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Explore the mathematical properties and physical applications of Green functions in Schwarzschild and Kerr black hole spacetimes in this comprehensive lecture by Marc Casals from the University of Leipzig. Delve into the global singularity structure, Fourier modes, and wave propagation properties of classical and quantum Green functions. Discover how these functions are applied to crucial aspects of black hole physics, including the late-time stage (ringdown) of gravitational waveforms, self-force problem for modeling black hole inspirals, black hole stability properties, and quantum effects. This 1 hour and 38 minute talk, presented at the Dublin Institute for Advanced Studies, offers valuable insights into the complex world of field perturbations in black hole spacetimes and their implications for our understanding of these cosmic phenomena.
