A scale dependent black hole in three-dimensional space-time

TL;DR

This paper explores a scale-dependent black hole solution in three-dimensional spacetime, revealing modifications to horizon structure and entropy laws due to quantum effects on gravitational couplings.

Contribution

It introduces a novel three-dimensional black hole model with scale-dependent parameters, extending classical solutions with quantum-inspired modifications.

Findings

Black hole entropy transitions from area law to area times radius law.

Horizon structure and asymptotics are affected by scale dependence.

The solution links classical BTZ parameters with quantum corrections.

Abstract

Scale dependence at the level of the effective action is a generic result of quantum field theory. Allowing for scale dependence of the gravitational couplings leads to a generalization of the corresponding field equations. In this work, those equations are solved by imposing the "null energy condition" in three-dimensional space time with stationary spherical symmetry. The constants of integration are given in terms of the classical BTZ parameters plus one additional constant, that parametrizes the strength of the scale dependence. The properties such as asymptotics, horizon structure, and thermodynamics are discussed. It is found that the black hole entropy shows a remarkable transition from the usual "area~law" to an "area~$\times$~radius" law.