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 \(\text{ Kerr-AdS}_4\) black holes (Holzegel and Smulevici in Anal PDE 7(5):1057–1090, 2014). We remark that this slow decay is suggestive of an instability at the nonlinear level.

我们考虑一类全局稳定的（无水平），五维超重力的渐近平面解。我们证明，在这样的孤子时空中，无质量线性标量波在时间上不能具有比对数倒数更快的均匀衰减率。这种缓慢的衰减可以归因于零大地测量学的稳定捕获。我们的证明使用了准模的构造，它是波动方程的时间周期近似解。该证明是基于先前的工作来证明\（\ text {Kerr-AdS} _4 \）黑洞的类似结果（Holzegel和Smulevici in Anal PDE 7（5）：1057-1090，2014）。我们注意到，这种缓慢的衰减暗示了非线性水平的不稳定性。