Exact charged black hole solutions in D-dimensions in f(R) gravity

Abstract: We consider Maxwell-f(R) gravity and obtain an exact charged black hole solution with dynamic curvature in D-dimensions. Considering a spherically symmetric metric ansatz and without specifying the form of f(R) we fnd a general black hole solution in D-dimensions. This general black hole solution can be reduced to the Reissner-Nordstr\"om (RN) black hole in D-dimensions in Einstein gravity and to the known charged black hole solutions with constant curvature in f(R) gravity. Restricting the parameters of the general solution we get polynomial solutions which reveal novel properties when compared to RN black holes. Specifcally we study the solution in (3 + 1)-dimensions in which the form of f(R) can be solved explicitly giving a dynamic curvature and compare it with the RN black hole. We also carry out a detailed study of its thermodynamics.