Charged spherically symmetric black holes in f(R) gravity and their stability analysis

A new class of analytic charged spherically symmetric black hole solutions, which behave asymptotically as flat or (anti-)de Sitter spacetimes, is derived for specific classes of f (R) gravity, i.e., f(R) = R -2 alpha root R and f(R) = R -2 alpha root R-8 Lambda, where Lambda is the cosmological constant. These black holes are characterized by the dimensional parameter alpha that makes solutions deviate from the standard solutions of general relativity. The Kretschmann scalar and squared Ricci tensor are shown to depend on the parameter alpha, which is not allowed to be zero. Thermodynamical quantities, like entropy, Hawking temperature, quasilocal energy, and the Gibbs free energy are calculated. From these calculations, it is possible to put a constraint on the dimensional parameter alpha to have 0 < alpha < 0.5 so that all thermodynamical quantities have a physical meaning. The interesting result of these calculations is the possibility of a negative black hole entropy. Furthermore, present calculations show that for negative energy particles inside a black hole,behave as if they have a negative entropy. This fact gives rise to instability for f(RR) < 0. Finally, we study the linear metric perturbations of the derived black hole solution. We show that for the odd-type modes our black hole is always stable and has a radial speed with fixed value equal to 1. We also use the geodesic deviation to derive further stability conditions.