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arXiv · 1007.4039

Highly-damped quasi-normal frequencies for piecewise Eckart potentials

Jozef Skakala·Matt Visser
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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.

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Jozef Skakala, Matt Visser. 2010-09-01. Highly-damped quasi-normal frequencies for piecewise Eckart potentials. https://doi.org/10.1103/physrevd.81.125023

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