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arXiv · 2606.23804

Black Hole Ringdown Nonlinearities in the Large-D Limit

Roberto Emparan·Amanda Green-Salinas·David Pereñiguez·Jaime Redondo-Yuste
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Abstract

We initiate the study of nonlinear effects in the ringdown phase of black hole mergers using the effective theory of black hole dynamics in the large-D limit. This framework offers several advantages: the quasinormal mode spectrum, including nonlinear corrections, is analytically tractable; numerical simulations of collisions are computationally inexpensive; and the extraction and analysis of the ringdown signal are clean and controlled. As a proof of concept, we derive analytic expressions for the third-order response of a static black hole driven by a single quasinormal mode, and apply them to study the ringdown following head-on collisions of non-spinning black holes across a range of velocities and mass ratios. We find that including nonlinear effects, up to quadratic and cubic order, improves the accuracy of quasinormal-mode modelling of black hole relaxation by several orders of magnitude. The results also show a clear growth in the strength of nonlinear effects as the collision velocity increases.

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Roberto Emparan, Amanda Green-Salinas, David Pereñiguez, Jaime Redondo-Yuste. 2026-06-22. Black Hole Ringdown Nonlinearities in the Large-D Limit. https://arxiv.org/abs/2606.23804

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