Extreme throat initial data set and horizon area--angular momentum inequality for axisymmetric black holes

TL;DR

This paper establishes that the area of extreme Kerr throat initial data is minimized among axisymmetric black hole data with fixed angular momentum, supporting the area-angular momentum inequality for such black holes.

Contribution

It derives a formula relating area variations to a mass functional and proves the area-angular momentum inequality for a class of initial data, including Bowen-York data.

Findings

The area of extreme Kerr throat data is a minimum for fixed angular momentum.

The area-angular momentum inequality holds for certain initial data.

The result supports the conjecture for generic axisymmetric black holes.

Abstract

We present a formula that relates the variations of the area of extreme throat initial data with the variation of an appropriate defined mass functional. From this expression we deduce that the first variation, with fixed angular momentum, of the area is zero and the second variation is positive definite evaluated at the extreme Kerr throat initial data. This indicates that the area of the extreme Kerr throat initial data is a minimum among this class of data. And hence the area of generic throat initial data is bounded from below by the angular momentum. Also, this result strongly suggests that the inequality between area and angular momentum holds for generic asymptotically flat axially symmetric black holes. As an application, we prove this inequality in the non trivial family of spinning Bowen-York initial data.