Shape of black holes

TL;DR

This paper explores the shape of black hole horizons, showing that rotation influences their geometry, making them resemble the extreme Kerr horizon at high spins, regardless of surrounding matter or spacetime geometry.

Contribution

It provides new results linking black hole rotation, horizon shape, and geometry, independent of external spacetime conditions, and relates these findings to the Hoop conjecture.

Findings

Black hole rotation causes horizon widening and shape limits.

High rotation enforces near-extreme Kerr horizon geometry.

Results depend only on horizon area and angular momentum.

Abstract

It is well known that celestial bodies tend to be spherical due to gravity and that rotation produces deviations from this sphericity. We discuss what is known and expected about the shape of black holes' horizons from their formation to their final, stationary state. We present some recent results showing that black hole rotation indeed manifests in the widening of their central regions, limits their global shapes and enforces their whole geometry to be close to the extreme Kerr horizon geometry at almost maximal rotation speed. The results depend only on the horizon area and angular momentum. In particular they are entirely independent of the surrounding geometry of the spacetime and of the presence of matter satisfying the strong energy condition. We also discuss the the relation of this result with the Hoop conjecture.