New method for exact results on quasinormal modes of black holes

We develop a new method for writing simple exact equations characterizing gravity solutions among which are black holes and in particular quasinormal modes. More precisely, we derive the full system of functional and thermodynamic Bethe ansatz nonlinear integral equations of quantum integrability. In particular, we prove that the quasinormal modes verify different equivalent exact quantization conditions and identify them with Bethe roots. We numerically solve the integral equation and compare the results with other methods. Eventually, we can definitely certify its simplicity, accuracy, and effectiveness. Furthermore, this method connects different unexpected fields and paves the way for innovative ways of investigations in gravity and gauge theories.