The Hoop Conjecture for Black Rings

TL;DR

This paper examines a conjecture relating the size of black hole horizons to their mass, demonstrating its validity for various five-dimensional black rings with different horizon topologies.

Contribution

It extends the hoop conjecture to five-dimensional black rings, showing the inequality holds beyond traditional black hole horizons.

Findings

The hoop inequality is satisfied by a wide variety of black rings.

The conjecture applies to horizons with S^2×S^1 topology.

Supports the universality of the hoop conjecture in higher dimensions.

Abstract

A precise formulation of the hoop conjecture for four-dimensional spacetimes proposes that the Birkhoff invariant \beta for an apparent horizon in a spacetime with mass M should satisfy \beta \le 4\pi M. The invariant \beta is the least maximal length of any sweepout of the 2-sphere apparent horizon by circles. An analogous conjecture in five spacetime dimensions was recently formulated, asserting that the Birkhoff invariant \beta for S^1\times S^1 sweepouts of the apparent horizon should satisfy \beta \le (16/3)\pi M. Although this hoop inequality was formulated for conventional five-dimensional black holes with 3-sphere horizons, we show here that it is also obeyed by a wide variety of black rings, where the horizon instead has S^2\times S^1 topology.