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

Understand

A new class of analytic charged spherically symmetric black hole solutions, which behave asymptotically as flat or (A)dS spacetimes, is derived for specific classes of $f(R)$ gravity, i.e., $f(R)=R-2\alpha\sqrt{R}$ and $f(R)=R-2\alpha\sqrt{R-8\Lambda}$, 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, quasi-local energy and the Gibbs free energy are calculated.