Exceptional point and hysteresis in perturbations of Kerr black holes

Abstract

We employ the isomonodromic method to study linear scalar massive perturbations of Kerr black holes for generic scalar masses $M\mu$ and generic black hole spins $a/M$. We find that the longest-living quasinormal mode and the first overtone coincide for $(M\mu {)}_c\simeq 0.3704981$ and $(a/M{)}_c\simeq 0.9994660$. We also show that the longest-living mode and the first overtone change continuously into each other as we vary the parameters around the point of degeneracy, providing evidence for the existence of a geometric phase around an exceptional point. We interpret our findings through a thermodynamic analogy.

v3: 8 pages, 4 figures. Typos corrected, figures updated, improved discussion

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• pp-Waves and the Hidden Symmetries of Black Hole Quasinormal Modes
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• Exceptional Lines and Excitation of (Nearly) Double-Pole Quasinormal Modes: A Semi-Analytic Study in the Nariai Black Hole
• Ergodic Hysteresis of the Kerr black hole spectrum
• Parity violating spectral dynamics of black holes in dynamical Chern-Simons gravity