Gravitational turbulence in spacetimes with stable light rings

Some black hole mimickers, black strings, and other higher-dimensional spacetimes exhibit stable light rings—regions where light or high-frequency gravitational waves can become trapped. In these regions, linear perturbations decay slowly, raising the possibility of nonlinear instabilities. In this talk, I will discuss the cubic nonlinear wave equation as a proxy for Einstein's equations, using a four-dimensional model geometry that exhibits stable trapping. By employing a combination of numerical and perturbative approaches, we characterize the mode spectrum and its behaviour across short and long timescales. Our findings support the notion that spacetimes with stable light rings develop weak, high-frequency ``radiation hair'' that does not generically lead to instability.