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Register a new userConstructing black hole entropy from gravitational collapse
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Based on a recent proposal for the gravitational entropy of free gravitational fields, we investigate the thermodynamic properties of black hole formation through gravitational collapse in the framework of the semitetrad 1+1+2 covariant formalism. In the simplest case of an Oppenheimer-Snyder-Datt collapse we prove that the change in gravitational entropy outside a collapsing body is related to the variation of the surface area of the body itself, even before the formation of horizons. As a result, we are able to relate the Bekenstein-Hawking entropy of the black hole endstate to the variation of the vacuum gravitational entropy outside the collapsing body.
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The global hyperbolicity assumption present in gravitational collapse singularity theorems is in tension with the quantum mechanical phenomenon of black hole evaporation. In this work I show that the causality conditions in Penroses theorem can be almost completely removed. As a result, it is possible to infer the formation of spacetime singularities even in the absence of predictability and hence compatibly with quantum field theory and black hole evaporation.
We review aspects of the thermodynamics of black holes and in particular take into account the fact that the quantum entanglement between the degrees of freedom of a scalar field, traced inside the event horizon, can be the origin of black hole entropy. The main reason behind such a plausibility is that the well-known Bekenstein-Hawking entropy-area proportionality -- the so-called `area law of black hole physics -- holds for entanglement entropy as well, provided the scalar field is in its ground state, or in other minimum uncertainty states, such as a generic coherent state or squeezed state. However, when the field is either in an excited state or in a state which is a superposition of ground and excited states, a power-law correction to the area law is shown to exist. Such a correction term falls off with increasing area, so that eventually the area law is recovered for large enough horizon area. On ascertaining the location of the microscopic degrees of freedom that lead to the entanglement entropy of black holes, it is found that although the degrees of freedom close to the horizon contribute most to the total entropy, the contributions from those that are far from the horizon are more significant for excited/superposed states than for the ground state. Thus, the deviations from the area law for excited/superposed states may, in a way, be attributed to the far-away degrees of freedom. Finally, taking the scalar field (which is traced over) to be massive, we explore the changes on the area law due to the mass. Although most of our computations are done in flat space-time with a hypothetical spherical region, considered to be the analogue of the horizon, we show that our results hold as well in curved space-times representing static asymptotically flat spherical black holes with single horizon.
In this article we compute the black hole entropy by finding a classical central charge of the Virasoro algebra of a Liouville theory using the Cardy formula. This is done by performing a dimensional reduction of the Einstein Hilbert action with the ansatz of spherical symmetry and writing the metric in conformally flat form. We obtain two coupled field equations. Using the near horizon approximation the field equation for the conformal factor decouples. The one concerning the conformal factor is a Liouville equation, it posses the symmetry induced by a Virasoro algebra. We argue that it describes the microstates of the black hole, namely the generators of this symmetry do not change the thermodynamical properties of the black hole.
Coalescing binary black holes emit anisotropic gravitational radiation. This causes a net emission of linear momentum that produces a gradual acceleration of the source. As a result, the final remnant black hole acquires a characteristic velocity known as recoil velocity or gravitational kick. The symmetries of gravitational wave emission are reflected in the interactions of the gravitational wave modes emitted by the binary. In this work we make use of the rich information encoded in the higher-order modes of the gravitational wave emission to infer the component of the kick along the line-of-sight (or textit{radial kick}). We do this by performing parameter inference on simulated signals given by numerical relativity waveforms for non-spinning binaries using numerical relativity templates of aligned-spin (non-precessing) binary black holes. We find that for suitable sources, namely those with mass ratio $qgeq 2$ and total mass $M sim 100M_odot$, and for modest radial kicks of $120km/s$, the $90%$ credible intervals of our posterior probability distributions can exclude a zero kick at a signal-to-noise ratio of $15$; using a single Advanced LIGO detector working at its early sensitivity. The measurement of a non-zero radial kick component would provide the first observational signature of net transport of linear momentum by gravitational waves away from their source.
The standard post-Newtonian approximation to gravitational waveforms, called T-approximants, from non-spinning black hole binaries are known not to be sufficiently accurate close to the last stable orbit of the system. A new approximation, called P-approximants, is believed to improve the accuracy of the waveforms rendering them applicable up to the last stable orbit. In this study we apply P-approximants to the case of a test-particle in equatorial orbit around a Kerr black hole parameterized by a spin parameter q that takes values between -1 and 1. In order to assess the performance of the two approximants we measure their effectualness (i.e. larger overlaps with the exact signal), and faithfulness (i.e. smaller biases while measuring the parameters of the signal) with the exact (numerical) waveforms. We find that in the case of prograde orbits, that is orbits whose angular momentum is in the same sense as the spin angular momentum of the black hole, T-approximant templates obtain an effectualness of ~ 0.99 for spins q < 0.75. For 0.75 < q < 0.95, the effectualness drops to about 0.82. The P-approximants achieve effectualness of > 0.99 for all spins up to q = 0.95. The bias in the estimation of parameters is much lower in the case of P-approximants than T-approximants. We find that P-approximants are both effectual and faithful and should be more effective than T-approximants as a detection template family when q>0. For q<0 both T- and P-approximants perform equally well so that either of them could be used as a detection template family.
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