Living on the Edge: Quantum Black Hole Physics from the Event Horizon

TL;DR

This paper develops a self-consistent, model-independent framework for calculating metric deformations near black hole horizons, enabling the computation of thermodynamic properties and testing the physical viability of quantum gravity models.

Contribution

It introduces a new method to compute the distance function near black hole horizons and derives model-independent formulas for thermodynamic quantities, addressing regularity and consistency conditions.

Findings

Explicit metric expansions near the horizon

Model-independent expressions for Hawking temperature and entropy

Identification of inconsistencies in some existing models

Abstract

Quantum gravity theories predict deformations of black hole solutions relative to their classical counterparts. A model-independent approach was advocated in \cite{Binetti:2022xdi} that uses metric deformations parametrised in terms of physical quantities, such as the proper distance. While such a description manifestly preserves the invariance of the space-time under coordinate transformations, concrete computations are hard to tackle since the distance is defined in terms of the deformed metric itself. In this work, for spherically symmetric and static metrics, we provide a self-consistent framework allowing us to compute the distance function in close vicinity to the event horizon of a black hole. By assuming a minimal degree of regularity at the horizon, we provide explicit (series) expansions of the metric. This allows us to compute important thermodynamical quantities of the black hole, such as the Hawking temperature and entropy, for which we provide model-independent expressions, beyond a large mass expansion. Moreover, imposing for example the absence of curvature singularities at the event horizon leads to non-trivial consistency conditions for the metric deformations themselves, which we find to be violated by some models in the literature.