Mass vs. Charge: Quantum Radiation from Zero Temperature Black Holes

TL;DR

This paper investigates how quantum effects alter the mass-charge relationship of extremal black holes, revealing a deviation from classical predictions due to conformal scalar fields and analyzing the implications of these modifications.

Contribution

It provides a detailed analysis of quantum corrections to the mass-charge ratio in extremal black holes within Einstein-Maxwell theory coupled to conformal scalars, including both analytical and numerical results.

Findings

Classical ratio M/|Q|=1 is modified to approximately 1 - k/6.

Numerical results show M/|Q| decreases monotonically with increasing k.

Quantum effects can significantly alter black hole properties in four dimensions.

Abstract

We study the mass-charge relation for the semiclassical extremal black hole of the $S$-wave sector Einstein-Maxwell theory coupled to $N$ conformal scalars. The classical ratio $M/{|Q|}=1$ is shown to be modified to $M/{|Q|} \simeq 1-k/6$ for small $ k \equiv N\hbar/(12\pi Q^{2})$. Furthermore, numerical study for $k<2$ shows that $M/|Q|$ is a monotonically decreasing function of $k$. We speculate on the consequence of such a modification in the 4-dimensional context.