Renormalized stress-energy tensor for stationary black holes

TL;DR

This paper advances the computation of the renormalized stress-energy tensor for stationary black holes using an improved mode-sum regularization method, demonstrating its application in Schwarzschild spacetime and discussing future enhancements.

Contribution

It details the application of the $t$-splitting PMR method for RSET calculation in stationary backgrounds, extending previous work and providing a practical example.

Findings

Successfully computed RSET for Schwarzschild black hole in various vacuum states.

Demonstrated the effectiveness of the $t$-splitting regularization scheme.

Discussed potential improvements for the regularization process.

Abstract

We continue the presentation of the pragmatic mode-sum regularization (PMR) method for computing the renormalized stress-energy tensor (RSET). We show in detail how to employ the $t$-splitting variant of the method, which was first presented for $\left\langle\phi^{2}\right\rangle_{ren}$, to compute the RSET in a stationary, asymptotically-flat background. This variant of the PMR method was recently used to compute the RSET for an evaporating spinning black hole. As an example for regularization, we demonstrate here the computation of the RSET for a minimally-coupled, massless scalar field on Schwarzschild background in all three vacuum states. We discuss future work and possible improvements of the regularization schemes in the PMR method.