Vacuum polarization of massive scalar fields in the spacetime of the electrically charged nonlinear black hole

TL;DR

This paper calculates the quantum stress-energy tensor for a massive scalar field in the spacetime of an electrically charged nonlinear black hole, highlighting differences from the Reissner-Nordström case near extremality.

Contribution

It constructs the approximate renormalized stress-energy tensor for a scalar field in nonlinear black hole spacetime using the DeWitt-Schwinger method, comparing it with the Reissner-Nordström solution.

Findings

Differences are most significant near the event horizon close to extremality.

The structure of the nonlinear black hole is analyzed using Lambert functions.

The stress-energy tensor differs notably from the Reissner-Nordström case near extremality.

Abstract

The approximate renormalized stress-energy tensor of the quantized massive conformally coupled scalar field in the spacetime of electrically charged nonlinear black hole is constructed. It is achieved by functional differentiation of the lowest order of the DeWitt-Schwinger effective action involving coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficient $a_{3}.$ The result is compared with the analogous result derived for the Reissner-Nordstr\"om black hole. It is shown that the most important differences occur in the vicinity of the event horizon of the black hole near the extremality limit. The structure of the nonlinear black hole is briefly studied by means of the Lambert functions.