Statistics – Computation
Scientific paper
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.
Price Richard H.
Sun Yonghe
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