Interpretation Of Black Hole Entropy Research Articles

Understanding gravitational entropy of black holes: A new proposal via curvature invariants

Partly motivated by the arrow of time problem in cosmology and the Weyl curvature hypothesis formulated by Roger Penrose, previous works in the literature have proposed - among other possibilities - the square of the Weyl curvature, as being the underlying entropy density function of black hole entropy, but the proposal suffers from a few drawbacks. In this work, we propose a new entropy density function also based solely on the Weyl curvature, but adopting some other combinations of curvature invariants. As an improvement we find that our method works for all static black hole solutions in four and five dimensional general relativity regardless of whether they are empty space solutions or not. It should also be possible to generalize our method to higher dimensions. This allows us to discuss the physical interpretation of black hole entropy, which remains somewhat mysterious. Extending to modified theories of gravity, our work also suggests that gravitational entropy in some theories is a manifestation of different physical effects since we need to choose different combinations of curvature quantities

Laws of black hole thermodynamics in semiclassical gravity

The first and second laws of black hole thermodynamics are verified to emerge from a generic semiclassical theory of gravity for which a Hamiltonian formulation can be defined. The first law is established in stationary spacetimes, and the second law is established in the here defined ‘piecewise stationary’ spacetimes. Black hole entropy is defined in the Noether charge approach, and the entropy for the matter in its exterior is the von Neumann entropy of the quantum fields. These results strongly support the interpretation of black hole entropy as an account of the information that is hidden behind the horizon.

Entropy of generic quantum isolated horizons

We review our recent proposal of a method to extend the quantization of spherically symmetric isolated horizons, a seminal result of loop quantum gravity, to a phase space containing horizons of arbitrary geometry. Although the details of the quantization remain formally unchanged, the physical interpretation of the results can be quite different. We highlight several such differences, with particular emphasis on the physical interpretation of black hole entropy in loop quantum gravity.

Quantum of areaΔA=8πlP2and a statistical interpretation of black hole entropy

In contrast to alternative values, the quantum of area $\ensuremath{\Delta}A=8\ensuremath{\pi}{l}_{P}^{2}$ does not follow from the usual statistical interpretation of black hole entropy; on the contrary, a statistical interpretation follows from it. This interpretation is based on the two concepts: nonadditivity of black hole entropy and Landau quantization. Using nonadditivity a microcanonical distribution for a black hole is found and it is shown that the statistical weight of a black hole should be proportional to its area. By analogy with conventional Landau quantization, it is shown that quantization of a black hole is nothing but the Landau quantization. The Landau levels of a black hole and their degeneracy are found. The degree of degeneracy is equal to the number of ways to distribute a patch of area $8\ensuremath{\pi}{l}_{P}^{2}$ over the horizon. Taking into account these results, it is argued that the black hole entropy should be of the form ${S}_{\mathrm{bh}}=2\ensuremath{\pi}\ifmmode\cdot\else\textperiodcentered\fi{}\ensuremath{\Delta}\ensuremath{\Gamma}$, where the number of microstates is $\ensuremath{\Delta}\ensuremath{\Gamma}=A/8\ensuremath{\pi}{l}_{P}^{2}$. The nature of the degrees of freedom responsible for black hole entropy is elucidated. The applications of the new interpretation are presented. The effect of noncommuting coordinates is discussed.

Near extremal black hole entropy as entanglement entropy viaAdS2/CFT1

We point out that the entropy of (near) extremal black holes can be interpreted as the entanglement entropy of dual conformal quantum mechanics via ${\mathrm{AdS}}_{2}/{\mathrm{CFT}}_{1}$. As an explicit example, we study near extremal Banados-Teitelboim-Zanelli black holes and derive this claim from ${\mathrm{AdS}}_{3}/{\mathrm{CFT}}_{2}$. We also analytically compute the entanglement entropy in the two dimensional CFT of a free Dirac fermion compactified on a circle at finite temperature. From this result, we clarify the relation between the thermal entropy and entanglement entropy, which is essential for the entanglement interpretation of black hole entropy.

