Zero temperature black holes in semiclassical gravity

TL;DR

This paper investigates the properties of zero temperature Reissner-Nordström black holes under semiclassical gravity, revealing constraints on their horizon location and showing certain solutions cannot be obtained perturbatively.

Contribution

It demonstrates that zero temperature black holes must have horizons at radii less than the charge magnitude and that such solutions are not accessible via perturbative methods.

Findings

Zero temperature black holes have horizons at r_h < |Q|.

Perturbative solutions cannot produce black holes with r_h < |Q|.

Realistic quantum fields influence black hole horizon structure.

Abstract

The semiclassical Einstein equations are solved to first order in $\epsilon = \hbar/M^2$ for the case of an extreme or nearly extreme Reissner-Nordstr\"{o}m black hole perturbed by the vacuum stress-energy of quantized free fields. It is shown that, for realistic fields of spin 0, 1/2, or 1, any zero temperature black hole solution to the equations must have an event horizon at $r_h < |Q|$, with $Q$ the charge of the black hole. It is further shown that no black hole solutions with $r_h < |Q|$ can be obtained by solving the semiclassical Einstein equations perturbatively.