On smoothness of Black Saturns

TL;DR

This paper proves the smoothness of the domain of outer communications in Black Saturn solutions, demonstrating smooth extension across horizons and analyzing causality conditions with numerical support.

Contribution

It establishes the smoothness of the metric across horizons and analyzes causality in Black Saturn spacetimes, providing new mathematical insights.

Findings

Smooth extension of metric across horizons

Stable causality when angular momentum vanishes

Numerical evidence for causality in general cases

Abstract

We prove smoothness of the domain of outer communications (d.o.c.) of the Black Saturn solutions of Elvang and Figueras. We show that the metric on the d.o.c. extends smoothly across two disjoint event horizons with topology R x S^3 and R x S^1 x S^2. We establish stable causality of the d.o.c. when the Komar angular momentum of the spherical component of the horizon vanishes, and present numerical evidence for stable causality in general.