Black Hole solutions in Einstein-Maxwell-Yang-Mills-Gauss-Bonnet Theory

TL;DR

This paper explores black hole solutions in Einstein-Maxwell-Yang-Mills-Gauss-Bonnet theory, revealing how different fields dominate at various distances and recovering known solutions like BTZ and RN in specific cases.

Contribution

It introduces new black hole solutions in Einstein-Gauss-Bonnet gravity coupled with Maxwell and Yang-Mills fields, analyzing their asymptotic behaviors and recovering classical solutions.

Findings

Maxwell field dominates near r=0 for N>4

Yang-Mills field dominates at infinity

Recovery of BTZ and RN metrics in specific cases

Abstract

We consider Maxwell and Yang-Mills (YM) fields together, interacting through gravity both in Einstein and Gauss-Bonnet (GB) theories. For this purpose we choose two different sets of Maxwell and metric ansaetze. In our first ansatz, asymptotically for $r\to 0$ (and $N>4$) the Maxwell field dominants over the YM field. In the other asymptotic region, $r\to \infty $, however, the YM field becomes dominant. For N=3 and N=4, where the GB term is absent, we recover the well-known Ba\U{f1}ados-Teitelboim-Zanelli (BTZ) and Reissner-Nordstr\U{f6}m (RN) metrics, respectively. The second ansatz corresponds to the case of constant radius function for $S^{N-2}$ part in the metric. This leads to the Bertotti-Robinson (BR) type solutions in the underlying theory.