Black hole entropy from near-horizon microstates

Abstract

Black holes whose near-horizon geometries are locally, but not necessarily globally, AdS 3 (three-dimensional anti-de Sitter space) are considered. Using the fact that quantum gravity on AdS 3 is a conformal field theory, we microscopically compute the black hole entropy from the asymptotic growth of states. Precise numerical agreement with the Bekenstein-Hawking area formula for the entropy is found. The result pertains to any consistent quantum theory of gravity, and does not use string theory or supersymmetry.

Testing Holographic Principle from Logarithmic and Higher Order Corrections to Black Hole Entropy

“…Since the BH entropy is the exponent of the partition functions at the "leading order", this result implies the relation (1.1) holds at the leading order. However, this is in contrast to Strominger's computation on the BTZ black hole entropy from a conformal field theory at spatial infinity [18] that implies a holography (1.1) at spatial infinity at the same (leading) order. So, at least for the leading order, both the holography at spatial infinity and that of the horizon give an identical result, and one can not distinguish between these very different approaches.…”

“…[12] or Ref. [18], where the classical effect was dominant; but, one can not distinguish between them at the leading order. However, quite interestingly, it is known [40] that this WZW approaches gives the correct '− 3 2 lnS BH ' term already, as is consistent with the (horizon) holographic principle, though this approach has some undesirable features of the non-unitary Hilbert space and infinite degeneracy of the vacuum [8].…”

“…In this subsection first, let us consider the screen at spatial infinity as in the usual AdS/CFT. To this end, I note that the associated Virasoro algebra has two independent sectors as in (3.2), which have eigenvalues of L 0 ,L 0 and central charges [37,18,38,3,14] as…”

Partition functions and elliptic genera from supergravity

“…The combined Virasoro/current algebras admit the following spectral flow automorphisms: 6) in the SU (2) case, and…”

“…For these we take 6) with N ∈ Z. The angular coordinate φ has the standard 2π periodicity, and fermions are taken to be periodic in φ.…”