Generalized black diholes

TL;DR

This paper presents an exact 5-parameter solution for a binary system of counter-rotating black holes with electromagnetic charges, extending previous models to include magnetic charges and generalized black diholes as dyons.

Contribution

The authors derive a new exact solution incorporating magnetic charges into a binary black hole system, extending the static dihole model to include rotation and electromagnetic duality.

Findings

Explicit functional form of horizon half-length parameter $\sigma$ derived.

Solution generalizes previous models by including magnetic charges and rotation.

Enhances the Smarr mass formula to account for magnetic charge contributions.

Abstract

A 5-parametric exact solution, describing a binary system composed of identical counter-rotating black holes endowed with opposite electromagnetic charges, is constructed. The addition of the angular momentum parameter to the static Emparan-Teo dihole model introduces magnetic charges into this two-body system. The solution can be considered as an extended model for describing generalized black diholes as dyons. We derive the explicit functional form of the horizon half-length parameter $\sigma$ as a function of the Komar parameters: Komar mass $M$, electric/magnetic charge $Q_{E }/ Q_{B}$, angular momentum $J$, and a coordinate distance $R$, where the parameters $(M, J, Q_E, Q_B, R)$ characterize the upper constituent of the system, while $(M, -J, -Q_E, -Q_B, R)$ are associated with the lower one. The addition of magnetic charges enhances the standard Smarr mass formula in order to take into account their contribution to the mass. The solution contains, as particular cases, two solutions already discussed in the literature.