Effective Metric Description of 2+1 Dimensional Quantum Black Holes

TL;DR

This paper introduces an effective metric framework for describing quantum corrections to 2+1 dimensional BTZ black holes, providing insights into horizon behavior, temperature corrections, and potential interior structure.

Contribution

It develops a novel effective metric approach constrained by symmetries and asymptotics, offering a new way to analyze quantum effects in 2+1D black holes.

Findings

Universal constraints on horizon parameters from finiteness of scalars

Derived corrected Hawking temperature in terms of effective metric parameters

Recast quantum BTZ model within the effective metric framework

Abstract

We develop an effective metric description of 2+1 dimensional black holes describing deviations from the classical Ba\~nados-Teitelboim-Zanelli (BTZ) black hole. The latter is a classical 2+1 dimensional rotating black hole with constant negative curvature. The effective metric is constrained by imposing the black hole symmetries and asymptotic classical behavior. The deformed metric is parametrized in terms of a physical quantity that we choose to be a physical distance. The latter can be solved for in three main regions of interest, the one around the horizon, origin, and spatial infinity. The finiteness of physical quantities at the horizon, such as the Ricci and Kretschmann scalars, leads to universal constraints on the physical parameters of the metric around the horizon. This allows us to further derive the general form of the corrected Hawking temperature in terms of the physical parameters of the effective metric. Assuming that the approach can be generalized to the interior of the black hole, we further develop an effective metric description near the origin. To illustrate the approach, we show how to recast the information encoded in a specific model of quantum BTZ known as quBTZ black hole in terms of the effective metric coefficients.