Some Conformal Positive Mass Theorems

TL;DR

This paper generalizes Simon's conformal positive mass theorem to spacetime settings and asymptotically hyperbolic manifolds, expanding its applicability in geometric analysis and mathematical physics.

Contribution

It extends the conformal positive mass theorem to new contexts: spacetime initial data sets and asymptotically hyperbolic manifolds.

Findings

Proved a conformal positive mass theorem for spacetime initial data sets.

Established a conformal positive mass theorem for asymptotically hyperbolic manifolds.

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.