Apparent Horizons with Nontrivial Topology and the Hyperhoop Conjecture in Six-Dimensional Space-Times

TL;DR

This paper tests the hyperhoop conjecture in six-dimensional space-times using numerical methods, confirming its validity and discovering new higher-dimensional black hole horizons with nontrivial topologies.

Contribution

It provides the first numerical confirmation of the hyperhoop conjecture's validity and identifies new higher-dimensional black hole horizons with complex topologies.

Findings

Hyperhoop conjecture holds for various parameters in six-dimensional space-times.

Existence of apparent horizons with topologies S^2 x S^2 and S^1 x S^3 confirmed.

Numerical methods successfully used to analyze higher-dimensional black hole horizons.

Abstract

We investigate the validity of the hyperhoop conjecture, which claims to determine a necessary and sufficient condition for the formation of black hole horizons in higher-dimensional space-times. Here we consider momentarily static, conformally flat initial data sets each describing a gravitational field of uniform massive k-sphere sources, for k=1,2, on the five-dimensional Cauchy surface. The numerical result shows the validity of the hyperhoop conjecture for a wide range of model parameters. We also confirm for the first time the existence of an apparent horizon homeomorphism to S**2 x S**2 or S**1 x S**3, which is a higher-dimensional generalization of the black ring.