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

TL;DR

This paper calculates the renormalized scalar current in a charged, black hole spacetime with a cosmological constant, providing numerical results for current components in a specific quantum state.

Contribution

It introduces a Hadamard point-split renormalization method for the current density in Reissner-Nordström-de Sitter spacetime and computes its expectation values numerically.

Findings

Numerical values of current components in the Unruh state

Dependence of current on field parameters and position

Methodology applicable to similar curved spacetimes

Abstract

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.