Description
While a formal solution to the problem of renormalization in semiclassical gravity has been understood for several decades, efficient computational prescriptions for implementing the renormalization in black hole spacetimes have only been developed in recent years. Since computing the renormalized expectation value of the stress-energy tensor is an essential step in solving the semiclassical Einstein equations, it is important that we have efficient schemes for its numerical computation. Working within the framework of the Taylor-Breen-Ottewill extended coordinate method, we present an extension of that method to the interior of spherically symmetric black holes that possess a Cauchy horizon. We obtain the renormalized vacuum polarization and stress-energy tensor in the interior of a Reissner-Nordström black hole and derive their behavior on the Cauchy horizon, highlighting how the mass of the field affects the regularity of the renormalized vacuum polarization on this horizon.