Schwarzschild Black Holes and Asymptotic $Ad{S}_2$

Abstract

We show that the entropy of D--dimensional Schwarzschild black holes are given by the entanglement entropy of a boundary of global $Ad{S}_2$ space that lives at asymptotic infinity. We dimensionally reduce General Relativity to two dimensions which leads to 2D dilatonic gravity which has black hole solutions with the same thermodynamics as D--dimensional Schwarzschild black holes. These dilatonic black holes can be transformed into certain $Ad{S}_2$ black holes by Weyl transformations which are symmetries of the theory that preserve the thermodynamics. In the asymptotic limit, the $Ad{S}_2$ black holes become global $Ad{S}_2$ which can be described by two entangled $Ad{S}_2$ Rindler spaces. The entanglement entropy of a single $Ad{S}_2$ Rindler space reproduces the Schwarzschild black hole entropy.

20 pages

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Cited by in corpus (2)

• Black Hole Entropy and the Pseudo Goldstone Bosons of Conformal Symmetry
• Computing Black Hole Entropy at Infinity