Abstract for the talk on 05.11.2018 (17:00 h)
Arbeitsgemeinschaft ANGEWANDTE ANALYSISStephen Green (MPI for Gravitational Physics)
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.