Anna Sancassani: Global charges on asymptotically corresponding initial data sets

A correspondence exists between initial data sets with constant mean curvature (CMC) and different values of the cosmological constant, as
was first observed by Piotr Chruściel and Paul Tod. This correspondence relates hyperboloidal initial data in Minkowski spacetime to hyperbolic
initial data for Anti-de Sitter spacetime. I will introduce a new definition of asymptotically corresponding initial data sets and prove a theorem that describes how charges defined on pairs of such initial data are related. As an application, I will revisit the special case where the backgrounds are the hyperbolic space as the initial data set for Anti-de Sitter and the hyperboloid in Minkowski spacetime. In this
setting, this result allows us to prove a positive mass theorem for asymptotically (AdS) hyperbolic initial data sets under some additional
conditions, effectively transferring via the correspondence the positive mass theorem for asymptotically hyperboloidal initial data proved by
Anna Sakovich.