Black Hole Solutions for Scale Dependent Couplings: The de Sitter and the Reissner-Nordstr\"om Case

TL;DR

This paper derives generalized black hole solutions incorporating scale-dependent gravitational couplings, extending classical (Anti)-de Sitter and Reissner-Nordström solutions, and compares them to traditional models.

Contribution

It introduces solutions to modified field equations with scale-dependent couplings, broadening the understanding of black holes in quantum gravity contexts.

Findings

Generalized (Anti)-de Sitter black hole solutions

Reissner-Nordström solutions with scale dependence

Comparison with classical black hole solutions

Abstract

Allowing for scale dependence of the gravitational couplings leads to a generalization of the corresponding field equations. In this work, those equations are solved for the Einstein-Hilbert and the Einstein-Maxwell case, leading to generalizations of the (Anti)-de Sitter and the Reissner-Nordstr\"om black holes. Those solutions are discussed and compared to their classical counterparts.