Integrability and Hidden Symmetries in Black Hole Dynamics

The last decade has produced a number of remarkable discoveries, such as the first direct observation of gravitational waves by the LIGO/Virgo collaboration and the first black hole image taken by the Event Horizon Telescope. These discoveries mark the beginning of a new precision era in black hole physics, which is expected to develop further by future experiments such as LISA, the Einstein Telescope and Cosmic Explorer.

In the era of precision black hole measurements, there is a need for precision theoretical methods and accurate predictions. In this talk I will describe an integrable sector of the gravitational scattering problem - analogous to the hydrogen atom in quantum mechanics - in which exact predictions can be made, and the implications for astrophysical black holes and binary mergers.