Instability of supersymmetric microstate geometries

TL;DR

This paper analyzes the classical stability of supersymmetric microstate geometries, revealing that stable trapping of null geodesics suggests potential nonlinear instabilities due to slow decay of linear perturbations.

Contribution

It provides a detailed study of linear perturbations and quasinormal modes, indicating slow decay rates that imply possible nonlinear instability in these geometries.

Findings

Null geodesics are stably trapped near the ergosurface.

Linear perturbations decay slower than any inverse power of time.

Potential nonlinear instability due to slow decay of perturbations.

Abstract

We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an "evanescent ergosurface": a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.