Non-Abelian Black Holes in Brans-Dicke Theory

TL;DR

This paper discovers non-Abelian black hole solutions within Brans-Dicke theory, extending known solutions from general relativity, and analyzes their properties, stability, and the influence of scalar fields in different conformal frames.

Contribution

It introduces new non-Abelian black hole solutions in Brans-Dicke theory and examines their stability and structural differences from general relativity.

Findings

Black hole masses are smaller than in general relativity.

Cusp structures indicating stability change appear only in the Einstein frame.

Brans-Dicke scalar field affects black hole structure.

Abstract

We find a black hole solution with non-Abelian field in Brans-Dicke theory. It is an extension of non-Abelian black hole in general relativity. We discuss two non-Abelian fields: "SU(2)" Yang-Mills field with a mass (Proca field) and the SU(2)$\times$SU(2) Skyrme field. In both cases, as in general relativity, there are two branches of solutions, i.e., two black hole solutions with the same horizon radius. Masses of both black holes are always smaller than those in general relativity. A cusp structure in the mass-horizon radius ($M_{g}$-$r_{h}$) diagram, which is a typical symptom of stability change in catastrophe theory, does not appear in the Brans-Dicke frame but is found in the Einstein conformal frame. This suggests that catastrophe theory may be simply applied for a stability analysis as it is if we use the variables in the Einstein frame. We also discuss the effects of the Brans-Dicke scalar field on black hole structure.