Vacuum polarization of the quantized massive scalar field in Reissner-Nordstr\"om spacetime

TL;DR

This paper develops an improved analytical approximation for the stress-energy tensor of a massive scalar field in Reissner-Nordström spacetime, showing significant accuracy improvements over previous models by including higher-order terms from the Schwinger-DeWitt expansion.

Contribution

It introduces a new approximation method for the stress-energy tensor using higher-order Schwinger-DeWitt coefficients, enhancing accuracy compared to existing numerical results.

Findings

Inclusion of second-order terms improves approximation accuracy.

The method provides a reliable analytical estimate of the stress-energy tensor.

Approximation of the field fluctuation $\

Abstract

The approximation of the renormalized stress-energy tensor of the quantized massive scalar field in Reissner-Nordstr\"om spacetime is constructed. It is achieved by functional differentiation of the first two nonvanishing terms of the Schwinger-DeWitt expansion involving the coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficients $[a_{3}]$ and $[a_{4}]$ with respect to the metric tensor. It is shown, by comparison with the existing numerical results, that inclusion of the second-order term leads to substantial improvement of the approximation of the exact stress-energy tensor. The approximation to the field fluctuation, $\langle \phi^{2} \rangle,$ is constructed and briefly discussed.