Solitons and hairy black holes in Einstein-non-Abelian-Proca theory in anti-de Sitter space-time

TL;DR

This paper introduces new soliton and hairy black hole solutions within Einstein-non-Abelian-Proca theory in anti-de Sitter space, revealing their properties, stability issues, and numerical solutions for static, spherically symmetric configurations.

Contribution

It provides the first numerical solutions for static, spherically symmetric solitons and hairy black holes in Einstein-non-Abelian-Proca theory in AdS space, analyzing their properties and stability.

Findings

Solutions are purely magnetic with at least one zero in the gauge function

All solutions are unstable under linear perturbations

Solutions share properties with asymptotically flat counterparts

Abstract

We present new soliton and hairy black hole solutions of Einstein-non-Abelian-Proca theory in asymptotically anti-de Sitter space-time with gauge group ${\mathfrak {su}}(2)$. For static, spherically symmetric configurations, we show that the gauge field must be purely magnetic, and solve the resulting field equations numerically. The equilibrium gauge field is described by a single function $\omega (r)$, which must have at least one zero. The solitons and hairy black holes share many properties with the corresponding solutions in asymptotically flat space-time. In particular, all the solutions we study are unstable under linear, spherically symmetric, perturbations of the metric and gauge field.