General Relativity And Quantum Cosmology

In this paper, an implicit nonsymplectic exact energy-preserving integrator is specifically designed for a ten-dimensional phase-space conservative Hamiltonian system with five degrees of freedom. It is based on a suitable discretization-averaging of the Hamiltonian gradient, with a second-order accuracy to numerical solutions. A one-dimensional disordered discrete nonlinear Schrödinger equation and a post-Newtonian Hamiltonian system of spinning compact binaries are taken as our two examples. We demonstrate numerically that the proposed algorithm exhibits good long-term performance in the preservation of energy, if roundoff errors are neglected. This result is independent of time steps, initial orbital eccentricities, and regular and chaotic orbital dynamical behavior. In particular, the application of appropriately large time steps to the new algorithm is helpful in reducing time-consuming and roundoff errors. This new method, combined with fast Lyapunov indicators, is well suited related to chaos in the two example problems. It is found that chaos in the former system is mainly responsible for one of the parameters. In the latter problem, a combination of small initial separations and high initial eccentricities can easily induce chaos.

We numerically solve for 2+1 asymptotically Lifshitz universal horizon solutions in Horava-Lifshitz gravity for dynamical exponents z=2 through z=8 . We find that for all z there is a thermodynamical first law and Smarr formula. Furthermore, we find that the energy-entropy relation expected for a thermal state in a two dimensional Lifshitz field theory, E= 2 z+2 TS , is also satisfied for universal horizons, including the correct z scaling.

Since the appearance of Einstein's paper {\em"On the Electrodynamics of Moving Bodies"} and the birth of special relativity, it is understood that the theory was basically coded within Maxwell's equations. The celebrated mass-energy equivalence relation, E=m c 2 , is derived by Einstein using thought experiments involving the kinematics of the emission of light (electromagnetic energy) and the relativity principle. Text book derivations often follow paths similar to Einstein's, or the analysis of the kinematics of particle collisions interpreted from the perspective of different inertial frames. All the same, in such derivations the direct dynamical link with hypothetical fundamental fields describing matter (e.g. Maxwell theory or other) is overshadowed by the use of powerful symmetry arguments, kinematics, and the relativity principle. Here we show that the formula can be derived directly form the dynamical equations of a massless matter model confined in a box (which can be thought of as a toy model of a composite particle). The only assumptions in the derivation are that the field equations hold and the energy-momentum tensor admits a universal interpretation in arbitrary coordinate systems. The mass-energy equivalence relation follows from the inertia or (taking the equivalence principle for granted) weight of confined field radiation. The present derivation offers an interesting pedagogical perspective on the formula providing a simple toy model on the origin of mass and a natural bridge to the foundations of general relativity.

Recent advances in emergent geometry and discretized approaches to quantum gravity have relied upon the notion of a discrete measure of graph curvature. We focus on the two main measures that have been studied, the so-called Ollivier-Ricci and Forman-Ricci curvatures. These two approaches have a very different origin, and both have advantages and disadvantages. In this work we study the relationship between the two measures for a class of graphs that are important in quantum gravity applications. We discover that under a specific set of circumstances they are equivalent, potentially opening up the possibility of exploiting the relative strengths of both approaches in models of emergent spacetime and quantum gravity.

The global gravitational-wave detector network achieves higher detection rates, better parameter estimates, and more accurate sky localisation, as the number of detectors, I increases. This paper quantifies network performance as a function of I for BayesWave, a source-agnostic, wavelet-based, Bayesian algorithm which distinguishes between true astrophysical signals and instrumental glitches. Detection confidence is quantified using the signal-to-glitch Bayes factor, B S,G . An analytic scaling is derived for B S,G versus I , the number of wavelets, and the network signal-to-noise ratio, SNR net , which is confirmed empirically via injections into detector noise of the Hanford-Livingston (HL), Hanford-Livingston-Virgo (HLV), and Hanford-Livingston-KAGRA-Virgo (HLKV) networks at projected sensitivities for the fourth observing run (O4). The empirical and analytic scalings are consistent; B S,G increases with I . The accuracy of waveform reconstruction is quantified using the overlap between injected and recovered waveform, O net . The HLV and HLKV network recovers 87% and 86% of the injected waveforms with O net >0.8 respectively, compared to 81% with the HL network. The accuracy of BayesWave sky localisation is ??0 times better for the HLV network than the HL network, as measured by the search area, A , and the sky areas contained within 50% and 90% confidence intervals. Marginal improvement in sky localisation is also observed with the addition of KAGRA.

