The double-Kerr equilibrium configurations involving one extreme object

TL;DR

This paper explores equilibrium configurations in double-Kerr systems involving an extreme object, revealing new conditions for balance and showing that the J=M^2 relation no longer holds in binary systems.

Contribution

It demonstrates the existence of equilibrium states with extreme objects, including cases with positive and negative masses, and challenges the traditional J=M^2 relation in binary Kerr systems.

Findings

Equilibrium states exist with one extreme Kerr object and specific mass conditions.

Negative mass is required for balance in certain extreme configurations.

The J=M^2 relation does not hold in binary Kerr systems.

Abstract

We demonstrate the existence of equilibrium states in the limiting cases of the double-Kerr solution when one of the constituents is an extreme object. In the `extreme-subextreme' case the negative mass of one of the constituents is required for the balance, whereas in the `extreme-superextreme' equilibrium configurations both Kerr particles may have positive masses. We also show that the well-known relation |J|=M^2 between the mass and angular momentum in the extreme single Kerr solution ceases to be a characteristic property of the extreme Kerr particle in a binary system.