Five-dimensional Black Hole and Particle Solution with Non-Abelian Gauge Field

TL;DR

This paper presents new five-dimensional black hole and particle solutions in Einstein-Yang-Mills theory with a cosmological constant, including analytic, numerical, and stability analyses of these localized objects.

Contribution

It introduces novel five-dimensional black hole and particle solutions with non-Abelian gauge fields, including an analytic solution and numerical examples, with stability analysis based on the cosmological constant.

Findings

New analytic black hole solution with various asymptotics

Numerical particle-like and black hole solutions without singularities

Stable solutions exist for negative cosmological constant

Abstract

We study the 5-dimensional Einstein-Yang-Mills system with a cosmological constant. Assuming a spherically symmetric spacetime, we find a new analytic black hole solution, which approaches asymptotically "quasi-Minkowski", "quasi anti-de Sitter", or "quasi de Sitter" spacetime depending on the sign of a cosmological constant. Since there is no singularity except for the origin which is covered by an event horizon, we regard it as a localized object. This solution corresponds to a magnetically charged black hole. We also present a singularity-free particle-like solution and a non-trivial black hole solution numerically. Those solutions correspond to the Bartnik-McKinnon solution and a colored black hole with a cosmological constant in the 4-dimensions. We analyze their asymptotic behaviors, spacetime structures and thermodynamical properties. We show that there is a set of stable solutions if a cosmological constant is negative.