Black hole thermodynamics from quantum gravity

TL;DR

This paper investigates how quantum fluctuations affect black hole thermodynamics, showing that they cause a breakdown of the semiclassical approximation and help define the black hole's temperature and entropy.

Contribution

It introduces a quantum gravity framework that links the breakdown of semiclassical approximation to the thermodynamical properties of black holes, including temperature and entropy.

Findings

Quantum fluctuations lead to semiclassical breakdown near horizons.

A 'stretched horizon' is defined using the breakdown boundary.

The derived temperature and entropy match black hole thermodynamics.

Abstract

The semiclassical approximation is studied on hypersurfaces approaching the union of future null infinity and the event horizon on a large class of four dimensional black hole backgrounds. Quantum fluctuations in the background geometry are shown to lead to a breakdown of the semiclassical approximation in these models. The boundary of the region where the semiclassical approximation breaks down is used to define a `stretched horizon'. It is shown that the same effect that brings about the breakdown in semiclassical evolution associates a temperature and an entropy to the region behind the stretched horizon, and identifies the microstates that underlie the thermodynamical properties. The temperature defined in this way is equal to that of the black hole and the entropy is equal to the Bekenstein entropy up to a factor of order unity.