The renormalized charged scalar current in the Reissner-Nordstr\"om-de Sitter spacetime

We perform a Hadamard point-split renormalization of the current density $j_{\nu }$ of a charged scalar field in a Reissner-Nordstr"om-de Sitter spacetime. We compute numerically the expectation values of the components $j_r$ and $j_t$ in the Unruh state in the exterior region and study their dependence on the field parameters and the position.