Charged spherically symmetric Taub-NUT black hole solutions in $f(R)$ gravity

Abstract: $f(R)$ theory is a modification of Einstein general relativity which has many interesting results in cosmology and astrophysics. To derive black hole solution in this theory is difficult due to the fact that it is fourth order differential equations. In this study, we use the first reliable deviation from general relativity which is given by the quadratic form of $f(R)=R+\beta R^2$, where $\beta$ is a dimensional parameter. We calculate the energy conditions of the charged black holes and show that all of them are satisfied for the Taub-NUT spacetime. Finally, we study some thermodynamic quantities such as entropy, temperature, specific heat and Gibbs free energy. The calculations of heat capacity and free energy show that the charged Taub-NUT black hole have positive values which means that it has thermal stability.