Séminaire Amplitudes et Gravitation sur l'Yvette (IHES/IPhT)
We consider linear perturbations around the Schwarzschild black hole in four dimensions. We describe two methods that provide the quantization condition for the quasinormal mode frequencies of the perturbation field. The first method is based on techniques from supersymmetric gauge theory and conformal field theory that allow to explicitly write the connection coefficients for the differential equation encoding the spectral problem. The second method is based on a small-frequency expansion of the solutions of the differential equation, and permits to obtain the corresponding expansion for the elements of the scattering matrix, which have poles in the quasinormal mode frequencies. The relations between the two approaches will be discussed, together with the respective advantages.
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Julio Parra-Martinez & Alessandro Podo
