Kerr-Newman black holes in f(R) theories

In the context of f(R) modified gravity theories, we study the Kerr-Newman black hole solutions. We study nonzero constant scalar curvature solutions and discuss the metric tensor that satisfies the modified field equations. We conclude that, in the absence of a cosmological constant, the black holes (BHs) existence is determined by the sign of a parameter h dependent of the mass, the charge, the spin and the scalar curvature. Different values of this parameter lead to diverse astrophysical objects, such as extremal and marginal extremal BHs. Thermodynamics of BHs are then studied, as well as their local and global stability. We analyze these features in a large variety of f(R) models. We remark the main differences with respect to general relativity and show the rich thermodynamical phenomenology that characterizes this framework.