Initial data for two Kerr-like black holes

TL;DR

This paper constructs initial data for two Kerr-like black holes with arbitrary positions and spins, extending Kerr initial data and providing a foundation for studying binary black hole systems.

Contribution

It introduces a new family of initial data for two Kerr-like black holes with arbitrary parameters, generalizing previous Kerr initial data.

Findings

Existence of initial data for two Kerr-like black holes with arbitrary parameters.

Reduction to Kerr initial data when one mass parameter is zero.

Discussion of potential generalizations.

Abstract

We prove the existence of a family of initial data for the Einstein vacuum equation which can be interpreted as the data for two Kerr-like black holes in arbitrary location and with spin in arbitrary direction. When the mass parameter of one of them is zero, this family reduces exactly to the Kerr initial data. The existence proof is based on a general property of the Kerr metric which can be used in other constructions as well. Further generalizations are also discussed.