Light rings and strong-field dynamics in binary black hole simulations

Even near the peak of gravitational-wave emission, where gravity is strongest, radiation from binary black holes is remarkably well described by perturbation theory about the final black hole state. We investigate the idea that the nascent effective potential of the remnant screens the escape of radiation from the nonlinear strong-field dynamics. Since quasinormal modes are known to correspond to the eikonal limit of perturbations orbiting the light ring, and the light ring is at the peak of the effective potential, the proposed picture could explain why quasinormal modes dominate the radiation close to the peak of the waveform. As a first step towards testing this idea, we are developing a method of identifying light rings in dynamical binary black hole spacetimes from numerical relativity simulations. Our approach uses a measure of the divergence of bundles of light rays. It connects the concepts of optical scalars, geodesic deviation, and Lyapunov exponents. Applying this method to binary black hole simulations, we aim to define a dynamical light ring and clarify why the ringdown is so accurately captured by linear theory.