Exact solution for two unequal counter-rotating black holes

Abstract

The complete solution for two unequal counter-rotating black holes separated by a massless strut, is developed in terms of four arbitrary parameters involving two quantities \sigma 1 and \sigma 2 as the half length of the two rods representing the black hole horizons, the total mass M and the relative distance R between the centers of the horizons. A further attempt for describing the explicit form of this solution in terms of the physical parameters: The two Komar masses M1 and M2, Komar angular momenta per unit mass a1 and a2 (a1 and a2 have opposite sign), and the coordinate distance R, guided us to a 4-parameter subclass in which the five physical parameters satisfy a simple algebraic relation and the interaction force in this scheme looks like Schwarzschild type.