Spherically symmetric solutions of a (4+n)-dimensional Einstein-Yang-Mills model with cosmological constant

TL;DR

This paper constructs and analyzes spherically symmetric solutions in a higher-dimensional Einstein-Yang-Mills model with a cosmological constant, revealing conditions for solutions with specific Higgs field configurations and their geometric properties.

Contribution

It provides new analytic solutions for higher-dimensional Einstein-Yang-Mills systems with a cosmological constant, including embedded abelian and non-abelian solutions with specific Higgs field behaviors.

Findings

Solutions with one non-zero Higgs field or constant Higgs fields exist for n > 1.

Embedded abelian solutions have diverging extra-dimensional manifold size.

Non-abelian solutions with diverging Higgs fields exist up to a maximum cosmological constant.

Abstract

We construct solutions of an Einstein-Yang-Mills system including a cosmological constant in 4+n space-time dimensions, where the n-dimensional manifold associated with the extra dimensions is taken to be Ricci flat. Assuming the matter and metric fields to be independent of the n extra coordinates, a spherical symmetric Ansatz for the fields leads to a set of coupled ordinary differential equations. We find that for n > 1 only solutions with either one non-zero Higgs field or with all Higgs fields constant and zero gauge fields exist. We give the analytic solutions available in this model. These are ``embedded'' abelian solutions with a diverging size of the manifold associated with the extra n dimensions. Depending on the choice of parameters, these latter solutions either represent naked singularities or they possess a single horizon. We also present solutions of the effective 4-dimensional Einstein-Yang-Mills-Higgs-dilaton model, where the higher dimensional cosmological constant induces a Liouville-type potential. The solutions are non-abelian solutions with diverging Higgs fields, which exist only up to a maximal value of the cosmological constant.