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On horizon constraints and Hawking radiation

David Mattingly
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Abstract

Questions about black holes in quantum gravity generally presuppose the presence of a horizon. Recently Carlip has shown that enforcing an initial data surface to be a horizon leads to the correct form for the Bekenstein-Hawking entropy of the black hole. Requiring a horizon also constitutes fixed background geometry, which generically leads to non-conservation of the matter stress tensor at the horizon. In this work, I show that the generated matter energy flux for a Schwarzschild black hole is in agreement with the first law of black hole thermodynamics, $8 πG ΔQ = κΔA$.

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David Mattingly. 2006-01-11. On horizon constraints and Hawking radiation. https://arxiv.org/abs/gr-qc/0601044

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