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

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-Nordström anti-de Sitter black hole.

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• Ghost-Free $F(R)$ Gravity with Lagrange Multiplier Constraint
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• Evaporation and anti-evaporation instability of a Schwarzschild-de Sitter braneworld: the case of five-dimensional F(R) gravity
• Mimetic f(T) Teleparallel gravity and cosmology
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• Isotropic stellar model in mimetic theory
• Higher dimensional charged static and rotating solutions in mimetic gravity
• Suppression of Bekenstein-Hawking radiation in $f(T)$-gravity
• Thermodynamics, Phase Transitions, and Geodesic Structure of F(R)-Phantom Banados-Teitelboim-Zanelli (BTZ) Black Holes