Mass and angular-momentum inequalities for axi-symmetric initial data sets I. Positivity of mass

TL;DR

This paper extends the positive energy theorem for axisymmetric initial data sets with positive scalar curvature to a broader class of asymptotically flat, simply connected manifolds, ensuring the positivity of mass in these cases.

Contribution

It generalizes Brill's positive energy theorem to all asymptotically flat, simply connected manifolds with positive scalar curvature, broadening its applicability.

Findings

Positive mass theorem holds for all such initial data sets.

Extension to more general topologies beyond original assumptions.

Reinforces the link between scalar curvature and mass positivity.

Abstract

We extend the validity of Brill's axisymmetric positive energy theorem to all asymptotically flat initial data sets with positive scalar curvature on simply connected manifolds.