Gravitational Solitons and the Squashed Seven-Sphere

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.

Minor typos corrected

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Cited by in corpus (7)

• Global Structure of Five-dimensional BPS Fuzzballs
• Collapse and Nonlinear Instability of AdS with Angular Momenta
• Rotating 5D Black Holes: Interactions and deformations near extremality
• Solitons in Five Dimensional Minimal Supergravity: Local Charge, Exotic Ergoregions, and Violations of the BPS Bound
• Branes and fluxes in special holonomy manifolds and cascading field theories
• Nonlinear stability of the Taub-NUT soliton in 6+1 dimensions
• Partition functions on squashed seven-spheres and holography