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### Quantum Black Hole Entropy From 4d Supersymmetric Cardy Formula

We study the canonical $\mathrm{AdS}/\mathrm{CFT}$ correspondence between 4d $SU(N)$ $\mathcal{N}=4$ super Yang-Mills theory (SYM) and type IIB superstring theory on ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$. We analyze the supersymmetric index of the $\mathcal{N}=4$ SYM on ${S}^{1}\ifmmode\times\else\texttimes\fi{}{M}_{3}$ which counts supersymmetric states with fixed quantum numbers. We compute an asymptotic behavior of the index in the limit of shrinking ${S}^{1}$ for any $N$ by a refinement of the 4d supersymmetric Cardy formula. The asymptotic behavior for the superconformal index case (${M}_{3}={S}^{3}$) at large $N$ agrees with the Bekenstein-Hawking entropy of a rotating electrically charged Bogomolnyi-Prasad-Sommerfeld (BPS) black hole in ${\mathrm{AdS}}_{5}$ via a Legendre transformation as recently shown in the literature. We also find that the agreement formally persists for finite $N$ if we slightly modify the $\mathrm{AdS}/\mathrm{CFT}$ dictionary between the Newton constant Jul 17, 2019 ... This implies the existence of a nonrenormalization property of the black hole entropy against quantum corrections.
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### Logarithmic Corrections To Black Hole Entropy, From The Cardy Formula

Many recent attempts to calculate black hole entropy from first principles rely on conformal field theory techniques. By examining the logarithmic ...
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### Black Hole Entropy And The Laws Of Thermodynamics | By Marco ...

The Remarkable Similarities Between the Black Holes Mechanics and Laws of Thermodynamics The Black Hole Formula for the Entropy ... It is reasonable to suppose that the entropy of a black hole should depend only on one or more of the three observable ...
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### A Microscopic Account Of Black Hole Entropy - Physics

String theory provides a microscopic description of the entropy of certain theoretical black holes—an important step toward understanding black hole thermodynamics. May 18, 2020 ... In this dual system, the formation and evaporation of black holes can be described by quantum field equations that don't allow information loss.
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### In Memoriam: Jacob Bekenstein (1947–2015) And Black Hole Entropy

Chances are you've never heard of physicist Jacob Bekenstein, who devised a nifty formula for calculating a black hole's entropy. Here's why you should remember his name Aug 17, 2015 ... The Bekenstein–Hawking entropy formula for a black hole. Credit: Public domain, via Wikimedia Commons. Advertisement. Sad news reached Jen-Luc ...
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### Black Hole Entropy Is Noether Charge

We consider a general, classical theory of gravity in $n$ dimensions, arising
from a diffeomorphism invariant Lagrangian. In any such theory, to each vector
field, $ξ^a$, on spacetime one can associate a local symmetry and, hence, a
Noether current $(n-1)$-form, ${\bf j}$, and (for solutions to the field
equations) a Noether charge $(n-2)$-form, ${\bf Q}$. Assuming only that the
theory admits stationary black hole solutions with a bifurcate Killing horizon,
and that the canonical mass and angular momentum of solutions are well defined
at infinity, we show that the first law of black hole mechanics always holds
for perturbations to nearby stationary black hole solutions. The quantity
playing the role of black hole entropy in this formula is simply $2 π$ times
the integral over $Σ$ of the Noether charge $(n-2)$-form associated with
the horizon Killing field, normalized so as to have unit surface gravity.
Furthermore, we show that this black hole entropy always is given by a local
geometrical expression on th Jul 29, 1993 ... The quantity playing the role of black hole entropy in this formula is simply 2 \pi times the integral over \Sigma of the Noether charge ...
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### Discussion Of A Possible Corrected Black Hole Entropy

Einstein’s equation could be interpreted as the first law of thermodynamics near the spherically symmetric horizon. Through recalling the Einstein gravity with a more general static spherical symmetric metric, we find that the entropy would have a correction in Einstein gravity. By using this method, we investigate the Eddington-inspired Born-Infeld (EiBI) gravity. Without matter field, we can also derive the first law in EiBI gravity. With an electromagnetic field, as the field equations have a more general spherically symmetric solution in EiBI gravity, we find that correction of the entropy could be generalized to EiBI gravity. Furthermore, we point out that the Einstein gravity and EiBI gravity might be equivalent on the event horizon. At last, under EiBI gravity with the electromagnetic field, a specific corrected entropy of black hole is given. Einstein's equation could be interpreted as the first law of thermodynamics near the spherically symmetric horizon. Through recalling the Einstein gravity ...
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### How Many Ways Are There To Make A Black Hole? · Frontiers For ...

Gravity is a universally attractive force, which tries to cause matter to clump. This means that in diverse physical systems, ranging from stars at the end of their lives burning nuclear fuel, to gas clouds which collapse under the weight of their own gravity, a natural endpoint can be the development of a black hole. This is an object where matter has been packed so densely that even light cannot escape gravity’s pull at its surface, or event horizon. Black holes are both commonplace—our own Milky Way galaxy hosts a giant black hole in its center!—and mysterious. In this article we discuss current thoughts about one of the mysteries of black holes—how one can explain the number of distinct (but similar) physical states they hide behind their event horizon. Physicists call this the black hole entropy. Oct 29, 2020 ... Physicists call this the black hole entropy. ... And they were able to produce a formula for the entropy of a black hole as a function of ...
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### Some Simple Black Hole Thermodynamics

the entropy of a black hole of event-horizon area. A = R2 can be written in terms of its mass using ... constant.7 Rearranging the radiation equation and.
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### Black Hole Entropy From Loop Quantum Gravity

We argue that the statistical entropy relevant for the thermal interactions
of a black hole with its surroundings is (the logarithm of) the number of
quantum microstates of the hole which are distinguishable from the hole's
exterior, and which correspond to a given hole's macroscopic configuration. We
compute this number explicitly from first principles, for a Schwarzschild black
hole, using nonperturbative quantum gravity in the loop representation. We
obtain a black hole entropy proportional to the area, as in the
Bekenstein-Hawking formula. Mar 30, 1996 ... We obtain a black hole entropy proportional to the area, as in the Bekenstein-Hawking formula. Comments: 5 pages, latex-revtex, no figures.
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### The Entropy Of Hawking Radiation

Black hole entropy = area of horizon. • The fine grained gravitational entropy formula. Entropy = Minimal area. • Compute the entropy of radiation coming ...
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