01-01
It is shown that the contraction limit of a de Sitter spacetime for the cosmological term going to infinity satisfies a number of properties, including the Weyl curvature hypothesis, which qualify it as a candidate to represent the bridging spacetime connecting two aeons in Penrose's conformal cyclic cosmology.
Space-time modeling of electricity spot prices
Abate, Girum Dagnachew; Haldrup, Niels
In this paper we derive a space-time model for electricity spot prices. A general spatial Durbin model that incorporates the temporal as well as spatial lags of spot prices is presented. Joint modeling of space-time effects is necessarily important when prices and loads are determined in a network...
Quantum mechanics in fractional and other anomalous spacetimes
Calcagni, Gianluca; Nardelli, Giuseppe; Scalisi, Marco
2012-01-01
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the wave-functions minimizing the uncertainty are found. In spite of the
A quasiperiodic Gibbons-Hawking metric and spacetime foam
Nergiz, S; Nergiz, Serdar; Saclioglu, Cihan
1995-01-01
We present a quasiperiodic self-dual metric of the Gibbons--Hawking type with one gravitational instanton per spacetime cell. The solution, based on an adaptation of Weierstrassian \\zeta and \\sigma functions to three dimensions, conforms to a definition of spacetime foam given by Hawking.
CONSTRUCTIONS OF THREE-TRANSMIT-ANTENNA SPACE-TIME CODES
Hongxi TONG; Fei YU
2007-01-01
In this paper, we give design methods for three-transmit-antenna space-time codes which have reasonable parameters. A few examples are given to show that some unitary space-time codes constructed with our methods are better than the previously best-known ones.
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.
On an Intriguing Signature-Reversal Exhibited by Cremonian Spacetimes
Saniga, M
2004-01-01
It is shown that a generic quadro-quartic Cremonian spacetime, which is endowed with one spatial and three time dimensions, can continuously evolve into a signature-reversed configuration, i.e. into the classical spacetime featuring one temporal and three space dimensions. An interesting cosmological implication of this finding is mentioned.
Late time tail of wave propagation on curved spacetime
Ching, E S C; Suen, W M; Young, K; Ching, E S C; Leung, P T; Suen, W M; Young, K
1994-01-01
The late time behavior of waves propagating on a general curved spacetime is studied. The late time tail is not necessarily an inverse power of time. Our work extends, places in context, and provides understanding for the known results for the Schwarzschild spacetime. Analytic and numerical results are in excellent agreement.
A C *-Algebraic Model for Locally Noncommutative Spacetimes
Heller, Jakob G.; Neumaier, Nikolai; Waldmann, Stefan
2007-06-01
Locally noncommutative spacetimes provide a refined notion of noncommutative spacetimes where the noncommutativity is present only for small distances. Here we discuss a non-perturbative approach based on Rieffel’s strict deformation quantization. To this end, we extend the usual C *-algebraic results to a pro-C *-algebraic framework.
Electromagnetic and gravitational fields in a Schwarzschild space-time
Porrill, J.; Stewart, J.M. (Cambridge Univ. (UK). Dept. of Applied Mathematics and Theoretical Physics)
1981-05-19
The propagation of electromagnetic fields and linearized perturbations of the vacuum Einstein equations on a Schwarzchild background space-time are discussed, and relations between the asymptotic form of the fields at null infinity and the data are established. Without suitable restrictions on the data, perturbations of a Schwarzschild space-time need not be weakly asymptotically simple.
A Complete Foliation of Schwarzschild Spacetime by Free Falling Hypersurfaces
M. Ayub Faridi; Amjad Pervez; Haris Rashid; Fazal-e-Aleem
2006-01-01
Free falling hypersurfaces in the Schwarzschild geometry have been studied to provide a complete foliation of spacetime. The hypersurfaces do not cross into the maximally extended spacetime and are well behaved everywhere except at the singularity r = 0 the mean extrinsic curvature becomes infinity.
Space-time discontinuous Galerkin finite element methods
Vegt, van der J.J.W.; Deconinck, H.; Ricchiuto, M.
2006-01-01
In these notes an introduction is given to space-time discontinuous Galerkin (DG) finite element methods for hyperbolic and parabolic conservation laws on time dependent domains. the space-time DG discretization is explained in detail, including the definition of the numerical fluxes and stabilizati
Space-time discontinuous Galerkin method for compressible flow
Klaij, C.M.
2006-01-01
The space-time discontinuous Galerkin method allows the simulation of compressible flow in complex aerodynamical applications requiring moving, deforming and locally refined meshes. This thesis contains the space-time discretization of the physical model, a fully explicit solver for the resulting
Photoelectric effect for twist-deformed space-time
Daszkiewicz, Marcin
2016-01-01
In this article, we investigate the impact of twisted space-time on the photoelectric effect, i.e., we derive the $\\theta$-deformed threshold frequency. In such a way we indicate that the space-time noncommutativity strongly enhances the photoelectric process.
Spacetime Processing Metasurfaces: GSTC Synthesis and Prospective Applications
Chamanara, Nima; Achouri, Karim; Caloz, Christophe
2016-01-01
The paper presents the general concept of spacetime processing metasurfaces, synthesized by generalized sheet transition conditions (GSTCs). It is shown that such metasurfaces can perform multiple simultaneous spatio-temporal processing transformations on incident electromagnetic waves. A time-reversal space-generalized-refraction metasurface and a multi-time-space-differentiating metasurfaces are presented as applications of the general spacetime processing metasurface concept.
