Reissner-Nordstr\"om Black Holes in Mimetic $F(R)$ Gravity

TL;DR

This paper explores conditions under which Reissner-Nordström-anti de Sitter black holes are solutions in mimetic F(R) gravity, analyzing metric perturbations and potential instabilities, revealing similarities and differences with ordinary F(R) gravity.

Contribution

It identifies the constraints for black hole solutions in mimetic F(R) gravity and compares perturbation behavior to ordinary F(R) gravity, highlighting potential instabilities.

Findings

Reissner-Nordström-anti de Sitter solutions exist under specific conditions in mimetic F(R) gravity.

Perturbation equations are identical to those in ordinary F(R) gravity at first order.

Black hole instabilities, such as anti-evaporation, are possible in mimetic F(R) gravity.

Abstract

In this paper we study under which conditions the Reissner-Nordstr\"om-anti de Sitter black hole can be a solution of the vacuum mimetic $F(R)$ gravity with Lagrange multiplier and mimetic scalar potential. As we demonstrate, the resulting picture in the mimetic $F(R)$ gravity case, is different in comparison to the ordinary $F(R)$ gravity case, with the two descriptions resulting to a different set of constraints that need to hold true. We also investigate the metric perturbations in the mimetic $F(R)$ gravity case, for the Reissner-Nordstr\"om-anti de Sitter black hole metric, at first order of the perturbed variables. Interestingly enough, the resulting equations are identical to the ones corresponding to the ordinary $F(R)$ gravity Reissner-Nordstr\"om-anti de Sitter black hole, at least at first order. We attribute this feature to the particular form of the Reissner-Nordstr\"om-anti de Sitter metric, and we speculate for which cases there could be differences between the mimetic and non-mimetic case. Since the perturbation equations are the same for the two cases, it is possible to have black hole instabilities in the mimetic $F(R)$ gravity case too, which can be interpreted as anti-evaporation of the black hole.