Instabilities of Magnetically Charged Black Holes

TL;DR

This paper investigates the stability of magnetically charged Reissner-Nordstrom black holes within a theory involving massive charged vector mesons, revealing conditions under which instabilities occur and suggesting the existence of stable 'hairy' black hole solutions.

Contribution

It demonstrates the existence of critical horizon radii for instability depending on vector meson parameters, extending understanding of black hole stability with non-Abelian fields.

Findings

Unstable modes appear below a critical horizon radius depending on parameters.

Stable solutions with nonzero vector fields ('hair') are implied outside the horizon.

Instabilities are absent in the anomalous case with specific charge and gyromagnetic ratio.

Abstract

The stability of the magnetically charged Reissner-Nordstrom black hole solution is investigated in the context of a theory with massive charged vector mesons. By exploiting the spherical symmetry of the problem, the linear perturbations about the Reissner-Nordstrom solution can be decomposed into modes of definite angular momentum $J$. For each value of $J$, unstable modes appear if the horizon radius is less than a critical value that depends on the vector meson gyromagnetic ratio $g$ and the monopole magnetic charge $q/e$. It is shown that such a critical radius exists (except in the anomalous case $q={1\over 2}$ with $0 \le g \le 2$), provided only that the vector meson mass is not too close to the Planck mass. The value of the critical radius is determined numerically for a number of values of $J$. The instabilities found here imply the existence of stable solutions with nonzero vector fields (``hair'') outside the horizon; unless $q=1$ and $g>0$, these will not be spherically symmetric.