Zero temperature black holes in semiclassical gravity

Abstract

The semiclassical Einstein equations are solved to first order in $\epsilon =\hslash /M^2$ for the case of an extreme or nearly extreme Reissner-Nordström 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.

7 pages, to appear in the Proceedings of the Ninth Marcel Grossmann Meeting, change in title