Holographic thermal field theory on curved spacetimes
Marolf, Donald; Wiseman, Toby
2013-01-01
The AdS/CFT correspondence relates certain strongly coupled CFTs with large effective central charge $c_\\text{eff}$ to semi-classical gravitational theories with AdS asymptotics. We describe recent progress in understanding gravity duals for CFTs on non-trivial spacetimes at finite temperature, both in and out of equilibrium. Such gravity methods provide powerful new tools to access the physics of these strongly coupled theories, which often differs qualitatively from that found at weak coupling. Our discussion begins with basic aspects of AdS/CFT and progresses through thermal CFTs on the Einstein Static Universe and on periodically identified Minkowski spacetime. In the latter context we focus on states describing so-called plasma balls, which become stable at large $c_\\text{eff}$. We then proceed to out-of-equilibrium situations associated with dynamical bulk black holes. In particular, the non-compact nature of these bulk black holes allows stationary solutions with non-Killing horizons that describe time...
Spacetime curvature induced corrections to Lamb shift
Zhou, Wenting
2012-01-01
The Lamb shift results from the coupling of an atom with vacuum fluctuations of quantum fields, so corrections are expected to arise when the spacetime is curved since the vacuum fluctuations are modified by the presence of spacetime curvature. Here, we calculate the curvature-induced correction to the Lamb shift outside a spherically symmetric object and demonstrate that this correction can be remarkably significant outside a compact massive astrophysical body. For instance, for a neutron star or a stellar mass black hole, the correction is $\\sim$ 25% at a radial distance of $4GM/c^2$, $\\sim$ 16% at $10GM/c^2$ and as large as $\\sim$ 1.6% even at $100GM/c^2$, where $M$ is the mass of the object, $G$ the Newtonian constant, and $c$ the speed of light. In principle, we can look at the spectra from a distant compact supper-massive body to find such corrections. Therefore, our results suggest a possible way of detecting fundamental quantum effects in astronomical observations.
Gauge-invariant perturbations of Schwarzschild spacetime
Shah, Abhay G; Aksteiner, Steffen; Andersson, Lars; Bäckdahl, Thomas
2016-01-01
We study perturbations of Schwarzschild spacetime in a coordinate-free, covariant form. The GHP formulation, having the advantage of not only being covariant but also tetrad-rotation invariant, is used to write down the previously known odd- and even-parity gauge-invariants and the equations they satisfy. Additionally, in the even-parity sector, a new invariant and the second order hyperbolic equation it satisfies are presented. Chandrasekhar's work on transformations of solutions for perturbation equations on Schwarzschild spacetime is translated into the GHP form, i.e., solutions for the equations of the even- and odd-parity invariants are written in terms of one another, and the extreme Weyl scalars; and solutions for the equations of these latter invariants are also written in terms of one another. Recently, further gauge invariants previously used by Steven Detweiler have been described. His method is translated into GHP form and his basic invariants are presented here. We also show how these invariants ...
Spacetime replication of continuous variable quantum information
Hayden, Patrick; Nezami, Sepehr; Salton, Grant; Sanders, Barry C.
2016-08-01
The theory of relativity requires that no information travel faster than light, whereas the unitarity of quantum mechanics ensures that quantum information cannot be cloned. These conditions provide the basic constraints that appear in information replication tasks, which formalize aspects of the behavior of information in relativistic quantum mechanics. In this article, we provide continuous variable (CV) strategies for spacetime quantum information replication that are directly amenable to optical or mechanical implementation. We use a new class of homologically constructed CV quantum error correcting codes to provide efficient solutions for the general case of information replication. As compared to schemes encoding qubits, our CV solution requires half as many shares per encoded system. We also provide an optimized five-mode strategy for replicating quantum information in a particular configuration of four spacetime regions designed not to be reducible to previously performed experiments. For this optimized strategy, we provide detailed encoding and decoding procedures using standard optical apparatus and calculate the recovery fidelity when finite squeezing is used. As such we provide a scheme for experimentally realizing quantum information replication using quantum optics.
Test particles in a magnetized conformastatic spacetime
Gutiérrez-Piñeres, Antonio C.; Capistrano, Abraão J. S.; Quevedo, Hernando
2016-06-01
A class of exact conformastatic solutions of the Einstein-Maxwell field equations is presented in which the gravitational and electromagnetic potentials are completely determined by a harmonic function. We derive the equations of motion for neutral and charged particles in a spacetime background characterized by this class of solutions. As an example, we focus on the analysis of a particular harmonic function, which generates a singularity-free and asymptotically flat spacetime that describes the gravitational field of a punctual mass endowed with a magnetic field. In this particular case, we investigate the main physical properties of equatorial circular orbits. We show that due to the electromagnetic interaction, it is possible to have charged test particles which stay at rest with respect to a static observer located at infinity. Additionally, we obtain an analytic expression for the perihelion advance of test particles and the corresponding explicit value in the case of a punctual magnetic mass. We show that the analytical expressions obtained from our analysis are sufficient for being confronted with observations in order to establish whether such objects can exist in nature.
Hydrodynamics of spacetime and vacuum viscosity
Eling, Christopher
2008-01-01
It has recently been shown that the Einstein equation can be derived by demanding a non-equilibrium entropy balance law dS = dQ/T + dS_i hold for all local acceleration horizons through each point in spacetime. The entropy change dS is proportional to the change in horizon area while dQ and T are the energy flux across the horizon and Unruh temperature seen by an accelerating observer just inside the horizon. The internal entropy production term dS_i is proportional to the squared shear of the horizon and the ratio of the proportionality constant to the area entropy density must be \\hbar/4\\pi. Here we will show that this derivation can be reformulated in the language of hydrodynamics. We postulate that the vacuum thermal state in the Rindler wedge of spacetime obeys the holographic principle. Hydrodynamic perturbations of this state exist and are manifested in the dynamics of a stretched horizon fluid at the horizon boundary. Using the equations of hydrodynamics we derive the entropy balance law and show the ...
