Vacuum States for AdS_2 Black Holes

TL;DR

This paper constructs various vacuum states in AdS_2 black hole spacetimes, analyzes their properties, and explores quantum effects like entanglement entropy, revealing insights into near-horizon black hole physics and boundary correlations.

Contribution

It introduces explicit constructions of Boulware, Hartle-Hawking, and SL(2,R) invariant vacua in AdS_2 black holes, including their Green functions and stress tensors, and examines quantum entropy effects.

Findings

Classical entropy is temperature-independent.

One-loop entanglement entropy is non-zero, indicating quantum correlations.

Correlation functions depend on the chosen vacuum state.

Abstract

An AdS_2 black hole spacetime is an AdS_2 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 AdS_2 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 AdS_2 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 AdS_2 vacuum.