  In the context of f(R) modified gravity theories, we study the Kerr-Newman
black-hole solutions. We study non-zero constant scalar curvature solutions and
discuss the metric tensor that satisfies the modified field equations. We
determine that, in absence of a cosmological constant, the black holes
existence is determined by the sign of a parameter dependent of the mass, the
charge, the spin and the scalar curvature. We obtain that for negative values
of the curvature, the extremal black hole is no longer given by a spin
parameter a_max = M (as is the case in General Relativity), but by a_max < M,
and that for positive values of the curvature there are two kinds of extremal
black holes: the usual one, that occurs for a_max > M, and the extreme marginal
one, where the exterior (but not interior) black hole's horizon vanishes
provided that a < a_min. Thermodynamics for this kind of black holes is then
studied, as well as their local and global stability. Finally we study
different f(R) models and see how these properties manifest for their
parameters phase space.
