Initial Data for Black Holes and Black Strings in 5d

TL;DR

This paper investigates the topology change of apparent horizons in five-dimensional spacetimes with a compactified dimension, revealing a discontinuous phase transition between spherical and ring-like horizons.

Contribution

It introduces initial data for black objects in 5d with a compact dimension and identifies a novel phase transition in horizon topology.

Findings

Horizon topology changes from S^3 to S^2 x S^1

Discontinuous phase transition observed

Possible phase diagram proposed

Abstract

We explore time-symmetric hypersurfaces containing apparent horizons of black objects in a 5d spacetime with one coordinate compactified on a circle. We find a phase transition within the family of such hypersurfaces: the horizon has different topology for different parameters. The topology varies from $S^3$ to $S^2 \times S^1$. This phase transition is discontinuous -- the topology of the horizon changes abruptly. We explore the behavior around the critical point and present a possible phase diagram.