Exact charged and rotating toroidal black hole in the Einstein $SU(N)$-Skyrme model

TL;DR

This paper presents an exact solution for a charged, rotating black hole with a toroidal horizon in the Einstein $SU(N)$-Skyrme model, incorporating rotation, electric charge, and flavor effects, with thermodynamic and stability analysis.

Contribution

It provides the first exact solution of a charged, rotating toroidal black hole in the Einstein $SU(N)$-Skyrme model, including thermodynamic and stability insights.

Findings

Rotation added via coordinate transformation.

Electric charge introduced through $U(1)$ gauge field.

Thermal analysis reveals flavor number's role.

Abstract

In this paper, we construct an exact solution of the Einstein $SU(N)$-Skyrme model in $D=4$ space-time dimensions describing a charged and rotating black hole with toroidal horizon. Rotation is added by applying an improper coordinate transformation to the known static toroidal black hole with Skyrme hair, while the electric charge is supplemented by considering a $U(1)$ gauge field interacting with Einstein gravity. We perform the thermal analysis in the grand canonical ensemble, explicitly showing the role that the flavor number plays. Some discussions about stability are also considered.