标题： 具有稳定光环的时空中的引力湍流的微扰和非线性分析 显示英文标题

标题： Perturbative and non-linear analyses of gravitational turbulence in spacetimes with stable light rings

摘要： 一些黑洞模仿者、黑洞弦以及其他高维时空表现出稳定的光环区域——在这些区域内光或高频引力波可以被捕获。 在这些区域内，线性扰动衰减缓慢，从而引发了非线性不稳定性机制的可能性。 在这项工作中，我们使用一个四维模型几何作为爱因斯坦方程的代理来研究三次非线性波动方程，该几何允许稳定的捕获。 通过采用微扰方法，我们证明了带有耗散项的球面上的非线性波动方程捕捉到了完整非线性问题的几个特征。 此框架使我们能够证实之前的猜想：对于任意小的初始扰动幅度，所有高阶能量范数都会增长。 此外，我们在较晚的时间分析了系统的模式谱，揭示了一个由直接能量级联主导的惯性范围。 这些发现进一步支持了这样一种观点：具有稳定光环的时空会发展出弱且高频的辐射“毛发”，这通常不会导致不稳定性。 显示英文摘要

摘要： Some black hole mimickers, as well as black strings and other higher-dimensional spacetimes, exhibit stable light rings-regions where light or high-frequency gravitational waves can be trapped. In these regions, linear perturbations decay slowly, raising the possibility of nonlinear instability mechanisms. In this work, we study the cubic nonlinear wave equation as a proxy for Einstein's equations, using a four-dimensional model geometry that allows stable trapping. By employing a perturbative approach, we show that the nonlinear wave equation on the sphere with dissipative terms captures several features of the full nonlinear problem. This framework allows us to confirm a previous conjecture: all higher-order energy norms grow for arbitrarily small initial fluctuation amplitudes. Additionally, we analyze the system's mode spectrum at late times, revealing an inertial range dominated by a direct energy cascade. These findings further support the notion that spacetimes with stable light rings develop weak, high-frequency radiation hair, which will not generically lead to instabilities.