Sequences of Bubbles and Holes: New Phases of Kaluza-Klein Black Holes

TL;DR

This paper constructs and analyzes new exact solutions in higher-dimensional gravity, revealing complex sequences of bubbles and black holes that expand the known phase diagram of Kaluza-Klein black objects.

Contribution

It introduces a large class of exact five- and six-dimensional solutions describing sequences of bubbles and black holes, including novel topologies and mappings between solutions.

Findings

Solutions occupy new region in phase diagram with higher tension

Existence of black holes with ring and tuboid topologies

Maps relating solutions across dimensions and configurations

Abstract

We construct and analyze a large class of exact five- and six-dimensional regular and static solutions of the vacuum Einstein equations. These solutions describe sequences of Kaluza-Klein bubbles and black holes, placed alternately so that the black holes are held apart by the bubbles. Asymptotically the solutions are Minkowski-space times a circle, i.e. Kaluza-Klein space, so they are part of the (\mu,n) phase diagram introduced in hep-th/0309116. In particular, they occupy a hitherto unexplored region of the phase diagram, since their relative tension exceeds that of the uniform black string. The solutions contain bubbles and black holes of various topologies, including six-dimensional black holes with ring topology S^3 x S^1 and tuboid topology S^2 x S^1 x S^1. The bubbles support the S^1's of the horizons against gravitational collapse. We find two maps between solutions, one that relates five- and six-dimensional solutions, and another that relates solutions in the same dimension by interchanging bubbles and black holes. To illustrate the richness of the phase structure and the non-uniqueness in the (\mu,n) phase diagram, we consider in detail particular examples of the general class of solutions.