Charged Rotating Black Holes in Equilibrium

TL;DR

This paper develops a method to explicitly solve for axially symmetric, stationary charged black holes in equilibrium, revealing how their total mass depends on the distance between black holes and providing new insights into their properties.

Contribution

It introduces a novel explicit integration method for the boundary-value problem of charged rotating black holes with disconnected horizons.

Findings

Total mass depends on the distance between black holes.

Derived relations between physical parameters of black holes.

Demonstrated the reduction of Einstein-Maxwell equations to algebraic systems.

Abstract

Axially symmetric, stationary solutions of the Einstein-Maxwell equations with disconnected event horizon are studied by developing a method of explicit integration of the corresponding boundary-value problem. This problem is reduced to non-leaner system of algebraic equations which gives relations between the masses, the angular momenta, the angular velocities, the charges, the distance parameters, the values of the electromagnetic field potential at the horizon and at the symmetry axis. A found solution of this system for the case of two charged non-rotating black holes shows that in general the total mass depends on the distance between black holes. Two-Killing reduction procedure of the Einstein-Maxwell equations is also discussed.