Opposite charged two-body system of identical counter-rotating black holes

TL;DR

This paper presents an exact solution for a system of two identical counter-rotating Kerr-Newman black holes with opposite electric and magnetic charges, detailing their physical parameters and horizon properties.

Contribution

It provides a new explicit solution describing such black hole pairs, including the relation of horizon size to physical parameters and the role of magnetic charges from rotation.

Findings

Derived explicit horizon length parameter sigma in terms of physical quantities.

Established the presence of magnetic charges arising from rotation of electrically charged black holes.

Proposed a generalized Smarr formula accounting for magnetic charges.

Abstract

A 4-parametric exact solution describing a two-body system of identical Kerr-Newman counter-rotating black holes endowed with opposite electric/magnetic charges is presented. The axis conditions are solved in order to really describe two black holes separated by a massless strut. Moreover, the explicit form of the horizon half length parameter sigma in terms of physical Komar parameters, i.e., the Komar mass M, electric charge QE, angular momentum J, and a coordinate distance R is derived. Additionally, magnetic charges QB arise from the rotation of electrically charged black holes. As a consequence, in order to account for the contribution to the mass of the magnetic charge, the usual Smarr mass formula should be generalized, as it is proposed by A. Tomimatsu, Prog. Theor. Phys. 72, 73 (1984).