Small deformations of extreme Kerr black hole initial data

TL;DR

This paper proves the existence of a family of initial data for Einstein's equations that are small deformations of the extreme Kerr black hole, maintaining key geometric properties.

Contribution

It introduces a new family of initial data representing small deformations of the extreme Kerr black hole while preserving asymptotic geometry, angular momentum, and horizon area.

Findings

Existence of a family of deformed initial data

Preservation of angular momentum and horizon area

Maintenance of asymptotic geometry similar to extreme Kerr

Abstract

We prove the existence of a family of initial data for Einstein equations which represent small deformations of the extreme Kerr black hole initial data. The data in this family have the same asymptotic geometry as extreme Kerr. In particular, the deformations preserve the angular momentum and the area of the cylindrical end.