Excitation of quasinormal ringing of a Schwarzschild black hole

Details Excitation of quasinormal ringing of a Schwarzschild black hole Excitation of quasinormal ringing of a Schwarzschild black hole

Aug 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988phrvd..38.1040s&link_type=abstract

Physical Review D (Particles and Fields), Volume 38, Issue 4, 15 August 1988, pp.1040-1052

Statistics

Computation

32

Black Holes

Scientific paper

Processes near the event horizon of a black hole excite a ringing of fields (electromagnetic, gravitational perturbation, etc.) at certain complex frequencies, called quasinormal frequencies, characteristic of the hole. Evidence for such oscillations consists almost entirely of their appearance in detailed numerical solutions of specific problems. Despite the importance of quasinormal ringing in the generation of gravitational radiation, little work has been done on clarifying the way in which the ringing is excited, or in estimating the strength of the excitation, without a detailed computer solution. We formulate here the theory of the excitation of ringing of Schwarzschild holes from Cauchy data, in which a coefficient Cq seems to describe the excitation, but is given by a formally divergent integral. The meaning of Cq is shown actually to be an analytic continuation of the integral in the complex frequency plane, and this idea is used as the basis of computational techniques for finding Cq. We then demonstrate that Cq does not in general describe the astrophysically interesting quantity, the near-horizon stimulation of the ringing. We introduce two approaches to the correct description. The first uses a modified Cq based on an ad hoc modification of the Cauchy data. The second is based on a series representation of Cq; a truncation of this series automatically selects the astrophysically interesting part of Cq.

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