Electromagnetic Casimir piston in higher dimensional spacetimes
Teo, L P
2011-01-01
We consider the Casimir effect of the electromagnetic field in a higher dimensional spacetime of the form $M\\times \\mathcal{N}$, where $M$ is the 4-dimensional Minkowski spacetime and $\\mathcal{N}$ is an $n$-dimensional compact manifold. The Casimir force acting on a planar piston that can move freely inside a closed cylinder with the same cross section is investigated. Different combinations of perfectly conducting boundary conditions and infinitely permeable boundary conditions are imposed on the cylinder and the piston. It is verified that if the piston and the cylinder have the same boundary conditions, the piston is always going to be pulled towards the closer end of the cylinder. However, if the piston and the cylinder have different boundary conditions, the piston is always going to be pushed to the middle of the cylinder. By taking the limit where one end of the cylinder tends to infinity, one obtains the Casimir force acting between two parallel plates inside an infinitely long cylinder. The asymptot...
Bi-metric pseudo-Finslerian spacetimes
Skakala, Jozef; Visser, Matt
2011-08-01
Finsler spacetimes have become increasingly popular within the theoretical physics community over the last two decades. However, because physicists need to use pseudo-Finsler structures to describe propagation of signals, there will be nonzero null vectors in both the tangent and cotangent spaces — this causes significant problems in that many of the mathematical results normally obtained for "usual" (Euclidean signature) Finsler structures either do not apply, or require significant modifications to their formulation and/or proof. We shall first provide a few basic definitions, explicitly demonstrating the interpretation of bi-metric theories in terms of pseudo-Finsler norms. We shall then discuss the tricky issues that arise when trying to construct an appropriate pseudo-Finsler metric appropriate to bi-metric spacetimes. Whereas in Euclidian signature the construction of the Finsler metric typically fails only at the zero vector, in Lorentzian signature the Finsler metric is typically ill-defined on the entire null cone. Consequently it is not a good idea to try to encode bi-metricity into pseudo-Finsler geometry. One has to be very careful when applying the concept of pseudo-Finsler geometry in physics.
Cosmological singularities in Bakry-\\'Emery spacetimes
Galloway, Gregory J
2013-01-01
We consider spacetimes consisting of a manifold with Lorentzian metric and a weight function or scalar field. These spacetimes admit a Bakry-\\'Emery-Ricci tensor which is a natural generalization of the Ricci tensor. We impose an energy condition on the Bakry-\\'Emery-Ricci tensor and obtain singularity theorems of a cosmological type, both for zero and for positive cosmological constant. That is, we find conditions under which every timelike geodesic is incomplete. These conditions are given by "open" inequalities, so we examine the borderline (equality) cases and show that certain singularities are avoided in these cases only if the geometry is rigid; i.e., if it splits as a Lorentzian product or, for a positive cosmological constant, a warped product, and the weight function is constant along the time direction. Then the product case is future timelike geodesically complete while, in the warped product case, worldlines of conformally static observers are complete. Our results answer a question posed by J Ca...
New class of LRS spacetimes with simultaneous rotation and spatial twist
Singh, Sayuri; Goswami, Rituparno; Maharaj, Sunil D
2016-01-01
We establish the existence and find the necessary and sufficient conditions for a new class of solutions of Locally Rotationally Symmetric spacetimes that have non vanishing rotation and spatial twist simultaneously. We transparently show that the existence of such solutions demand non vanishing and bounded heat flux and these solutions are self similar. We provide a brief algorithm indicating how to solve the system of field equations with the given Cauchy data on an initial spacelike Cauchy surface. Finally we argue that these solutions can be used as a first approximation from spherical symmetry to study rotating, inhomogeneous, dynamic and radiating astrophysical stars.
Spontaneous Emission of an Atom in a Spacetime with Two Parallel Reflecting Boundaries
HUANG Tie-Tie; ZHU Zhi-Ying; ZHU Yun-Feng; YU Hong-Wei
2009-01-01
@@ We consider an inertial two-level atom in interaction with a real massless scalar quantum field in a spacetime between two parallel reflecting plane boundaries, and calculate the contributions of vacuum fluctuations and radiation reaction to the rate of change of the atomic energy. Our results show that there exists a regime of the separation L between the two boundaries such that the excited atom's spontaneous emission is impossible. There also exist certain values of the atom's position such that the corrections due to the presence of boundaries balance each other, so that the atom's spontaneous emission rate is the same as if there were no boundaries at all.
Aranha, R F; Tonini, E V
2012-01-01
We examine numerically the process of gravitational wave recoil in the merger of two black holes in non head-on collision, in the realm of Robinson-Trautman spacetimes. Characteristic initial data for the system are constructed, and the evolution covers the post-merger phase up to the final configuration of the remnant black hole. The net momentum flux carried out by gravitational waves and the associated impulses are evaluated. Our analysis is based on the Bondi-Sachs conservation laws for the energy momentum of the system. The net kick velocity $V_{k}$ imparted to the merged system by the total gravitational wave impulse is also evaluated. Typically for a non head-on collision the net momentum flux carried out by gravitational waves is nonzero for equal-mass colliding black holes. The distribution of $V_{k}$ as a function of the symmetric mass ratio $\\eta$ is well fitted by a modified Fitchett $\\eta$-scaling law, the additional parameter modifying the law being a measure of the nonzero gravitational wave mo...
