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−2αR and f(R)=R−2αR−8Λ, where Λ is the cosmological constant. These black holes are characterized by the dimensional parameter α 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 α, 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 α to have 0