Slow decay of waves in gravitational solitons

TL;DR

This paper demonstrates that in five-dimensional supergravity soliton spacetimes, massless scalar waves decay extremely slowly, at best logarithmically, due to stable null geodesic trapping, hinting at potential nonlinear instabilities.

Contribution

It proves that scalar waves in these soliton spacetimes cannot decay faster than logarithmically, extending previous results from black hole spacetimes to horizonless solitons.

Findings

Scalar waves decay at most logarithmically over time.

Stable trapping of null geodesics causes slow decay.

Potential nonlinear instability suggested by slow decay.

Abstract

We consider a family of globally stationary (horizonless), asymptotically flat solutions of five-dimensional supergravity. We prove that massless linear scalar waves in such soliton spacetimes cannot have a uniform decay rate faster than inverse logarithmically in time. This slow decay can be attributed to the stable trapping of null geodesics. Our proof uses the construction of quasimodes which are time periodic approximate solutions to the wave equation. The proof is based on previous work to prove an analogous result in Kerr-AdS black holes \cite{holzegel:2013kna}. We remark that this slow decay is suggestive of an instability at the nonlinear level.