Gravitational Solitons and the Squashed Seven-Sphere

TL;DR

This paper explores higher-dimensional gravitational solitons, analyzing their stability, and introduces new solutions connecting known metrics with special holonomy, including stability results for black holes.

Contribution

It presents new higher-dimensional gravitational solitons, examines their stability properties, and connects different solutions with special holonomy in a unified framework.

Findings

Taub-NUT solutions are stable against small disturbances but unstable against large ones.

A continuous family of asymptotically-conical solitons connects kink metrics with Spin(7) holonomy.

Five-dimensional Myers-Perry black holes are linearly stable against certain perturbations.

Abstract

We discuss some aspects of higher-dimensional gravitational solitons and kinks, including in particular their stability. We illustrate our discussion with the examples of (non-BPS) higher-dimensional Taub-NUT solutions as the spatial metrics in (6+1) and (8+1) dimensions. We find them to be stable against small but non-infinitesimal disturbances, but unstable against large ones, which can lead to black-hole formation. In (8+1) dimensions we find a continuous non-BPS family of asymptotically-conical solitons connecting a previously-known kink metric with the supersymmetric A_8 solution which has Spin(7) holonomy. All the solitonic spacetimes we consider are topologcally, but not geometrically, trivial. In an appendix we use the techniques developed in the paper to establish the linear stability of five-dimensional Myers-Perry black holes with equal angular momenta against cohomogeneity-2 perturbations.