Charged spherically symmetric black holes in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo mathvariant="bold" stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo mathvariant="bold" stretchy="false">)</mml:mo></mml:math>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., $f(R)=R\ensuremath{-}2\ensuremath{\alpha}\sqrt{R}$ and $f(R)=R\ensuremath{-}2\ensuremath{\alpha}\sqrt{R\ensuremath{-}8\mathrm{\ensuremath{\Lambda}}}$, where $\mathrm{\ensuremath{\Lambda}}$ is the cosmological constant. These black holes are characterized by the dimensional parameter $\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}$, 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 $\ensuremath{\alpha}$ to have $0&lt;\ensuremath{\alpha}&lt;0.5$ 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 ${f}_{RR}&lt;0$. 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.

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