Two remarks on near-horizon geometries

TL;DR

This paper demonstrates that extreme black holes with certain symmetries have near-horizon geometries with increased symmetry and provides a simple proof for the horizon topology theorem of degenerate horizons.

Contribution

It establishes enhanced symmetry properties for near-horizon geometries of extreme black holes and offers a straightforward proof of a key horizon topology theorem.

Findings

Extreme black holes with orthogonally transitive abelian isometry groups have symmetric near-horizon geometries.

A simple proof of the horizon topology theorem for degenerate horizons is provided.

The results deepen understanding of black hole horizon structures.

Abstract

We show that any extreme black hole with an orthogonally transitive abelian isometry group has a near-horizon geometry with enhanced symmetry. We also point out a simple proof of the horizon topology theorem of Galloway and Schoen for degenerate horizons.