Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2003-03-25
J.Math.Phys. 45 (2004) 327
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
REVTeX4, 11pp with one EPS figure. N.B.: 'Alec' is my first, and 'Maassen van den Brink' my family name. v2: discussion and Re
Scientific paper
10.1063/1.1626805
The Regge-Wheeler equation for black-hole gravitational waves is analyzed for large negative imaginary frequencies, leading to a calculation of the cut strength for waves outgoing to infinity. In the--limited--region of overlap, the results agree well with numerical findings [Class. Quantum Grav._20_, L217 (2003)]. Requiring these waves to be outgoing into the horizon as well subsequently yields an analytic formula for the highly damped Schwarzschild quasinormal modes,_including_ the leading correction. Just as in the WKB quantization of, e.g., the harmonic oscillator, solutions in different regions of space have to be joined through a connection formula, valid near the boundary between them where WKB breaks down. For the oscillator, this boundary is given by the classical turning points; fascinatingly, the connection here involves an expansion around the black-hole singularity r=0.
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