The Finsler spacetime framework. Backgrounds for physics beyond metric geometry
Pfeifer, Christian
2013-11-15
The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the
Geodesics in the (anti-)de Sitter spacetime
Tho, Nguyen Phuc Ky
2016-01-01
A class of exact solutions of the geodesic equations in (anti-)de Sitter spacetimes is presented. The geodesics for test particles in $AdS_4$ and $dS_4$ spacetimes are respectively sinusoidal and hyperbolic sine world lines. The world line for light rays is straight lines as known. The world lines of test particles are not dependent on their energy as noted. Spontaneous symmetry breaking of $AdS_4$ spacetime provides a physical explanation for arising of the virtual particle and antiparticle pairs in the vacuum. Interestingly, the energy of a pair and the time its particles moving along their geodesics can be related by a relation similar to Heisenberg uncertainty one pertaining quantum vacuum fluctuations. The sinusoidal geodesics of $AdS_4$ spacetime can describe the world lines of the virtual particles and antiparticles. The hyperbolic sine geodesics of $dS_4$ spacetime can explain why galaxies move apart with positive accelerations.
Einstein Revisited Gravitation In Curved Spacetime Without Event Horizons
Leiter, D L; Leiter, Darryl J.; Robertson, Stanley L.
2001-01-01
It has been shown [1] that Einstein General Relativity can be expressed covariantly in a bi-metric spacetime context, without the uncertainties which arise from the effects of gravitational energy-momentum pseudotensors. We construct a new bi-metric general relativity theory based on a new physical paradigm which allows the operational procedures of local spacetime measurements in general spacetime frames of reference to be defined in a similar manner as that for local spacetime measurements in special relativistic inertial frames. The paradigm [2]uses the Principle of Equivalence to define the symmetric metric tensor of curved spacetime as an exponential function of a symmetric gravitational potential tensor. This exponential function and the requirement that the equations of motion have an N-body interactive form imply that the gravitational potential tensor must obey a superposition principle. This requirement uniquely determines the tensor covariant field equations of the new bi-metric General Relativity....
Entropy of Movement Outcome in Space-Time.
Lai, Shih-Chiung; Hsieh, Tsung-Yu; Newell, Karl M
2015-07-01
Information entropy of the joint spatial and temporal (space-time) probability of discrete movement outcome was investigated in two experiments as a function of different movement strategies (space-time, space, and time instructional emphases), task goals (point-aiming and target-aiming) and movement speed-accuracy constraints. The variance of the movement spatial and temporal errors was reduced by instructional emphasis on the respective spatial or temporal dimension, but increased on the other dimension. The space-time entropy was lower in targetaiming task than the point aiming task but did not differ between instructional emphases. However, the joint probabilistic measure of spatial and temporal entropy showed that spatial error is traded for timing error in tasks with space-time criteria and that the pattern of movement error depends on the dimension of the measurement process. The unified entropy measure of movement outcome in space-time reveals a new relation for the speed-accuracy.
Effects of spacetime anisotropy on the galaxy rotation curves
Chang, Zhe; Li, Xin; Lin, Hai-Nan; Wang, Sai
2013-01-01
The observations on galaxy rotation curves show significant discrepancies from the Newtonian theory. This issue could be explained by the effect of the anisotropy of the spacetime. Conversely, the spacetime anisotropy could also be constrained by the galaxy rotation curves. Finsler geometry is a kind of intrinsically anisotropic geometry. In this paper, we study the effect of the spacetime anisotropy at the galactic scales in the Finsler spacetime. It is found that the Finslerian model has close relations with the Milgrom's MOND. By performing the best-fit procedure to the galaxy rotation curves, we find that the anisotropic effects of the spacetime become significant when the Newtonian acceleration \\(GM/r^2\\) is smaller than the critical acceleration \\(a_0\\). Interestingly, the critical acceleration \\(a_0\\), although varies between different galaxies, is in the order of magnitude \\(cH_0/2\\pi\\sim 10^{-10} \\rm{m\\,\\, s^{-2}}\\).
BTZ extensions of globally hyperbolic singular flat spacetimes
Brunswic, Léo
2016-01-01
Minkowski space is the local model of 3 dimensionnal flat spacetimes. Recent progress in the description of globally hyperbolic flat spacetimes showed strong link between Lorentzian geometry and Teichm{\\"u}ller space. We notice that Lorentzian generalisations of conical singularities are useful for the endeavours of descripting flat spacetimes, creating stronger links with hyperbolic geometry and compactifying spacetimes. In particular massive particles and extreme BTZ singular lines arise naturally. This paper is three-fold. First, prove background local properties which will be useful for future work. Second, generalise fundamental theorems of the theory of globally hyperbolic flat spacetimes. Third, defining BTZ-extension and proving it preserves Cauchy-maximality and Cauchy-completeness.
