Schwarzschild Black Holes and Asymptotic $AdS_2$

Abstract

We show that the entropy of D--dimensional Schwarzschild black holes are given by the entanglement entropy of a boundary of global $AdS_2$ 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 $AdS_2$ black holes by Weyl transformations which are symmetries of the theory that preserve the thermodynamics. In the asymptotic limit, the $AdS_2$ black holes become global $AdS_2$ which can be described by two entangled $AdS_2$ Rindler spaces. The entanglement entropy of a single $AdS_2$ Rindler space reproduces the Schwarzschild black hole entropy.