Mass in General Relativity

The goal of this work is to study notions of mass for asymptotically flat and asymptotically locally hyperbolic manifolds. In particular, we study the ADM-mass, and the Bartnik mass for asymptotically flat manifolds, and their corresponding analogues in asymptotically locally hyperbolic space. Our main motivations lie in the many questions associated to the non-negativity of mass for these types of manifolds, as well as the borderline cases when there is zero mass. In this work, we prove several results that help us better understand the implication of having no mass in both settings