Beyond the speed of light on Finsler spacetimes
Pfeifer, Christian, E-mail: christian.pfeifer@desy.de [II. Institut fuer Theoretische Physik und Zentrum fuer Mathematische Physik, Universtitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany); Wohlfarth, Mattias N.R., E-mail: mattias.wohlfarth@desy.de [II. Institut fuer Theoretische Physik und Zentrum fuer Mathematische Physik, Universtitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)
2012-06-06
As a prototypical massive field theory we study the scalar field on the recently introduced Finsler spacetimes. We show that particle excitations exist that propagate faster than the speed of light recognized as the boundary velocity of observers. This effect appears already in Finsler spacetime geometries with very small departures from Lorentzian metric geometry. It switches on for a sufficiently large ratio of the particle four-momentum and mass, and is the consequence of a modified version of the Coleman-Glashow velocity dispersion relation. The momentum dispersion relation on Finsler spacetimes is shown to be the same as on metric spacetimes, which differs from many quantum gravity models. If similar relations resulted for fermions on Finsler spacetimes, these generalized geometries could explain the potential observation of superluminal neutrinos claimed by the Opera Collaboration.
Beyond the speed of light on Finsler spacetimes
Pfeifer, Christian; Wohlfarth, Mattias N. R.
2012-06-01
As a prototypical massive field theory we study the scalar field on the recently introduced Finsler spacetimes. We show that particle excitations exist that propagate faster than the speed of light recognized as the boundary velocity of observers. This effect appears already in Finsler spacetime geometries with very small departures from Lorentzian metric geometry. It switches on for a sufficiently large ratio of the particle four-momentum and mass, and is the consequence of a modified version of the Coleman-Glashow velocity dispersion relation. The momentum dispersion relation on Finsler spacetimes is shown to be the same as on metric spacetimes, which differs from many quantum gravity models. If similar relations resulted for fermions on Finsler spacetimes, these generalized geometries could explain the potential observation of superluminal neutrinos claimed by the Opera Collaboration.
Spinning, Precessing, Black Hole Binary Spacetime via Asymptotic Matching
Nakano, Hiroyuki; Campanelli, Manuela; West, Eric J
2016-01-01
We briefly discuss a method to construct a global, analytic, approximate spacetime for precessing, spinning binary black holes. The spacetime construction is broken into three parts: the inner zones are the spacetimes close to each black hole, and are approximated by perturbed Kerr solutions; the near zone is far from the two black holes, and described by the post-Newtonian metric; and finally the wave (far) zone, where retardation effects need to be taken into account, is well modeled by the post-Minkowskian metric. These individual spacetimes are then stitched together using asymptotic matching techniques to obtain a global solution that approximately satisfies the Einstein field equations. Precession effects are introduced by rotating the black hole spin direction according to the precessing equations of motion, in a way that is consistent with the global spacetime construction.
Hypersurface-deformation algebroids and effective space-time models
Bojowald, Martin; Buyukcam, Umut; D'Ambrosio, Fabio
2016-01-01
In canonical gravity, covariance is implemented by brackets of hypersurface-deformation generators forming a Lie algebroid. Lie algebroid morphisms therefore allow one to relate different versions of the brackets that correspond to the same space-time structure. An application to examples of modified brackets found mainly in models of loop quantum gravity can in some cases map the space-time structure back to the classical Riemannian form after a field redefinition. For one type of quantum corrections (holonomies), signature change appears to be a generic feature of effective space-time, and is shown here to be a new quantum space-time phenomenon which cannot be mapped to an equivalent classical structure. In low-curvature regimes, our constructions prove the existence of classical space-time structures assumed elsewhere in models of loop quantum cosmology, but also shows the existence of additional quantum corrections that have not always been included.
The Weyl tensor correlator in cosmological spacetimes
Fröb, Markus B
2014-01-01
We give a general expression for the Weyl tensor two-point function in a general Friedmann-Lema\\^itre-Robertson-Walker spacetime. We work in reduced phase space for the perturbations, i.e., quantize only the dynamical degrees of freedom without adding any gauge-fixing term. The general formula is illustrated by a calculation in slow-roll single-field inflation to first order in the slow-roll parameters $\\epsilon$ and $\\delta$, and the result is shown to have the correct de Sitter limit as $\\epsilon, \\delta \\to 0$. Furthermore, it is seen that the Weyl tensor correlation function does not suffer from infrared divergences, unlike the two-point functions of the metric and scalar field perturbations. Lastly, we show how to recover the usual tensor power spectrum from the Weyl tensor correlation function.
The Computational Power of Minkowski Spacetime
Biamonte, Jacob D
2009-01-01
The Lorentzian length of a timelike curve connecting both endpoints of a classical computation is a function of the path taken through Minkowski spacetime. The associated runtime difference is due to time-dilation: the phenomenon whereby an observer finds that another's physically identical ideal clock has ticked at a different rate than their own clock. Using ideas appearing in the framework of computational complexity theory, time-dilation is quantified as an algorithmic resource by relating relativistic energy to an $n$th order polynomial time reduction at the completion of an observer's journey. These results enable a comparison between the optimal quadratic \\emph{Grover speedup} from quantum computing and an $n=2$ speedup using classical computers and relativistic effects. The goal is not to propose a practical model of computation, but to probe the ultimate limits physics places on computation.
Relative-locality effects in Snyder spacetime
Mignemi, S., E-mail: smignemi@unica.it [Dipartimento di Matematica e Informatica, Università di Cagliari, viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy); Samsarov, A., E-mail: andjelo.samsarov@irb.hr [Rudjer Bošković Institute, Bijenička cesta 54, 10002 Zagreb (Croatia)
2017-05-18
Most models of noncommutative geometry and doubly special relativity suggest that the principle of absolute locality should be replaced by the milder notion of relative locality. In particular, they predict the occurrence of a delay in the time of arrival of massless particle of different energies emitted by a distant observer. In this letter, we show that this is not the case with Snyder spacetime, essentially because the Lorentz invariance is not deformed in this case. Distant observers may however measure different times of flight for massive particles. - Highlights: • We discuss the dynamics of the Snyder model from the point of view of relative locality. • We show that no time delay is present for particles emitted by distant observers. • We ascribe this fact to the Lorentz invariance of the model. • Distant observers may however measure different times of flight for massive particle.
