Excitation of quasinormal ringing of a Schwarzschild black hole
Abstract
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 C_{q} seems to describe the excitation, but is given by a formally divergent integral. The meaning of C_{q} 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 C_{q}. We then demonstrate that C_{q} does not in general describe the astrophysically interesting quantity, the nearhorizon stimulation of the ringing. We introduce two approaches to the correct description. The first uses a modified C_{q} based on an ad hoc modification of the Cauchy data. The second is based on a series representation of C_{q}; a truncation of this series automatically selects the astrophysically interesting part of C_{q}.
 Publication:

Physical Review D
 Pub Date:
 August 1988
 DOI:
 10.1103/PhysRevD.38.1040
 Bibcode:
 1988PhRvD..38.1040S
 Keywords:

 97.60.Lf;
 02.70.+d;
 04.30.+x;
 Black holes