The effects of running gravitational coupling on three dimensional black holes

TL;DR

This paper explores how a scale-dependent gravitational coupling, inspired by asymptotic safe gravity, affects the properties, horizons, and thermodynamics of three-dimensional BTZ black holes, revealing violations of energy conditions.

Contribution

It introduces a novel analysis of three-dimensional black holes with running gravitational coupling based on asymptotic safe gravity, extending understanding of quantum gravity effects.

Findings

Altered horizon structure due to scale dependence

Modified thermodynamic properties of black holes

Violation of null energy condition in this framework

Abstract

In the present work, we investigate the consequences of running gravitational coupling on the properties of the three-dimensional BTZ black hole. We take as starting point the functional form of gravitational coupling obtained in the context of asymptotic safe gravity theory. By using the standard scale setting relation where $k\sim \xi/r^n$, we compute the solution of the Einstein field equations. We get and analyze the horizon and the thermodynamic properties of this new class of black hole solutions. The impact of the scale--dependent parameter $\xi$ on the cosmological "constant" and metric functions are briefly discussed. We find that the null energy condition is also violated in this setup when scale-dependent gravity and Newton's coupling (coming from the asymptotic safety scenario of gravity) are simultaneously taken into account.