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Abstract:
The phase-integral method has proved to be a powerful tool for studying the quasinormal modes of black holes. A generalization of the WKB methods of quantum mechanics, its treatment of the complex coordinate plane brings a number of important simplifications and potentially powerful computational aids to bear on the problem of computing eigenfrequencies with large imaginary parts. It holds great promise of further applications to related problems, such as the quasinormal modes of relativistic stars. However, in some respects the method is incomplete, particularly in its assessment of error bounds. The authors make available to researchers in the field of relativity a simple and self-contained introduction to the fundamental concepts of the phase-integral method, in which they also point out areas that seem to need further development. As an example of the use of the method, they derive the two-transition-point phase-integral formula for quasinormal modes of the Schwarzschild black hole, which is an accurate asymptotic approximation for the first modes. They provide the foundation for related papers in which they use the method to develop accurate asymptotic expressions for highly damped modes.
