Nonlinear Frontiers in General Relativity

General relativity, our modern theory of gravity, connects the matter content of the universe to spacetime geometry through the Einstein equation. It endows geometry with rich dynamics: solutions describe cosmology, black holes, neutron stars and gravitational waves, all of which came together in the binary merger events detected by LIGO and Virgo. The nonlinear nature of the Einstein equation gives rise to these dynamics, but at the same time makes finding solutions a challenge.

In this talk I will describe two nonlinear frontiers of general relativity research. At the "dynamical frontier" weakly dissipative systems give rise to new nonlinear dynamics, including instabilities and even turbulence in the spacetime geometry. A major finding is the emergence of new approximate conservation laws that control turbulent cascades. These systems are often relevant to conjectured holographic dualities, and may manifest astrophysically. At the "deep learning frontier" I will describe data challenges facing gravitational-wave astronomy, and approaches to try to solve them with deep neural networks.