Black Hole Quasinormal Mode Resonances

Black hole quasinormal mode frequencies can be very close to each other ("avoided crossings") or even completely degenerate ("exceptional points") when the system is characterized by more than one parameter. We investigate this resonant behavior and demonstrate that near exceptional points, the two modes are just different covers of the same complex function on a Riemann surface. We also study the characteristic time domain signal due to the resonance in the frequency domain, illustrating the analogy between black hole signals at resonance and harmonic oscillators driven by a resonant external force. We consider a specific toy model displaying a resonance between the fundamental mode and the first overtone, and we find that taking into account the linear growth in time due to the resonance is necessary to accurately recover the quasinormal mode frequencies.