A Note on Schwarzschild de Sitter Black Holes in Mimetic $F(R)$ Gravity

TL;DR

This paper examines conditions for Schwarzschild de Sitter black holes to be solutions in mimetic $F(R)$ gravity, revealing slight modifications from standard $F(R)$ gravity and differences in perturbation equations.

Contribution

It identifies specific conditions under which Schwarzschild de Sitter black holes solve mimetic $F(R)$ gravity and compares perturbation equations to those in ordinary $F(R)$ gravity.

Findings

Mimetic $F(R)$ gravity slightly differs from standard $F(R)$ gravity.

Perturbation equations are not always identical to those in ordinary $F(R)$ gravity.

In some cases, perturbation equations match those of Reissner-Nordström anti-de Sitter black holes.

Abstract

In this brief note we investigate the conditions under which a Schwarzschild de Sitter black hole spacetime is a solution of the mimetic $F(R)$ gravity with Lagrange multiplier and potential. As we demonstrate, the resulting mimetic $F(R)$ gravity is a slight modification of the ordinary $F(R)$ gravity case, however the resulting perturbation equations are not in all cases identical to the ordinary $F(R)$ gravity case. In the latter case, the perturbation equations are identical to the ones corresponding to the Reissner-Nordstr\"{o}m anti-de Sitter black hole.