On the global structure of the Pomeransky-Senkov black holes

TL;DR

This paper constructs and analyzes extended Pomeransky-Senkov black hole solutions, revealing their global structure, horizon properties, and singularity topology, with numerical evidence supporting stable causality.

Contribution

It provides new analytic extensions of Pomeransky-Senkov metrics, clarifies the nature of singularities and horizons, and explores the global topology and causality properties.

Findings

Singularities lie beyond event horizons.

The topology of the singular set depends on parameters.

Numerical evidence suggests stable causality in the domain of outer communications.

Abstract

We construct analytic extensions of the Pomeransky-Senkov metrics with multiple Killing horizons and asymptotic regions. We show that, in our extensions, the singularities associated to an obstruction to differentiability of the metric lie beyond event horizons. We analyze the topology of the non-empty singular set, which turns out to be parameter-dependent. We present numerical evidence for stable causality of the domain of outer communications. The resulting global structure is somewhat reminiscent of that of Kerr space-time.