Lydia Bieri - University of Michigan
Title: New Structures in Gravitational Waves
Abstract: Mathematical General Relativity (GR) explores the structures and resulting dynamics of gravitational systems. These are described by the Einstein equations, which can be written as a system of nonlinear, hyperbolic partial differential equations. Recent years have seen fruitful interactions between physical questions and geometric analysis, sparking new breakthroughs, in particular related to gravitational radiation. Gravitational waves transport information from faraway regions of the Universe. They were observed for the first time by Advanced LIGO in 2015. So far, most studies in GR have been devoted to sources like binary black hole mergers or generally to sources that are stationary outside of a compact set. However, when extended neutrino halos are present, the situation changes. Mathematically, we describe these systems by asymptotically-flat manifolds solving the Einstein equations. In this talk, I will present new results on gravitational radiation for sources that are not stationary outside of a compact set, but whose gravitational fields fall off more slowly towards infinity. A panorama of new gravitational effects opens up when delving deeper into these more general spacetimes. In particular, whereas the former sources produce memory effects (permanent change of the spacetime) that are finite and of purely electric parity, the latter in addition generate memory of magnetic type, and both types grow. These new effects emerge naturally from the Einstein equations.
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