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arXiv · 1511.09117

Reissner-Nordström Black Holes in Mimetic $F(R)$ Gravity

V. K. Oikonomou
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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 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-Nordström-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-Nordström-anti de Sitter black hole, at least at first order. We attribute this feature to the particular form of the Reissner-Nordström-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.

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V. K. Oikonomou. 2015-11-30. Reissner-Nordström Black Holes in Mimetic $F(R)$ Gravity. https://doi.org/10.3390/universe2020010

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