We study the entanglement production for Dirac and Klein-Gordon fields in an expanding spacetime characterized by the presence of torsion. Torsion is here considered according to the Einstein-Cartan theory with a conformally flat Friedmann-Robertson-Walker spacetime. In this framework, torsion is seen as an external field, fulfilling precise constraints directly got from the cosmological constant principle. For Dirac field, we find that torsion increases the amount of entanglement. This turns out to be particularly evident for small values of particle momentum. We discuss the roles of Pauli exclusion principle in view of our results, and, in particular, we propose an interpretation of the two maxima that occur for the entanglement entropy in presence of torsion. For Klein-Gordon field, and differently from the Dirac case, the model can be exactly solved by adopting the same scale factor as in the Dirac case. Again, we show how torsion affects the amount of entanglement, providing a robust physical motivation behind the increase or decrease of entanglement entropy. A direct comparison of our findings is also discussed in view of previous results derived in absence of torsion. To this end, we give prominence on how our expectations would change in terms of the coupling between torsion and the scale factor for both Dirac and Klein-Gordon fields.

In this paper, we revisit the possibilities of Bañados-Silk-West (BSW) effect in Kerr-Newman-Taub-NUT (KNTN) spacetime for two neutral particles moving over the equatorial plane and constant θ in Boyer-Lindquist coordinate. Contrary to a previous study on this topic, we found that BSW effect for two particles confined to move over the equatorial plane is not possible. Numerical calculations shows that BSW effect in constant θ geodesics is possible under certain circumstances.

Loop Quantum Gravity (LQG) is a non-perturbative attempt at quantization of a classical phase space description of gravity in terms of SU(2) connections and electric fields. As emphasized recently [1], on this phase space, classical gravitational evolution in time can be understood in terms of certain gauge covariant generalizations of Lie derivatives with respect to a spatial SU(2) Lie algebra valued vector field called the Electric Shift. We present a derivation of a quantum dynamics for Euclidean LQG which is informed by this understanding. In addition to the physically motivated nature of the action of the Euclidean Hamiltonian constraint so derived, the derivation implies that the spin labels of regulating holonomies are determined by corresponding labels of the spin network state being acted upon thus eliminating the `spin j -ambiguity' pointed out by Perez. By virtue of Thiemann's seminal work, the Euclidean quantum dynamics plays a crucial role in the construction of the Lorentzian quantum dynamics so that our considerations also have application to Lorentzian LQG.

We study how conserved quantities such as angular momentum and center of mass evolve with respect to the retarded time at null infinity, which is described in terms of a Bondi-Sachs coordinate system. These evolution formulae complement the classical Bondi mass loss formula for gravitational radiation. They are further expressed in terms of the potentials of the shear and news tensors. The consequences that follow from these formulae are (1) Supertranslation invariance of the fluxes of the CWY conserved quantities. (2) A conservation law of angular momentum ? la Christodoulou. (3) A duality paradigm for null infinity. In particular, the supertranslation invariance distinguishes the CWY angular momentum and center of mass from the classical definitions.

We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate r between two values r 1 and r 2 . The solution is given in three regions, one being the well-known analytical Schwarzschild solution in the outer vacuum region, one being determined analytically in the inner vacuum region, and one being determined mostly analytically but partially numerically, within the matter region. The solutions for the temporal coefficient of the metric and for the pressure within this region are given in terms of a non-elementary but fairly straightforward real integral. We show that in this solution there is a singularity at the origin, and give the parameters of that singularity in terms of the geometrical and physical parameters of the shell. This does not correspond to an infinite concentration of matter, but in fact to zero energy density at the center. It does, however, imply that the spacetime within the spherical cavity is not flat, so that there is a non-trivial gravitational field there, in contrast with Newtonian gravitation. This gravitational field has the effect of stabilizing the geometrical configuration of the matter, since any particle of the matter that wanders out into the vacuum regions tends to be brought back to the bulk of the matter by the gravitational field.