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Generalized Bohr-Sommerfeld formula for Schwarzschild black hole normal modes

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Schutz,  Bernard F.
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;
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Citation

Andersson, N., Araujo, M. E., & Schutz, B. F. (1993). Generalized Bohr-Sommerfeld formula for Schwarzschild black hole normal modes. Classical and Quantum Gravity, 10(4), 757-765. doi:10.1088/0264-9381/10/4/010.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-73E2-5
Abstract
A generalized Bohr-Sommerfeld-type formula determining the quasinormal-mode frequencies of Schwarzschild black holes is derived using the phase-integral method with three transition points. The formula is valid provided that these points are well separated from each other, and is remarkably accurate for the high-overtone modes. It makes a great improvement over the conventional Bohr-Sommerfeld formula, derived from two transition points.