Highly-damped quasi-normal frequencies for piecewise Eckart potentials

Understand

Highly-damped quasi-normal frequencies are very often of the form omega_n = (offset) + i n (gap).

• We investigate the genericity of this phenomenon by considering a model potential that is piecewise Eckart (piecewise Poeschl-Teller), and developing an analytic "quantization condition" for the highly-damped quasi-normal frequencies.
• We find that this omega_n = (offset) + i n (gap) behaviour is generic but not universal, with the controlling feature being whether or not the ratio of the rates of exponential falloff in the two asymptotic directions is a rational number.
• These observations are of direct relevance to any physical situation where highly-damped quasi-normal modes (damped modes) are important --- in particular (but not limited to) to black hole physics, both theoretical and observational.