Self-gravitating Yang Monopoles in all Dimensions

TL;DR

This paper constructs and analyzes spherically symmetric magnetic monopole solutions in higher-dimensional Einstein-Yang-Mills theories, revealing their properties, horizons, and asymptotic behaviors across different cosmological constants.

Contribution

It introduces a family of self-gravitating Yang monopole solutions in all dimensions, extending known results and analyzing their horizon structure and spacetime properties.

Findings

Existence of monopole solutions in all (2k+2) dimensions.

Presence of event horizons for masses above a critical value.

Asymptotic spacetime is Minkowski or anti-de Sitter depending on Lambda.

Abstract

The (2k+2)-dimensional Einstein-Yang-Mills equations for gauge group SO(2k) (or SU(2) for k=2 and SU(3) for k=3) are shown to admit a family of spherically-symmetric magnetic monopole solutions, for both zero and non-zero cosmological constant Lambda, characterized by a mass m and a magnetic-type charge. The k=1 case is the Reissner-Nordstrom black hole. The k=2 case yields a family of self-gravitating Yang monopoles. The asymptotic spacetime is Minkowski for Lambda=0 and anti-de Sitter for Lambda<0, but the total energy is infinite for k>1. In all cases, there is an event horizon when m>m_c, for some critical mass $m_c$, which is negative for k>1. The horizon is degenerate when m=m_c, and the near-horizon solution is then an adS_2 x S^{2k} vacuum.