Black Hole Solutions for Scale Dependent Couplings: The de Sitter and the Reissner-Nordström Case

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.