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Quasi-normal modes: a simple derivation of the level spacing of the frequencies

T Padmanabhan

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LETTER TO THE EDITOR

It is known that the imaginary parts of the frequencies of the quasi-normal modes of the Schwarzschild black hole are equally spaced, with the level spacing dependent only on the surface gravity. We generalize this result to a wider class of spacetimes and provide a simple derivation of the imaginary parts of the frequencies. The analysis shows that the result is closely linked to the thermal nature of horizons and arises from the exponential redshift of the wave modes close to the horizon.


PACS

04.70.-s Physics of black holes

04.20.-q Classical general relativity

MSC

83C57 Black holes

Subjects

Gravitation and cosmology

Dates

Issue 1 (7 January 2004)

Received 5 October 2003

Published 20 November 2003



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