Highly damped quasinormal frequencies are very often of the form ${\omega }_n=(\mathrm{\text{offset}})+in(\mathrm{\text{gap}})$. We investigate the genericity of this phenomenon by considering a model potential that is piecewise Eckart (piecewise Pöschl-Teller), and developing an analytic “quantization condition” for the highly damped quasinormal frequencies. We find that this ${\omega }_n=(\mathrm{\text{offset}})+in(\mathrm{\text{gap}})$ behavior 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 quasinormal modes (damped modes) are important—in particular (but not limited to) to black hole physics, both theoretical and observational.

• Received 3 May 2010

DOI:https://doi.org/10.1103/PhysRevD.81.125023