RELIC RADIATION FROM AN EVAPORATING BLACK HOLE

This paper presents a non-string-theoretic calculation of the microcanonical entropy of relic integer-spin Hawking radiation, at fixed total energy E, from an evanescent, neutral, non-rotating four-dimensional black hole. The only conserved macroscopic quantity is the total energy E which, for a black hole that evaporates completely, is the total energy of the relic radiation. Through a boundary-value approach, in which data for massless, integer-spin perturbations are set on initial and final space-like hypersurfaces, the statistical-mechanics problem becomes, in effect, a one-dimensional problem, with the "volume" of the system determined by the real part of the time separation at spatial infinity — the variable conjugate to the total energy. We count the number of field configurations on the final space-like hypersurface that have total energy E, assuming that initial perturbations are weak. We find that the density of states resembles the well-known Cardy formula. The Bekenstein–Hawking entropy is recovered if the real part of the asymptotic time separation is of the order of the semi-classical black-hole lifetime. We thereby obtain a statistical interpretation of black-hole entropy. Corrections to the microcanonical entropy are computed, and we find agreement with other approaches in terms of a logarithmic correction to the black-hole area law, which is universal (independent of black-hole parameters). This result depends crucially upon the discreteness of the energy levels. We discuss the similarities of our approach with the transition from the black-hole to the fundamental-string regime in the final stages of black-hole evaporation. In addition, we find that the squared coupling, g2, which regulates the transition from a black hole to a highly-excited string state, and vice versa, can be related to the angle, δ, in the complex-time plane, through which we continue analytically the time separation at spatial infinity. Thus, in this scenario, the strong-coupling regime corresponds to a Euclidean black hole, while the physical limit of a Lorentzian space–time (the limit as δ → 0+) corresponds to the weak-coupling regime. This resembles the transition of a black hole to a highly-excited string-like state, which subsequently decays into massless particles, thereby avoiding the naked singularity.

Thermal gravity, black holes, and cosmological entropy

Taking seriously the interpretation of black hole entropy as the logarithm of the number of microstates, we argue that thermal gravitons may undergo a phase transition to a kind of black hole condensate. The phase transition proceeds via nucleation of black holes at a rate governed by a saddlepoint configuration whose free energy is of order the inverse temperature in Planck units. Whether the universe remains in a low entropy state as opposed to the high entropy black hole condensate depends sensitively on its thermal history. Our results may clarify an old observation of Penrose regarding the very low entropy state of the universe.

Inextendible Schwarzschild black hole with a single exterior: How thermal is the Hawking radiation?

Several approaches to Hawking radiation on Schwarzschild spacetime rely in some way or another on the fact that the Kruskal manifold has two causally disconnected exterior regions. To assess the physical input implied by the presence of the second exterior region, we investigate the Hawking(-Unruh) effect for a real scalar field on the ${\mathrm{RP}}^{3}$ geon: an inextendible, globally hyperbolic, space and time orientable eternal black hole spacetime that is locally isometric to Kruskal but contains only one exterior region. The Hartle-Hawking-like vacuum $|{0}_{\mathrm{G}}〉,$ which can be characterized alternatively by the positive frequency properties along the horizons or by the complex analytic properties of the Feynman propagator, turns out to contain exterior region Boulware modes in correlated pairs, and any operator in the exterior that only couples to one member of each correlated Boulware pair has thermal expectation values in the usual Hawking temperature. Generic operators in the exterior do not have this special form; however, we use a Bogoliubov transformation, a particle detector analysis, and a particle emission-absorption analysis that invokes the analytic properties of the Feynman propagator, to argue that $|{0}_{\mathrm{G}}〉$ appears as a thermal bath with the standard Hawking temperature to any exterior observer at asymptotically early and late Schwarzschild times. A (naive) saddle-point estimate for the path-integral-approach partition function yields for the geon only half of the Bekenstein-Hawking entropy of a Schwarzschild black hole with the same ADM mass: possible implications of this result for the validity of path-integral methods or for the statistical interpretation of black-hole entropy are discussed. Analogous results hold for a Rindler observer in a flat spacetime whose global properties mimic those of the geon.

Correspondence principle for black holes and strings

For most black holes in string theory, the Schwarzschild radius in string units decreases as the string coupling is reduced. We formulate a correspondence principle, which states that (i) when the size of the horizon drops below the size of a string, the typical black hole state becomes a typical state of strings and D-branes with the same charges, and (ii) the mass does not change abruptly during the transition. This provides a statistical interpretation of black hole entropy. This approach does not yield the numerical coefficient, but gives the correct dependence on mass and charge in a wide range of cases, including neutral black holes.

Is Bekenstein's conjecture true for charged black holes?

It is known that the thermal radiation from an uncharged, nonrotating black hole into a vacuum carries an entropy about $\frac{4}{3}$ times the entropy lost by the hole. For a black hole placed in a radiation bath with a temperature infinitesimally close to that of the hole, the entropy of the radiation is equal to the hole's entropy loss. This previously known result is here extended to the case of a charged black hole, which gives further support to the statistical interpretation of black hole entropy.