The QuasiNormal Modes of the Schwarzschild Black Hole
Abstract
The quasinormal modes of a black hole represent solutions of the relevant perturbation equations which satisfy the boundary conditions appropriate for purely outgoing (gravitational) waves at infinity and purely ingoing waves at the horizon. For the Schwarzschild black hole the problem reduces to one of finding such solutions for a onedimensional wave equation (Zerilli's equation) for a potential which is positive everywhere and is of shortrange. The notion of quasinormal modes of such onedimensional potential barriers is examined with two illustrative examples; and numerical solutions for Zerilli's potential are obtained by integrating the associated Riccati equation.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 August 1975
 DOI:
 10.1098/rspa.1975.0112
 Bibcode:
 1975RSPSA.344..441C
 Keywords:

 Black Holes (Astronomy);
 Quantum Mechanics;
 Schwarzschild Metric;
 Complex Variables;
 Gravitational Waves;
 Numerical Integration;
 Perturbation Theory;
 Riccati Equation;
 Wave Equations;
 Astrophysics;
 BLACK HOLES (ASTRONOMY);
 QUANTUM MECHANICS;
 SCHWARZSCHILD METRIC;
 COMPLEX VARIABLES;
 GRAVITATIONAL WAVES;
 NUMERICAL INTEGRATION;
 PERTURBATION THEORY;
 RICCATI EQUATION;
 WAVE EQUATIONS