Non-Abelian Magnetized Blackholes and Unstable Attractors

TL;DR

This paper investigates the instability of non-Abelian gauge field configurations in magnetic backgrounds coupled to gravity, revealing that such blackhole solutions are unstable and challenging the applicability of the attractor mechanism in non-Abelian contexts.

Contribution

It extends the analysis of gauge field instabilities to gravitational backgrounds, demonstrating that non-Abelian blackholes are unstable and questioning the direct application of the attractor mechanism.

Findings

Non-Abelian gauge field fluctuations contain tachyonic modes indicating instability.

Spherically symmetric non-Abelian blackholes are unstable when coupled to gravity.

The attractor mechanism does not straightforwardly apply to extremal non-Abelian blackholes.

Abstract

Fluctuations of non-Abelian gauge fields in a background magnetic flux contain tachyonic modes and hence the background is unstable. We extend these results to the cases where the background flux is coupled to Einstein gravity and show that the corresponding spherically symmetric geometries, which in the absence of a cosmological constant are of the form of Reissner-Nordstrom blackholes or the AdS_2xS^2, are also unstable. We discuss the relevance of these instabilities to several places in string theory including various string compactifications and the attractor mechanism. Our results for the latter imply that the attractor mechanism shown to work for the extremal Abelian charged blackholes, cannot be applied in a straightforward way to the extremal non-Abelian colored blackholes.