Abstract Null Geometry, the Constraint Tensor and Applications

Explore a comprehensive lecture on abstract null geometry, the constraint tensor, and their applications in spacetime physics. Delve into the concept of metric hypersurface data in the null case and discover how a geometry on a manifold with a degenerate metric of signature (0,+,+) is constructed. Learn about the unique family of connections related by group transformations and understand the incorporation of extrinsic curvature to define the constraint tensor. Examine how this abstract null geometry effectively describes null hypersurfaces in spacetime from a detached perspective. Investigate two practical applications: one in the context of degenerate horizons and another concerning the characteristic initial value problem of Einstein field equations. Gain valuable insights from this 46-minute talk, presented by Marc Mars as part of the Workshop on "Non-regular Spacetime Geometry" at the Erwin Schrödinger International Institute for Mathematics and Physics.