The quasi-normal modes of the Schwarzschild black hole

Details The quasi-normal modes of the Schwarzschild black hole The quasi-normal modes of the Schwarzschild black hole

Aug 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975rspsa.344..441c&link_type=abstract

Royal Society (London), Proceedings, Series A, vol. 344, no. 1639, Aug. 12, 1975, p. 441-452. Research supported by the Universi

Mathematics

Complex Variables

211

Black Holes (Astronomy), Quantum Mechanics, Schwarzschild Metric, Complex Variables, Gravitational Waves, Numerical Integration, Perturbation Theory, Riccati Equation, Wave Equations

Scientific paper

The quasi-normal 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 one-dimensional wave equation (Zerilli's equation) for a potential which is positive everywhere and is of short-range. The notion of quasi-normal modes of such one-dimensional potential barriers is examined with two illustrative examples; and numerical solutions for Zerilli's potential are obtained by integrating the associated Riccati equation.

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