Remarks on the mass-angular momentum relations for two extreme Kerr sources in equilibrium

TL;DR

This paper examines the mass-angular momentum relations in binary systems of extremal Kerr particles, confirming the Kerr inequality for individual components but identifying cases where the total system violates this inequality.

Contribution

It provides a detailed analysis of extremal Kerr binary configurations using exact solutions, highlighting when the Kerr inequality holds or is violated for total system parameters.

Findings

Kerr inequality holds for individual extremal components.

Total system mass and angular momentum can violate the Kerr inequality.

Identifies specific conditions for inequality violation in binary systems.

Abstract

The general analysis of the relations between masses and angular momenta in the configurations composed of two balancing extremal Kerr particles is made on the basis of two exact solutions arising as extreme limits of the well-known double-Kerr spacetime. We show that the inequality M^2 >= |J| characteristic of an isolated Kerr black hole is verified by all the extremal components of the Tomimatsu and Dietz-Hoenselaers solutions. At the same time, the inequality can be violated by the total masses and total angular momenta of these binary systems, and we identify all the cases when such violation occurs.