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#### High-overtone normal modes of Schwarzschild black holes

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##### Citation

Guinn, J. W., Will, C. M., Kojima, Y., & Schutz, B. F. (1990). High-overtone normal
modes of Schwarzschild black holes.* Classical and quantum gravity,* *7*(2),
L47-L53. doi:10.1088/0264-9381/7/2/006.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-74BA-A

##### Abstract

The frequencies of normal-mode oscillations of Schwarzschild black holes are studied using a higher-order WKB approach. The method is mathematically equivalent to locating the poles in the transmission amplitude for one-dimensional quantum mechanical tunnelling through a potential barrier. The transmission amplitude is expressed in terms of contour integrals of WKB functions around turning points of the effective barrier in the Regge-Wheeler equation. In the limit of large overtone number n, the dimensionless frequency sigma identical to omega M (M=black-hole mass) for l=2 gravitational modes is given by sigma =-i(2n+1)/8+1/2A(1+i)(2n+1)-12/+. . ., where A approximately=1.0. The compare their results with numerical computations of Leaver and find striking and unexplained differences.