Vacuum Polarization on the Schwarzschild Metric with a Cosmic String

TL;DR

This paper develops a new method to compute vacuum polarization renormalization in axially symmetric space-times, specifically applied to Schwarzschild space-time with a cosmic string, with potential extension to Kerr space-time.

Contribution

It introduces a generalized framework for vacuum polarization renormalization that does not depend on Legendre functions, suitable for axially symmetric geometries like Kerr.

Findings

Framework applicable to Schwarzschild with cosmic string

Method potentially extendable to Kerr space-time

Advances renormalization techniques in non-spherical symmetry

Abstract

We consider the problem of the renormalization of the vacuum polarization in a symmetry space-time with axial but not spherical symmetry, Schwarzschild space-time threaded by an infinite straight cosmic string. Unlike previous calculations, our framework to compute the renormalized vacuum polarization does not rely on special properties of Legendre functions, but rather has been developed in a way that we expect to be applicable to Kerr space-time.