Some Conformal Positive Mass Theorems

Abstract: W. Simon proved a conformal positive mass theorem, which was used to prove uniqueness of black holes later. In this note, we will generalize Simon's conformal positive mass theorem in two directions. First we will consider spacetime version of conformal positive mass theorems on asymptotically flat initial data set. Next, we will prove a conformal positive mass theorem on asymptotically hyperbolic manifolds.