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Explore the spectral properties of rotating analog black holes through a mathematical physics lecture that examines quasinormal modes and pseudospectra using the hyperboloidal approach. Investigate how rotation affects spectral stability in the draining bathtub model, discovering that increased rotation causes prograde overtones to migrate toward the more stable fundamental mode region of the pseudospectrum. Learn how this migration suggests enhanced robustness for prograde overtones, with direct perturbative analysis confirming that angular momentum can mitigate spectral instabilities in dissipative systems. Gain insights into the mathematical framework connecting analog black hole physics with spectral analysis techniques, understanding the relationship between rotation parameters and gravitational potential perturbations in these theoretical models.
