Exceptional point and hysteresis in perturbations of Kerr black holes

We employ the isomonodromic method to study linear scalar massive perturbations of Kerr black holes for generic scalar masses M and generic black hole spins a/M. A degeneracy between the longest-living quasinormal mode and the first overtone is found for (M) c 0. 3704981 and (a/M) c 0. 9994660. We 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.