Pseudo-Riemannian Geometry and invariants in General Relativity

Generalized parallel spinors and reductions of Einstein's equations

30 May 2022, 16:50

45m

AR V-101 (University of Stavanger)

Speaker

Bernardo Araneda (Max Planck Institute for Gravitational Physics)

Description

We introduce a conformally invariant connection that charaterizes integrable complex structures (and their Lorentzian analogues) in terms of parallel spinors, and we show how this can be used to: reduce the conformal Einstein equations for algebraically special spaces to a single scalar equation, reconstruct the conformal structure, and understand the geometry underlying the perturbation theory of black holes and the relation to the twistor programme of Roger Penrose.