Stable Black Hole with Yang-Mills Hair

TL;DR

This paper reports a stable, asymptotically flat Einstein-Yang-Mills black hole solution with SU(2) gauge fields, which challenges the no-hair conjecture and suggests potential implications for primordial black holes and dark matter.

Contribution

It provides the first stable Einstein-Yang-Mills black hole solution with nontrivial gauge fields, serving as a counterexample to the no-hair conjecture and indicating new black hole types in the early Universe.

Findings

The solution is stable both linearly and nonlinearly.

It approaches Schwarzschild solution asymptotically.

It may serve as a candidate for primordial black holes and dark matter.

Abstract

We present stable solution of static spherically symmetric Einstein-Yang-Mills equations with the SU(2) gauge group. This solution is asymptotically flat and regular at r = 0 and with nontrivial Yang-Mills(YM) connection. With quantized values of the Arnowitt-Deser-Misner (ADM) mass, the solutions asymptotically approach the Schwarzschild solution and have zero global YM charges. Numerical evidences suggest that this solution is both linearly and nonlinearly stable and has a ring of generic curvature singularities along the horizon. An effective counterexample to the no-hair conjecture is provided by this stable solution. Moreover, the stable black hole solution suggests that the coupling of gauge field to gravity in early Universe will generate a new type of black holes. Their stability means that these might be a possible new source of primordial black holes left over from the early Universe and serves as a possible new candidate for dark matter.