Seeking for toroidal event horizons from initially stationary BH configurations

TL;DR

This paper investigates the formation of toroidal event horizons from initially stationary black hole configurations with ring singularities, exploring the conditions under which naked singularities might occur.

Contribution

It extends standard black hole initial data to include ring singularities and analyzes the potential for toroidal horizons and naked singularities in such setups.

Findings

Evidence suggests large ring radii may lead to zero-width horizons.

Configurations with large rings might indicate naked singularities.

No apparent horizon forms when the ring's radius exceeds about twice its mass.

Abstract

We construct and evolve non-rotating vacuum initial data with a ring singularity, based on a simple extension of the standard Brill-Lindquist multiple black-hole initial data, and search for event horizons with spatial slices that are toroidal when the ring radius is sufficiently large. While evolutions of the ring singularity are not numerically feasible for large radii, we find some evidence, based on configurations of multiple BHs arranged in a ring, that this configuration leads to singular limit where the horizon width has zero size, possibly indicating the presence of a naked singularity, when the radius of the ring is sufficiently large. This is in agreement with previous studies that have found that there is no apparent horizon surrounding the ring singularity when the ring's radius is larger than about twice its mass.