Maximal analytic extensions of the Emparan-Reall black ring

TL;DR

This paper constructs and analyzes a maximal, globally hyperbolic analytic extension of the Emparan-Reall black ring, demonstrating geodesic completeness or finite-time approach to singularities, and establishing uniqueness among natural extensions.

Contribution

It provides the first explicit maximal analytic extension of the Emparan-Reall black ring, proving its maximality, uniqueness, and geodesic properties.

Findings

Extension is maximal and globally hyperbolic

Causal geodesics are either complete or reach singular boundary in finite time

Alternative extensions are also constructed

Abstract

We construct a Kruskal-Szekeres-type analytic extension of the Emparan-Reall black ring, and investigate its geometry. We prove that the extension is maximal, globally hyperbolic, and unique within a natural class of extensions. The key to those results is the proof that causal geodesics are either complete, or approach a singular boundary in finite affine time. Alternative maximal analytic extensions are also constructed.