Nonlinearities in black hole ringdowns: Quadratic quasinormal modes and the memory effect.

Quasinormal modes (QNMs) are the damped sinusoidal oscillations found in the final ringdown stage of a binary black hole merger. Linear QNMs have been found in numerical relativity simulations and the gravitational wave data of several high-mass binary black hole merger events. However, recent work (e.g. Mitman et al. 2023) has shown that quadratic QNMs are also detectable in numerical relativity simulations and may be found in future high signal-to-noise ratio gravitational wave events.
These quadratic QNMs are intrinsically nonlinear. By including them in our models, we are moving beyond using just linear perturbation theory, allowing us to produce a more complete QNM model for the ringdown. Quadratic QNMs and other nonlinear effects are expected be important, and even dominate, close to the merger. Detecting them will allow us to test Einstein's general relativity in new and more powerful ways and may help in investigating the gravitational wave "memory effect".
This project will develop and apply techniques to investigate these nonlinearities in the ringdown, starting with approaches used in recent discoveries of quadratic QNMs, then exploring novel methods. For example, previous work focussed on the time-dependence (i.e. the complex frequency) of QNMs. However, there is also the possibility of mapping the spatial (i.e. angular) shape, which may offer a new way to identify and validate quadratic QNMs in the ringdown. In the second half of the project, it may be possible to test these quadratic models using the latest available gravitational wave data.