Physics – Mathematical Physics
Scientific paper
2010-05-25
JHEP 1103:073,2011
Physics
Mathematical Physics
V1: 29 pages; V2: Reformatted, 31 pages. Title changed to reflect major additions and revisions. Now describes exact QNFs for
Scientific paper
10.1007/JHEP03(2011)073
The study of exact quasi-normal modes [QNMs], and their associated quasi-normal frequencies [QNFs], has had a long and convoluted history - replete with many rediscoveries of previously known results. In this article we shall collect and survey a number of known analytic results, and develop several new analytic results - specifically we shall provide several new QNF results and estimates, in a form amenable for comparison with the extant literature. Apart from their intrinsic interest, these exact and approximate results serve as a backdrop and a consistency check on ongoing efforts to find general model-independent estimates for QNFs, and general model-independent bounds on transmission probabilities. Our calculations also provide yet another physics application of the Lambert W function. These ideas have relevance to fields as diverse as black hole physics, (where they are related to the damped oscillations of astrophysical black holes, to greybody factors for the Hawking radiation, and to more speculative state-counting models for the Bekenstein entropy), to quantum field theory (where they are related to Casimir energies in unbounded systems), through to condensed matter physics, (where one may literally be interested in an electron tunelling through a physical barrier).
Boonserm Petarpa
Visser Matt
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