General Relativity and Gravitation最新文献

We give a family of exact solutions of (N=1) supergravity field equations in (D=4) dimensions that describe the collision of plane-fronted gravitino waves.

The late-time behaviour of the solutions of the Fackerell–Ipser equation (which is a wave equation for the spin-zero component of the electromagnetic field strength tensor) on the closure of the domain of outer communication of sub-extremal Kerr spacetime is studied numerically. Within the Kerr family, the case of Schwarzschild background is also considered. Horizon-penetrating compactified hyperboloidal coordinates are used, which allow the behaviour of the solutions to be observed at the event horizon and at future null infinity as well. For the initial data, pure multipole configurations that have compact support and are either stationary or non-stationary are taken. It is found that with such initial data the solutions of the Fackerell–Ipser equation converge at late times either to a known static solution (up to a constant factor) or to zero. As the limit is approached, the solutions exhibit a quasinormal ringdown and finally a power-law decay. The exponents characterizing the power-law decay of the spherical harmonic components of the field variable are extracted from the numerical data for various values of the parameters of the initial data, and based on the results a proposal for a Price’s law relevant to the Fackerell–Ipser equation is made. Certain conserved energy and angular momentum currents are used to verify the numerical implementation of the underlying mathematical model. In the construction of these currents a discrete symmetry of the Fackerell–Ipser equation, which is the product of an equatorial reflection and a complex conjugation, is also taken into account.

We derive the equation governing the axial-perturbations in the space-time of a non-rotating uncharged primordial black hole (PBH), produced in early Universe, whose metric has been taken as the generalized McVittie metric. The generalized McVittie metric is a cosmological black hole metric, proposed by Faraoni and Jacques in 2007 (Phys. Rev. D 76:063510, 2007). This describes the space-time of a Schwarzschild black hole embedded in FLRW-Universe, while allowing its mass-change. Our derivation has basic similarities with the procedure of derivation of Chandrasekhar, for deriving the Regge-Wheeler equation for Schwarzschild metric (Chandrasekhar The Mathematical Theory of Black holes, Oxford University Press, New York, 1983); but it has some distinct differences with that due to the complexity and time-dependency of the generalized McVittie metric. We show that after applying some approximations which are very well valid in the early radiation-dominated Universe, the overall equation governing the axial perturbations can be separated into radial and angular parts, among which the radial part is the intended one, as the angular part is identical to the case of Schwarzschild metric as expected. We identify the potential from the Schrödinger-like format of the equation and draw some physical interpretation from it.

The gravitational interaction of (classical and quantum) spinning bodies is currently the focus of many works using a variety of approaches. This note is a comment on a short paper by Jean-Marie Souriau, now reprinted in the GRG Golden Oldies collection. Souriau’s short 1970 note was a pioneering contribution to a symplectic description of the dynamics of spinning particles in general relativity which remained somewhat unnoticed. We explain the specificity of Souriau’s approach and emphasize its potential interest within the current flurry of activity on the gravitational interaction of spinning particles.

This paper was a pioneering contribution to a symplectic description of the dynamics of spinning particles in general relativity which remained somewhat unnoticed. In particular, it introduced the pre-symplectic 2-form (sigma ) describing the dynamics of spinning particles coupled to an Einsteinian curved background. The method throws light on approaches to spinning black holes and neutron stars.

It is often argued that the Planck length (or mass) is the scale of quantum gravity, as shown by comparing the Compton length with the gravitational radius of a particle. However, the Compton length is relevant in scattering processes but does not play a significant role in bound states. We will derive a possible ground state for a dust ball composed of a large number of quantum particles entailing a core with the size of a fraction of the horizon radius. This suggests that quantum gravity becomes physically relevant for systems with compactness of order one for which the nonlinearity of General Relativity cannot be discarded. A quantum corrected geometry can then be obtained from the effective energy-momentum tensor of the core or from quantum coherent states for the effective gravitational degrees of freedom. These descriptions replace the classical singularity of black holes with integrable structures in which tidal forces remain finite and there is no inner Cauchy horizon. The extension to rotating systems is briefly mentioned.

