A mode-sum prescription for the renormalized stress energy tensor on black hole spacetimes

TL;DR

This paper introduces an efficient mode-sum method for calculating the renormalized stress-energy tensor of quantum scalar fields in black hole spacetimes, enabling better analysis of quantum effects and backreaction.

Contribution

The paper presents a novel, highly efficient mode-sum prescription applicable to scalar fields with arbitrary parameters in spherically symmetric black hole backgrounds.

Findings

Successfully computed the renormalized stress-energy tensor in Schwarzschild spacetime.

Analyzed the null energy condition using the computed tensor.

Discussed implications for semi-classical backreaction effects.

Abstract

In this paper, we describe an extremely efficient method for computing the renormalized stress-energy tensor of a quantum scalar field in spherically-symmetric black hole spacetimes. The method applies to a scalar field with arbitrary field parameters. We demonstrate the utility of the method by computing the renormalized stress-energy tensor for a scalar field in the Schwarzschild black hole spacetime, applying our results to discuss the null energy condition and the semi-classical backreaction.