Accurate Black Hole Quasinormal Modes, Regge Poles, and Greybody Factors from Light Ring Ladder Symmetry

Abstract

The characteristic oscillations of a black hole can be understood in terms of null rays trapped near its unstable light ring, with this correspondence becoming exact in the high-frequency limit. In this regime, we uncover a hidden ladder symmetry in the perturbation equations, which maps the calculation of quasinormal modes, Regge poles, and greybody factors for a spherically symmetric black hole onto the quantum-mechanical problem of an anharmonic oscillator. This provides a systematic, efficient framework for computing the black hole response, with improved convergence properties compared with existing approximation schemes. As an explicit application, we analytically compute all three quantities for a Schwarzschild black hole through eighteenth order in inverse angular momentum, obtaining highly accurate results. We explore different resummation schemes and find that they can further improve the accuracy of the Regge poles and, particularly, the greybody factors. Our framework can be readily extended to rotating black holes and to modified theories of gravity.