Semiclassical lukewarm black holes

TL;DR

This paper constructs and analyzes semiclassical solutions for lukewarm black holes, incorporating quantum effects of a massive scalar field and electromagnetic field, and compares two different parametrization approaches for the metric corrections.

Contribution

It introduces two parametrizations for semiclassical lukewarm black holes and computes quantum corrections to the classical solutions, providing a detailed analysis of back-reaction effects.

Findings

Calculated zeroth-order classical solution.

Determined quantum corrections to metric potentials and horizons.

Established transformation formulas between parametrizations.

Abstract

The perturbative solutions to the semiclassical Einstein field equations describing spherically-symmetric and static lukewarm black hole are constructed. The source term is composed of the (classical) stress-energy tensor of the electromagnetic field and the renormalized stress-energy tensor of the quantized massive scalar field in a large mass limit. We used two different parametrizations. In the first parametrization we calculated the zeroth-order solution. Subsequently, making use of the quantum part of the total stress-energy tensor constructed in the classical background we calculated the corrections to the metric potentials and the corrections to the horizons. This procedure can be thought of as switching the quantized field on and analyzing its influence on the classical background via the back-reaction. In the second parametrization we are looking for a self-consistent lukewarm solution from the very beginning. This requires knowledge of a generic tensor which depends functionally on the metric tensor. The transformation formulas relating the line element in both parametrizations are given.