Remarks on stationary vacuum black holes

TL;DR

This paper completes the proof of the no-hair theorem for stationary vacuum black holes, clarifies horizon properties without assuming analyticity, and shows near-horizon geometries are Kerrian under regularity conditions.

Contribution

It finalizes the no-hair theorem proof and demonstrates horizon characteristics and near-horizon geometries without analyticity assumptions.

Findings

Proof of the no-hair theorem completed.

Horizon surface gravity and angular velocity defined without analyticity.

Near-horizon geometries are Kerrian under regularity conditions.

Abstract

We finish the proof of the no-hair theorem for stationary, analytic, connected, suitably regular, four dimensional vacuum black holes. We show how to define the surface gravity and the angular velocity of horizons without assuming analyticity. We point out that, under the usual regularity conditions, vacuum near-horizon geometries are Kerrian without assuming analyticity.