Berlin 2015 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 6: Quantenfeldtheorie I

MP 6.3: Talk

Wednesday, March 18, 2015, 10:10–10:30, HFT-FT 101

Hartle-Hawking-Israel states for radiating static black holes — •Ko Sanders — Universität Leipzig, ITP

The discovery of black hole radiation (Hawking, 1975) was soon followed by the conjecture that a free scalar quantum field on a (Schwarzschild) black hole admits a (unique) ground state, which restricts to a thermal state at the Hawking temperature in the exterior region (Hartle and Hawking, 1976; Israel, 1976). This conjecture was later extended to more general static black holes and interacting fields (Jacobson, 1994) and the state is known as the Hartle-Hawking-Israel state (HHI-state). In the cases where such a state exists, it provides a relatively simple and direct link between the geometry of (e.g.) a black hole and the thermal properties of the Hawking radiation.

After a brief review of previous results, we will discuss our recent proof of the existence of such a HHI-state and its main properties in the rather general setting of static spacetimes with a bifurcate Killing horizon (arXiv:1310.5537). The key idea of the proof is simple: the Killing time variable, which defines the Wick rotation, becomes ill-defined near the Killing horizon, so we systematically replace it by a Gaussian normal coordinate. The crucial task is to establish the analogs of analyticity and reflection positivity in this new coordinate. This requires detailed arguments from geometry and analysis.