Einstein-Yang-Mills-Chern-Simons solutions in D=2n+1 dimensions

TL;DR

This paper explores finite energy, static, spherically symmetric solutions in odd-dimensional Einstein-Yang-Mills-Chern-Simons systems, revealing new stable non-Abelian black holes and particle-like configurations with finite mass and charge.

Contribution

It introduces novel non-Abelian solutions in higher odd dimensions with Chern-Simons terms, including stable black holes and solitons, expanding understanding of gauge-gravity systems.

Findings

Constructed numerical solutions for D=5,7,9 with finite mass and charge.

Discovered stability of certain non-Abelian black holes under perturbations.

Identified instability of Reissner-Nordstrom black holes in D=5.

Abstract

We investigate finite energy solutions of the Einstein--Yang-Mills--Chern-Simons system in odd spacetime dimensions, D=2n+1, with n>1. Our configurations are static and spherically symmetric, approaching at infinity a Minkowski spacetime background. In contrast with the Abelian case, the contribution of the Chern-Simons term is nontrivial already in the static, spherically symmetric limit. Both globally regular, particle-like solutions and black holes are constructed numerically for several values of D. These solutions carry a nonzero electric charge and have finite mass. For globally regular solutions, the value of the electric charge is fixed by the Chern-Simons coupling constant. The black holes can be thought as non-linear superpositions of Reissner-Nordstrom and non-Abelian configurations. A systematic discussion of the solutions is given for D=5, in which case the Reissner-Nordstrom black hole becomes unstable and develops non-Abelian hair. We show that some of these non-Abelian configurations are stable under linear, spherically symmetric perturbations. A detailed discussion of an exact D=5 solution describing extremal black holes and solitons is also provided.