Vacuum states for AdS2 black holes

Abstract

An AdS2 black hole spacetime is an AdS2 spacetime together with a preferred choice of time. The Boulware, Hartle-Hawking and SL(2,ℝ) invariant vacua are constructed, together with their Green functions and stress tensors, for both massive and massless scalars in an AdS2 black hole. The classical Bekenstein-Hawking entropy is found to be independent of the temperature, but at one loop a non-zero entanglement entropy arises. This represents a logarithmic violation of finite-temperature decoupling for AdS2 black holes which arise in the near-horizon limit of an asymptotically flat black hole. Correlation functions of the SL(2, R) invariant boundary quantum mechanics are computed as functions of the choice of AdS2 vacuum.