Stress-energy tensor of the quantized massive fields in Schwarzschild-Tangherlini spacetimes. The back reaction

TL;DR

This paper calculates the stress-energy tensor of quantized massive scalar fields in higher-dimensional Schwarzschild-Tangherlini spacetimes using the Schwinger-DeWitt approach, analyzing quantum back reaction effects on black hole properties.

Contribution

It introduces an approximation method for the stress-energy tensor in higher dimensions and examines quantum back reaction effects on black hole mass and temperature.

Findings

Quantum-corrected mass increases lead to temperature decreases for minimal and conformal coupling.

The approach generalizes the effective action construction from Hadamard-DeWitt coefficients.

The vacuum polarization formula is derived and briefly analyzed.

Abstract

We construct and study the approximate stress-energy tensor of the quantized massive scalar field in higher dimensional Schwarzschild-Tangherlini spacetimes. The stress-energy tensor is calculated within the framework of the Schwinger-DeWitt approach. It is shown that in $N$-dimensional spacetime the main approximation can be obtained from the effective action constructed form the coincidence limit of the Hadamard-DeWitt coefficient $a_{k},$ where $k-1$ is the integer part of $N/2$. The back reaction of the quantized field upon the black hole spacetime is analyzed and the quantum-corrected Komar mass and the Hawking temperature is calculated. It is shown that for the minimal and conformal coupling the increase of the Komar mass of the quantum corrected black hole leads to the decrease of its Hawking temperature. This is not generally true for more exotic values of the coupling parameter. The general formula describing the vacuum polarization, $ \langle \phi^{2} \rangle,$ is constructed and briefly examined.