Soft hairy horizons in three spacetime dimensions
Afshar, Hamid; Merbis, Wout; Perez, Alfredo; Tempo, David; Troncoso, Ricardo
2016-01-01
We discuss some aspects of soft hairy black holes and a new kind of "soft hairy cosmologies", including a detailed derivation of the metric formulation, results on flat space, and novel observations concerning the entropy. Remarkably, like in the case with negative cosmological constant, we find that the asymptotic symmetries for locally flat spacetimes with a horizon are governed by infinite copies of the Heisenberg algebra that generate soft hair descendants. It is also shown that the generators of the three-dimensional Bondi-Metzner-Sachs algebra arise from composite operators of the affine u(1) currents through a twisted Sugawara-like construction. We then discuss entropy macroscopically, thermodynamically and microscopically and discover that a microscopic formula derived recently for boundary conditions associated to the Korteweg-de Vries hierarchy fits perfectly our results for entropy and ground state energy. We conclude with a comparison to related approaches.
Bianchi Class B Spacetimes with Electromagnetic Fields
Yamamoto, Kei
2011-01-01
We carry out a thorough analysis on a class of cosmological spacetimes which admit three space-like Killing vectors of Bianchi class B and contain electromagnetic fields. Using dynamical system analysis, we show that a family of vacuum plane-wave solutions of the Einstein-Maxwell equations is the stable attractor for expanding universes. Phase dynamics are investigated in detail for particular symmetric models. We integrate the system exactly for some special cases to confirm the qualitative features. Some of the obtained solutions have not been presented previously to the best of our knowledge. Finally, based on those solutions, we discuss the relation between those homogeneous models and perturbations of open FLRW universes. We argue that the vacuum plane-wave modes correspond to a certain long-wavelength limit of electromagnetic perturbations.
Newman-Janis Ansatz in conformastatic spacetimes
Gutiérrez-Piñeres, Antonio C
2016-01-01
The Newman-Janis Ansatz was used first to obtain the stationary Kerr metric from the static Schwarzschild metric. Many works have been devoted to investigate the physical significance of this Ansatz, but no definite answer has been given so far. We show that this Ansatz can be applied in general to conformastatic vacuum metrics, and leads to stationary generalizations which, however, do not preserve the conformal symmetry. We investigate also the particular case when the seed solution is given by the Schwarzschild spacetime and show that the resulting rotating configuration does not correspond to a vacuum solution, even in the limiting case of slow rotation. In fact, it describes in general a relativistic fluid with anisotropic pressure and heat flux. This implies that the Newman-Janis Ansatz strongly depends on the choice of representation for the seed solution. We interpret this result as as a further indication of its applicability limitations.
Quantization on Space-Time Hyperboloids
Biernat, Elmar P
2011-01-01
We quantize a relativistic massive complex spin-0 field and a relativistic massive spin-1/2 field on a space-time hyperboloid. We call this procedure point-form canonical quantization. Lorentz invariance of the hyperboloid implies that the 4 generators for translations become dynamic and interaction dependent, whereas the 6 generators for Lorentz transformations remain kinematic and interaction free. We expand the fields in terms of usual plane waves and prove the equivalence to equal-time quantization by representing the Poincare generators in a momentum basis. We formulate a generalized scattering theory for interacting fields by considering evolution of the system generated by the interaction dependent four-momentum operator. Finally we expand our generalized scattering operator in powers of the interaction and show its equivalence to the Dyson expansion of usual time-ordered perturbation theory.
The thermodynamics of quantum spacetime histories
Smolin, Lee
2015-01-01
We show that the simplicity constraints, which define the dynamics of spin foam models, imply, and are implied by, the first law of thermodynamics, when the latter is applied to causal diamonds in the quantum spacetime. This result reveals an intimate connection between the holographic nature of gravity, as reflected by the Bekenstein entropy, and the fact that general relativity and other gravitational theories can be understood as constrained topological field theories. To state and derive this correspondence we describe causal diamonds in the causal structure of spin foam histories and generalize arguments given for the near horizon region of black holes by Frodden, Gosh and Perez and Bianchi. This allows us to apply a recent argument of Jacobson to show that if a spin foam history has a semiclassical limit described in terms of a smooth metric geometry, that geometry satisfies the Einstein equations. These results suggest also a proposal for a quantum equivalence principle.
De-Sitter spacetime as a superconductor
Momeni, D
2016-01-01
A superconductor is a material with infinite electric conductivity. Superconductivity and magnetism are happening as two opposite phenomena: superconductors need weak external magnetic fields (the Meissner effect) while generally with a strong external magnetic field we loose superconductivity. In \\cite{ref:I}-\\cite{Chernodub:2011tv} , the author showed that a very strong magnetic field can turn an empty space into a superconductor. We extended this idea to the constant curvature spaces, de Sitter (dS) spacetime and by a careful analysis of the modes for a spinor with arbitrary spin, we show that in a very similar condensation scenario as was proposed for flat space, we could transform dS to a superconductor.
Macroscopic quantum mechanics in a classical spacetime.
