Highly-damped quasi-normal frequencies for piecewise Eckart potentials
arXiv:1007.4039 · doi:10.1103/PhysRevD.81.125023
Abstract
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.
v1: 4 pages; letter-length summary of results reported in considerably more detail in arXiv:1004.2539; v2: minor typos fixed in equation (34); matches published version