The geometric trinity of gravity comprises three distinct formulations of general relativity: (i) the standard formulation describing gravity in terms of spacetime curvature, (ii) the teleparallel equivalent of general relativity describing gravity in terms of spacetime torsion, and (iii) the symmetric teleparallel equivalent of general relativity (STEGR) describing gravity in terms of spacetime non-metricity. In this article, we complete a geometric trinity of non-relativistic gravity, by (a) taking the non-relativistic limit of STEGR to determine its non-relativistic analogue, and (b) demonstrating that this non-metric theory is equivalent to Newton–Cartan theory and its teleparallel equivalent, i.e., the curvature and the torsion based non-relativistic theories that are both geometrised versions of classical Newtonian gravity.

In the present work, we study the initial moments of a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological model, considering Hořava-Lifshitz (HL) as the gravitational theory. The matter content of the model is a radiation perfect fluid. In order to study the initial moments of the universe in the present model, we consider quantum cosmology. More precisely the quantum mechanical tunneling mechanism. In that mechanism, the universe appears after the wavefunction associated to that universe tunnels through a potential barrier. We started studying the classical model. We draw the phase portrait of the model and identify qualitatively all types of dynamical behaviors associated to it. Then, we write the Hamiltonian of the model and apply the Dirac quantization procedure to quantize a constrained theory. We find the appropriate Wheeler-DeWitt equation and solve it using the Wentzel-Kramers-Brillouin (WKB) approximation. Using the WKB solution, to the Wheeler-DeWitt equation, we compute the tunneling probabilities for the birth of that universe ((TP_{WKB})). Since the WKB wavefunction depends on the radiation energy (E) and the free parameters coming from the HL theory ((g_c), (g_r), (g_s), (g_Lambda )), we compute the behavior of (TP_{WKB}) as a function of E and all the HL’s parameters (g_c), (g_r), (g_s), (g_Lambda ). As a new result, due to the HL theory, we notice that, in the present model, the universe cannot tunnel through the barrier close to the origin. It happens because that tunneling probability is nil. Therefore, here, the universe cannot starts from a zero size and is free from the big bang singularity.

We analyze the orbits of a unit mass body in a background Reissner–Nordstr(ddot{textrm{o}})m (RN) black hole in (d) (=) ((3+1)) from the perspectives of Geometric Torsion (GT) modified gravity theory in ((4+1)) dimensional bulk. A 4-form flux in bulk GT theory in (d) (=) ((4+1)) has been shown to ensure a mass dipole correction to the ((3+1)) dimensional gravity theory by Gupta, Kar and Rang recently. We argue that the dipole correction contributes topologically to the known exact geometries in General Theory of Relativity (GTR). Furthermore, the topological correction has been identified with non-Newtonian potential underlying a (B_2 wedge F_2) coupling term to Einstein–Hilbert action. The winding numbers ensured by the BF coupling to (d=(3+1)) action in the framework presumably provide a clue towards a tunneling instanton in theory.

Classical General Relativity is a dynamical theory of spacetime metrics of Lorentzian signature. In particular the classical metric field is nowhere degenerate in spacetime. In its initial value formulation with respect to a Cauchy surface the induced metric is of Euclidian signature and nowhere degenerate on it. It is only under this assumption of non-degeneracy of the induced metric that one can derive the hypersurface deformation algebra between the initial value constraints which is absolutely transparent from the fact that the inverse of the induced metric is needed to close the algebra. This statement is independent of the density weight that one may want to equip the spatial metric with. Accordingly, the very definition of a non-anomalous representation of the hypersurface deformation algebra in quantum gravity has to address the issue of non-degeneracy of the induced metric that is needed in the classical theory. In the Hilbert space representation employed in Loop Quantum Gravity (LQG) most emphasis has been laid to define an inverse metric operator on the dense domain of spin network states although they represent induced quantum geometries which are degenerate almost everywhere. It is no surprise that demonstration of closure of the constraint algebra on this domain meets difficulties because it is a sector of the quantum theory which is classically forbidden and which lies outside the domain of definition of the classical hypersurface deformation algebra. Various suggestions for addressing the issue such as non-standard operator topologies, dual spaces (habitats) and density weights have been proposed to address this issue with respect to the quantum dynamics of LQG. In this article we summarise these developments and argue that insisting on a dense domain of non-degenerate states within the LQG representation may provide a natural resolution of the issue thereby possibly avoiding the above mentioned non-standard constructions.