Abstract

As a perturbed black hole relaxes into its Kerr state following a merger, it rings down by producing quasinormal modes (QNMs). These are oscillations at specific complex frequencies and with angular structures determined by first-order perturbation theory. Spatial information can be extracted from numerical simulations by fitting a feature of known time dependence; a program we call black hole cartography. We demonstrate that QNMs can be reconstructed using our method by recovering the predictions of first-order perturbation theory. Furthermore, we apply the technique to quadratic QNMs (appearing at second-order) and demonstrate that we can determine their angular structures. This is a step towards an improved understanding of non-linearities in the ringdown, which will be important for observations with future gravitational wave detectors.