A poor man's positive energy theorem

TL;DR

This paper demonstrates that the positive energy theorem for certain stationary, asymptotically flat spacetimes can be derived straightforwardly from the Lorentzian splitting theorem, simplifying previous proofs.

Contribution

It provides a new, simpler proof of the positive energy theorem using the Lorentzian splitting theorem, avoiding more complex methods.

Findings

Positivity of energy follows from the Lorentzian splitting theorem.

The proof applies to stationary, asymptotically flat, non-singular domains.

Simplifies understanding of the positive energy theorem in general relativity.

Abstract

We show that positivity of energy for stationary, asymptotically flat, non-singular domains of outer communications is a simple corollary of the Lorentzian splitting theorem.