Vacuum states for AdS(2) black holes

An AdS(2) black hole spacetime is an AdS(2) spacetime together with a prefe rred choice of time. The Boulware, Hartle-Hawking and SL(2; R) invariant va cua are constructed, together with their Green functions and stress tensors , for both massive and massless scalars in an AdS(2) black hole. The classi cal Bekenstein-Hawking entropy is found to be independent of the temperatur e, but at one loop a non-zero entanglement entropy arises. This represents a logarithmic violation of finite-temperature decoupling for AdS(2) black h oles which arise in the near-horizon limit of an asymptotically at black ho le. Correlation functions of the SL(2; R) invariant boundary quantum mechan ics are computed as functions of the choice of AdS(2) vacuum.