Reissner–Nordström Anti-de Sitter Black Holes in Mimetic F(R) Gravity

Abstract

In this paper, we study under which conditions the Reissner–Nordström anti-de Sitter black hole can be a solution of the vacuum mimetic F ( R ) gravity with Lagrange multiplier and mimetic scalar potential. As the author demonstrates, the resulting picture in the mimetic F ( R ) gravity case is a trivial extension of the standard F ( R ) approach, and in effect, the metric perturbations in the mimetic F ( R ) gravity case, for the Reissner–Nordström anti-de Sitter black hole metric, at the first order of the perturbed variables are the same at the leading order.

Keywords

• mimetic gravity
• modified gravity
• F(R) gravity