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.
Highlights
Type IIB supergravity admits supersymmetric “microstate geometry” solutions [1,2,3,4,5,6,7,8,9,10]
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
By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time
Summary
Type IIB supergravity admits supersymmetric “microstate geometry” solutions [1,2,3,4,5,6,7,8,9,10] These are asymptotically flat, geodesically complete, stationary solutions without horizons. Near infinity, they approach the product of 5 dimensional flat spacetime with 5 compact dimensions. In 5d, the stationary Killing vector field V is timelike everywhere except on a certain timelike hypersurface, where is it is null. This surface has infinite redshift relative to infinity, and has been called an “evanescent ergosurface” [11]
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