SU(2)-Colored (A)dS Black Holes in Conformal Gravity

TL;DR

This paper explores complex black hole solutions in four-dimensional conformal gravity coupled with U(1) and SU(2) gauge fields, analyzing their thermodynamics, exact solutions, and extending results to Einstein-Yang-Mills gravity.

Contribution

It introduces new black hole solutions with multiple charges in conformal gravity and derives their thermodynamic laws, including an extremal case with unique properties.

Findings

Derived the thermodynamical first law for these black holes.

Found an extremal black hole with zero mass and entropy but non-trivial gauge charges.

Reexamined colored black holes and their thermodynamics in Einstein-Yang-Mills gravity.

Abstract

We consider four-dimensional conformal gravity coupled to the U(1) Maxwell and SU(2) Yang-Mills fields. We study the structure of general black hole solutions carrying five independent parameters: the mass, the electric U(1) and magnetic SU(2) charges, the massive spin-2 charge and the thermodynamical pressure associated with the cosmological constant, which is an integration constant in conformal gravity. We derive the thermodynamical first law of the black holes. We obtain some exact solutions including an extremal black hole with vanishing mass and entropy, but with non-trivial SU(2) Yang-Mills charges. We derive the remainder of the first law for this special solution. We also reexamine the colored black holes and derive their first law in Einstein-Yang-Mills gravity with or without a cosmological constant.