black_hole_physics

We present a formal proof that the spectral ratio $\rho = \gamma_1/\gamma_0$ of quasi-normal mode (QNM) damping rates remains universal in the extremal Kerr limit ($\chi \to 1$). While individual mode lifetimes $\tau_n = 1/\gamma_n$ diverge as the fundamental damping rate $\gamma_0 \to 0$, the ratio $\rho \approx 3$ is preserved.