Quantized massive scalar fields in the spacetime of a charged dilatonic black hole

TL;DR

This paper calculates the quantum stress-energy tensor of a massive scalar field in the spacetime of a charged dilatonic black hole using an approximate effective action, focusing on special couplings and small charge expansions.

Contribution

It introduces a method to compute the renormalized stress-energy tensor using the HaMiDeW coefficient a_{3} in dilatonic black hole backgrounds, including new compact trace expressions.

Findings

Explicit form of the stress-energy tensor for specific couplings

Analysis of small charge expansion effects

Compact expression for the tensor trace

Abstract

Employing the approximate effective action constructed from the coincidence limit of the Hadamard-Minakshisundaram-DeWitt (HaMiDeW) coefficient a_{3}, the renormalized stress-energy tensor of the quantized massive scalar field in the spacetime of a static and electrically charged dilatonic black hole is calculated. Special attention is paid to the minimally and conformally coupled fields propagating in geometries with a=1, and to the power expansion of the general stress-energy tensor for small values of charge. A compact expression for the trace of the stress-energy tensor is presented.