Cauchy hypersurfaces, cosmological time and crowns in GH-regular domains in Anti-de Sitter space

Anti-de Sitter space is a spacetime of constant negative curvature, playing a similar role for spacetimes as hyperbolic space does for Riemannian manifolds. Cauchy hypersurfaces in a spacetime are a way to describe space at an instant of time, motivated by physics. By taking levelsets of the cosmological time function, Barbot constructed Cauchy hypersurfaces in GH-regular domains in Anti-de Sitter space. In this short introductory talk I will speak about how we can construct new Cauchy hypersurfaces using the cosmological time function and crowns.