On horizon constraints and Hawking radiation

TL;DR

This paper explores the implications of horizon constraints in quantum gravity, demonstrating that matter energy flux at a black hole horizon aligns with thermodynamic laws, and discusses the effects of fixed background geometry on matter conservation.

Contribution

It shows that horizon constraints lead to correct black hole entropy and energy flux, linking horizon conditions with thermodynamic consistency in quantum gravity.

Findings

Matter energy flux matches the first law of black hole thermodynamics.

Horizon constraints reproduce Bekenstein-Hawking entropy.

Fixed background geometry affects matter stress tensor conservation.

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, $8 \pi G \Delta Q = \kappa \Delta A$.