Abstract:
The Formalism of Hypersurface Data, originally introduced by M. Mars (10.1007/s10714-013-1579-9, 10.1007/s00009-020-01608-1) is a framework for studying the geometry of hypersurfaces as independent manifolds, i.e., without requiring them to be embedded in any ambient space. This unconventional approach has turned out to be extremely useful in a variety of contexts, including initial value problems (such as the characteristic problem or the Killing initial data problem), the matching of spacetimes, the geometry of horizons, and perturbations of hypersurfaces. In this talk, I will introduce the fundamental concepts and key aspects of the hypersurface data formalism, and discuss how its application to the issue of spacetime matching has led to significant results, particularly in the case of matching across null boundaries.