On the interaction between two Kerr black holes

TL;DR

This paper analyzes the interaction between two Kerr black holes using advanced mathematical techniques, deriving exact formulas for their force, angular velocity, extremality conditions, and temperature behavior, revealing complex dragging effects.

Contribution

It provides a detailed analysis of the double-Kerr system, establishing equivalence between solution methods and deriving new exact formulas for physical interactions and properties.

Findings

The force between black holes is exactly computed in terms of physical parameters.

Angular velocity decreases from Kerr value to zero as black holes approach.

Temperature of black holes peaks at a finite distance for high angular momentum.

Abstract

The double-Kerr solution is generated using both a Backlund transformation and the Belinskii-Zakharov inverse-scattering technique. We build a dictionary between the parametrisations naturally obtained in the two methods and show their equivalence. We then focus on the asymptotically flat double-Kerr system obeying the axis condition which is Z_2^\phi invariant; for this system there is an exact formula for the force between the two black holes, in terms of their physical quantities and the coordinate distance. We then show that 1) the angular velocity of the two black holes decreases from the usual Kerr value at infinite distance to zero in the touching limit; 2) the extremal limit of the two black holes is given by |J|=cM^2, where c depends on the distance and varies from one to infinity as the distance decreases; 3) for sufficiently large angular momentum the temperature of the black holes attains a maximum at a certain finite coordinate distance. All of these results are interpreted in terms of the dragging effects of the system.