Quasinormal modes of Schwarzschild black holes on the real axis

We study the scattering of gravitational waves by a Schwarzschild black hole and its perturbed siblings to investigate influences proposed spectral instability quasinormal modes on ringdown signal. Our results indicate that information dominant signals, which are ascribed fundamental (i.e., least damping) mode unperturbed holes, is imprinted in phase shift defined from transmission amplitude ($1/{A}_{\mathrm{in}}$ our notation). This approximately parallels fact resonance quantum systems $S$ matrix. The around oscillation frequency modified only perturbatively even if quasinormal-mode spectrum destabilized perturbative bump at distant location, signifying stability At same time, low frequencies modulated substantially reflecting late-time excitation echo signals associated with after destabilization.