Yang, Huan; Miao, Haixing; Lee, Da-Shin; Helou, Bassam; Chen, Yanbei
2013-04-26
We apply the many-particle Schrödinger-Newton equation, which describes the coevolution of a many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schrödinger-Newton equation for their centers of mass, which can be monitored and manipulated at quantum levels by state-of-the-art optomechanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, its quantum uncertainty is found to evolve at a frequency different from its classical eigenfrequency-with a difference that depends on the internal structure of the object-and can be observable using current technology. For several objects, the Schrödinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet quantum uncertainty cannot be transferred from one object to another.
Space-time curvature and cosmology
Nurgaliev, I. S.; Ponomarev, V. N.
1982-10-01
The possibility is considered of obtaining a steady-state cosmological solution in the framework of the Einstein-Cartan theory. It is found that the Einstein-Cartan equations without the cosmological constant admit a solution in the form of the static de Sitter metric for a specific value of the spin-spin gravitational interaction constant, whose introduction is required by gauge theory. It is shown that the steady-state solution might serve as a model for the pre-Friedmann stage of the expansion of the universe, when the spin-curvature interaction was comparable to the interaction between space-time curvature and energy-momentum. A value of about 10 to the -20th is obtained for the spin-spin interaction constant in the case where the de Sitter stage occurs at quantum densities (10 to the 94th g/cu cm).
Particle-physics constraints on multifractal spacetimes
Calcagni, Gianluca; Rodríguez-Fernández, David
2016-01-01
We study electroweak interactions in the multiscale theory with $q$-derivatives, a framework where spacetime has the typical features of a multifractal. In the simplest case with only one characteristic time, length and energy scale $t_*$, $\\ell_*$, and $E_*$, we consider (i) the muon decay rate and (ii) the Lamb shift in the hydrogen atom, and constrain the corrections to the ordinary results. We obtain the independent absolute upper bounds (i) $t_* 35\\,\\text{MeV}$. Under some mild theoretical assumptions, the Lamb shift alone yields the even tighter ranges $t_*450\\,\\text{GeV}$. To date, these are the first robust constraints on the scales at which the multifractal features of the geometry can become important in a physical process.
Entropy of Vaidya-deSitter Spacetime
LI Xiang; ZHAO Zheng
2001-01-01
As a statistical model of black hole entropy, the brick-wall method based on the thermal equilibrium in a large scale cannot be applied to the cases out of equilibrium, such as the non-static hole or the case with two horizons.However, the leading term of hole entropy called the Bekenstein-Hawking entropy comes from the contribution of the field near the horizon. According to this idea, the entropy of Vaidya-deSitter spacetime is calculated. A difference from the static case is that the result proportional to the area of horizon relies on a time-dependent cut-off. The condition of local equilibrium near the horizon is used as a working postulate.
Newman-Janis Ansatz in conformastatic spacetimes
Gutiérrez-Piñeres, Antonio C.; Quevedo, Hernando
2016-11-01
The Newman-Janis Ansatz was used first to obtain the stationary Kerr metric from the static Schwarzschild metric. Many works have been devoted to investigate the physical significance of this Ansatz, but no definite answer has been given so far. We show that this Ansatz can be applied in general to conformastatic vacuum metrics, and leads to stationary generalizations which, however, do not preserve the conformal symmetry. We investigate also the particular case when the seed solution is given by the Schwarzschild spacetime and show that the resulting rotating configuration does not correspond to a vacuum solution, even in the limiting case of slow rotation. In fact, it describes in general a relativistic fluid with anisotropic pressure and heat flux. This implies that the Newman-Janis Ansatz strongly depends on the choice of representation for the seed solution. We interpret this result as a further indication of its applicability limitations.
Equatorial circular motion in Kerr spacetime
Pugliese, Daniela; Ruffini, Remo
2011-01-01
We analyze the properties of circular orbits of test particles on the equatorial plane of a rotating central mass whose gravitational field is described by the Kerr spacetime. For rotating black holes and naked singularities we explore all the spatial regions where circular orbits can exist and analyze the behavior of the energy and the angular momentum of the corresponding test particles. In particular, we find all the radii at which a test particle can have zero angular momentum due to the repulsive gravity effects generated by naked singularities. We classify all the stability zones of circular orbits. It is shown that the geometric structure of the stability zones of black holes is completely different from that of naked singularities.
Circular motion in NUT space-time
Jefremov, Paul
2016-01-01
We consider circular motion in the NUT (Newman-Unti-Tamburino) space-time. Among other things, we determine the location of circular time-like geodesic orbits, in particular of the innermost stable circular orbit (ISCO) and of the marginally bound circular orbit. Moreover, we discuss the von Zeipel cylinders with respect to the stationary observers and with respect to the Zero Angular Momentum Observers (ZAMOs). We also investigate the relation of von Zeipel cylinders to inertial forces, in particular in the ultra-relativistic limit. Finally, we generalise the construction of thick accretion tori ("Polish doughnuts") which are well known on the Schwarzschild or Kerr background to the case of the NUT metric. We argue that, in principle, a NUT source could be distinguished from a Schwarzschild or Kerr source by observing the features of circular matter flows in its neighbourhood.
Perturbation of FRW Spacetime in NP Formalism
Sharma, S K
2014-01-01
Perturbation of FRW spacetime is carried out in NP formalism. The equation governing the scalar, vector and tensor modes take on a very simple and transparent form. All of them can be combined in one master equation for all helicities. The solutions for the closed, flat and open FRW are analytic continuation of the same functions, so only the solutions in the closed model are described. The scalar equation is the same as that of the conformally coupled massless Klein-Gordon field, the vectorial ones are the same as Maxwell equations, and the tensorial ones are for spin-2 fields. The corresponding eigen-functions are all determined, and in particular, the Green's function and the Lienard-Wiechert type potential also solved. These solutions reduce to the familiar form in flat space.
