The Hyperboloidal and Spacetime Positive Mass Theorem in All Dimensions

TL;DR

This paper extends the spacetime positive mass theorem to all dimensions for asymptotically flat and hyperboloidal initial data, building on recent Riemannian positive mass results.

Contribution

It provides a proof of the spacetime positive mass theorem in arbitrary dimensions using recent advances in Riemannian geometry.

Findings

Proves the spacetime positive mass theorem in all dimensions.

Applies to asymptotically flat and hyperboloidal initial data sets.

Builds on recent work by Brendle--Wang on Riemannian positive mass theorem.

Abstract

Using the recent work of Brendle--Wang on the Riemannian positive mass theorem, we prove the spacetime positive mass theorem for asymptotically flat and asymptotically hyperboloidal initial data sets in arbitrary dimensions.