Quasinormal-Mode Collider Spectroscopy

Black-hole (BH) quasinormal modes encode the properties of merger remnants and provide powerful tests of strong-field gravity. The BH spectroscopy has predominantly treated them as independent linear oscillations. Nonlinear ringdown can additionally reveal how these modes interact and which intermediate states mediate their interactions. Inspired by cosmological collider physics, we introduce quasinormal-mode collider spectroscopy (QCS), a framework for organizing and predicting nonlinear BH responses. We establish two structural results. First, at an isolated, nondegenerate intermediate pole, a cubic strain residue factorizes into an excitation amplitude and a quadratic conversion coefficient. This factorization imposes rank constraints across output channels and choices of second-order initial data, providing consistency tests of the intermediate-mode description. Second, the intermediate pole residue can be reconstructed from its horizon and infinity radiation. With the first-order field and third-order data held fixed, this reconstruction extends to the full cubic waveform difference generated by changing the second-order initial data. QCS thus connects lower-order radiation to higher-order observables and provides a framework for probing the interaction structure of nonlinear ringdown.