The authors construct explicit closed quantization contours encircling the origin for radial Schrödinger problems and use a logarithmic coordinate change to equate closed-cycle and open-connection quantization while incorporating the Maslov phase via renormalization-group arguments.
Resonance and absorption spectra of the Schwarzschild black hole for massive scalar perturbations: a complex angular momentum analysis
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abstract
We reexamine some aspects of scattering by a Schwarzschild black hole in the framework of complex angular momentum techniques. More precisely, we consider, for massive scalar perturbations, the high-energy behavior of the resonance spectrum and of the absorption cross section by emphasizing analytically the role of the mass. This is achieved (i) by deriving asymptotic expansions for the Regge poles of the $S$-matrix and then for the associated weakly damped quasinormal frequencies and (ii) by taking into account the analytic structure of the greybody factors which allows us to extract by resummation the physical information encoded in the absorption cross section.
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Exact WKB method for radial Schr\"odinger equation
The authors construct explicit closed quantization contours encircling the origin for radial Schrödinger problems and use a logarithmic coordinate change to equate closed-cycle and open-connection quantization while incorporating the Maslov phase via renormalization-group arguments.