Evaporating Quantum Lukewarm Black Holes Final State From Back-Reaction Corrections of Quantum Scalar Fields

TL;DR

This paper calculates the quantum stress tensor for a scalar field around a Lukewarm black hole and predicts that evaporation leads to a stable remnant black hole with shifted horizons, challenging certain cosmic hypotheses.

Contribution

It provides a detailed analysis of back-reaction effects on Lukewarm black holes and predicts their end state as stable remnants with shifted horizons.

Findings

Final state is a stable remnant black hole.

Horizon locations are shifted due to back-reaction.

No deviation from the cosmic sensor-ship hypothesis.

Abstract

We obtain renormalized stress tensor of a mass-less, charge-less dynamical quantum scalar field, minimally coupled with a spherically symmetric static Lukewarm black hole. In two dimensional analog the minimal coupling reduces to the conformal coupling and the stress tensor is found to be determined by the nonlocal contribution of the anomalous trace and some additional parameters in close relation to the work presented by Christensen and Fulling. Lukewarm black holes are a special class of Reissner- Nordstr\"{o}m-de Sitter space times where its electric charge is equal to its mass. Having the obtained renormalized stress tensor we attempt to obtain a time-independent solution of the well known metric back reaction equation. Mathematical derivations predict that the final state of an evaporating quantum Lukewarm black hole reduces to a remnant stable mini black hole with moved locations of the horizons. Namely the perturbed black hole (cosmological) horizon is compressed (extended) to scales which is smaller (larger) than the corresponding classical radius of the event horizons. Hence there is not obtained an deviation on the cosmic sensor-ship hypothesis.