New Black Holes in Five Dimensions

TL;DR

This paper introduces new five-dimensional black hole solutions that generalize known metrics, including rotating black holes, black rings, and static distorted horizons, expanding the landscape of higher-dimensional gravitational solutions.

Contribution

The authors construct a new class of stationary Ricci-flat metrics in five dimensions, extending the Myers-Perry solutions and including novel static and lens space horizon geometries.

Findings

New five-dimensional black hole metrics with additional parameters.

Limiting cases recover known black holes and rings.

Discovery of static solutions with lens space horizons.

Abstract

We construct new stationary Ricci-flat metrics of cohomogeneity 2 in five dimensions, which generalise the Myers-Perry rotating black hole metrics by adding a further non-trivial parameter. We obtain them via a construction that is analogous to the construction by Plebanski and Demianski in four dimensions of the most general type D metrics. Limiting cases of the new metrics contain not only the general Myers-Perry black hole with independent angular momenta, but also the single rotation black ring of Emparan and Reall. In another limit, we obtain new static metrics that describe black holes whose horizons are distorted lens spaces L(n;m)= S^3/\Gamma(n;m), where m\ge n+2\ge 3. They are asymptotic to Minkowski spacetime factored by \Gamma(m;n). In the general stationary case, by contrast, the new metrics describe spacetimes with an horizon and with a periodicity condition on the time coordinate; these examples can be thought of as five-dimensional analogues of the four-dimensional Taub-NUT metrics.