Charged black holes in the infinite derivative theory of gravity

The infinite derivative theory of gravity is a generalization of Einstein gravity with many interesting properties, but the black hole solutions in this theory are still not fully understood. In the paper, we concentrate on studying the charged black holes in such a theory. Adding the electromagnetic field part to the effective action, we show how the black hole solutions around the Reissner–Nordström metric can be solved perturbatively and iteratively. We further calculate the corresponding temperature, entropy and electrostatic potential of the black holes and verify the first law of thermodynamics.