Area - Angular momentum inequality for axisymmetric black holes

TL;DR

This paper proves an inequality relating the area and angular momentum of axially symmetric black hole horizons, establishing a fundamental geometric constraint in general relativity.

Contribution

It introduces a new local inequality $A \,\geq\, 8\pi|J|$ for axially symmetric minimal surfaces, applicable to black hole horizons and initial data.

Findings

The inequality holds for stable minimal surfaces in axially symmetric initial data.

It applies to horizons of black holes in asymptotically flat spacetimes.

The result confirms a key conjecture in black hole physics.

Abstract

We prove the local inequality $A \geq 8\pi|J|$, where $A$ and $J$ are the area and angular momentum of any axially symmetric closed stable minimal surface in an axially symmetric maximal initial data. From this theorem it is proved that the inequality is satisfied for any surface on complete asymptotically flat maximal axisymmetric data. In particular it holds for marginal or event horizons of black holes.