An Analytic Representation for the QuasiNormal Modes of Kerr Black Holes
Abstract
The gravitational quasinormal frequencies of both stationary and rotating black holes are calculated by constructing exact eigensolutions to the radiative boundaryvalue problem of Chandrasekhar and Detweiler. The method is that employed by Jaffe in his determination of the electronic spectra of the hydrogen molecule ion in 1934, and analytic representations of the quasinormal mode wavefunctions are presented here for the first time. Numerical solution of Jaffe's characteristic equation indicates that for each lpole there is an infinite number of damped Schwarzschild quasinormal modes. The real parts of the corresponding frequencies are bounded, but the imaginary parts are not. Figures are presented that illustrate the trajectories the five leastdamped of these frequencies trace in the complex frequency plane as the angular momentum of the black hole increases from zero to near the Kerr limit of maximum angular momentum per unit mass, a = M, where there is a coalescence of the more highly damped frequencies to the purely real value of the critical frequency for superradiant scattering.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 December 1985
 DOI:
 10.1098/rspa.1985.0119
 Bibcode:
 1985RSPSA.402..285L
 Keywords:

 Black Holes (Astronomy);
 Boundary Value Problems;
 Schwarzschild Metric;
 Recursive Functions;
 Vibration Damping;
 Vibration Mode;
 Astrophysics;
 BLACK HOLES (ASTRONOMY);
 BOUNDARY VALUE PROBLEMS;
 SCHWARZSCHILD METRIC;
 RECURSIVE FUNCTIONS;
 VIBRATION DAMPING;
 VIBRATION MODE