Constraining noncommutative spacetime from GW150914
Kobakhidze, Archil; Lagger, Cyril; Manning, Adrian
2016-09-01
The gravitational wave signal GW150914, recently detected by LIGO and Virgo collaborations, is used to place a bound on the scale of quantum fuzziness of noncommutative space-time. We show that the leading noncommutative correction to the phase of the gravitational waves produced by a binary system appears at the second order of the post-Newtonian expansion. This correction is proportional to Λ2≡|θ0 i|2/(lPtP)2, where θμ ν is the antisymmetric tensor of noncommutativity. To comply with GW150914 data, we find that √{Λ }≲3.5 , namely at the order of the Planck scale. This is the most stringent bound on the noncommutative scale, exceeding the previous constraints from particle physics processes by ˜15 orders of magnitude.
Spacetime Conformal Fluctuations and Quantum Dephasing
Bonifacio, Paolo M
Any quantum system interacting with a complex environment undergoes decoherence. Empty space is filled with vacuum energy due to matter fields in their ground state and represents an underlying environment that any quantum particle has to cope with. In particular quantum gravity vacuum fluctuations should represent a universal source of decoherence. To study this problem we employ a stochastic approach that models spacetime fluctuations close to the Planck scale by means of a classical, randomly fluctuating metric (random gravity framework). We enrich the classical scheme for metric perturbations over a curved background by also including matter fields and metric conformal fluctuations. We show in general that a conformally modulated metric induces dephasing as a result of an effective nonlinear newtonian potential obtained in the appropriate nonrelativistic limit of a minimally coupled Klein-Gordon field. The special case of vacuum fluctuations is considered and a quantitative estimate of the expected effect...
MMSE Optimal Algebraic Space-Time Codes
Rajan, G Susinder
2007-01-01
Design of Space-Time Block Codes (STBCs) for Maximum Likelihood (ML) reception has been predominantly the main focus of researchers. However, the ML decoding complexity of STBCs becomes prohibitive large as the number of transmit and receive antennas increase. Hence it is natural to resort to a suboptimal reception technique like linear Minimum Mean Squared Error (MMSE) receiver. Barbarossa et al and Liu et al have independently derived necessary and sufficient conditions for a full rate linear STBC to be MMSE optimal, i.e achieve least Symbol Error Rate (SER). Motivated by this problem, certain existing high rate STBC constructions from crossed product algebras are identified to be MMSE optimal. Also, it is shown that a certain class of codes from cyclic division algebras which are special cases of crossed product algebras are MMSE optimal. Hence, these STBCs achieve least SER when MMSE reception is employed and are fully diverse when ML reception is employed.
Pulsar Magnetospheres: Beyond the Flat Spacetime Dipole
Gralla, Samuel E; Philippov, Alexander
2016-01-01
Most studies of the pulsar magnetosphere have assumed a pure magnetic dipole in flat spacetime. However, recent work suggests that the effects of general relativity are in fact of vital importance and that realistic pulsar magnetic fields may have a significant nondipolar component. We introduce a general analytical method for studying the axisymmetric force-free magnetosphere of a slowly-rotating star of arbitrary magnetic field, mass, radius and moment of inertia, including all the effects of general relativity. We confirm that spacelike current is generically present in the polar caps (suggesting a pair production region), irrespective of the stellar magnetic field. We show that general relativity introduces a ~60% correction to the formula for the dipolar component of the surface magnetic field inferred from spindown. Finally, we show that the location and size of the polar caps can be modified dramatically by even modestly strong higher moments. This can affect emission processes occurring near the star ...
Mass and Thermodynamic Volume in Lifshitz Spacetimes
Brenna, Wilson G; Park, Miok
2015-01-01
We examine the concept of black hole thermodynamic volume and its consistency with thermodynamic mass in spacetimes that are not asymptotically flat but instead have anisotropic Lifshitz scaling symmetry. We find that the generalized Smarr relation in anti de Sitter space -- extended to include a pressure-volume term -- holds here as well, and that there exists a definition of thermodynamic mass and thermodynamic volume that satisfy both this relation and the $1^{st}$ law of thermodynamics. We compare the thermodynamic mass with other known quantities such as ADM, Brown-York and Hollands-Ishibashi-Marolf masses. We also conjecture methods for obtaining a thermodynamic mass where there is ambiguity due to the cosmological constant lengthscale depending on the horizon radius lengthscale.
Gauge Invariant Perturbations of the Schwarzschild Spacetime
Chen, Hector; Whiting, Bernard F
2016-01-01
Beginning with the pioneering work of Regge and Wheeler (Phys. Rev. 108, 1957), there have been many studies of perturbations away from the Schwarzschild spacetime background. In particular several authors (e.g. Moncrief, Ann. Phys 88, 1974) have investigated gauge invariant quantities of the Regge-Wheeler (RW) gauge. Steven Detweiler also investigated perturbations of Schwarzschild in his own gauge, which he denoted the "easy (EZ) gauge", and which he was in the process of adapting for use in the second-order self-force problem. We present here a compilation of some of his working results, arising from notes for which there seems to have been no manuscript in preparation. In particular, we list the gauge invariant quantities used by Detweiler, as well as explain the process by which he found them.