Do semiclassical zero temperature black holes exist?

TL;DR

This paper investigates whether macroscopic zero temperature black holes can exist within semiclassical gravity, concluding that such solutions are not possible in physically realistic scenarios and are only microscopic and isolated.

Contribution

It demonstrates that macroscopic zero temperature black holes do not exist in semiclassical gravity for various quantum fields, highlighting their microscopic and isolated nature.

Findings

Macroscopic zero temperature black holes do not exist in semiclassical solutions.

Zero temperature solutions, if any, are microscopic and isolated.

No smooth transition from classical extremal to semiclassical zero temperature black holes.

Abstract

The semiclassical Einstein equations are solved to first order in $\epsilon = \hbar/M^2$ for the case of a Reissner-Nordstr\"{o}m black hole perturbed by the vacuum stress-energy of quantized free fields. Massless and massive fields of spin 0, 1/2, and 1 are considered. We show that in all physically realistic cases, macroscopic zero temperature black hole solutions do not exist. Any static zero temperature semiclassical black hole solutions must then be microscopic and isolated in the space of solutions; they do not join smoothly onto the classical extreme Reissner-Nordst\"{o}m solution as $\epsilon \to 0$.