Proof of Positive Energy Theorem by spacetime foliations

TL;DR

This paper introduces a new foliation gauge to prove the positive energy theorem in general relativity, using an approach based solely on differential geometry, building on prior foundational work.

Contribution

It presents an alternative, geometrically grounded proof of the positive energy theorem with a novel foliation gauge, simplifying previous methods.

Findings

Established positivity of total energy in general relativity.

Introduced a new foliation gauge for spacetime analysis.

Built on and generalized prior foundational results.

Abstract

Here we present an alternative approach, requiring only basic tools of differential geometry. This method was conceived by Kijowski and first presented during the IV Marcel Grossman Meeting on General Relativity in Rome (1986). It was later published in a generalized form by J. Jezierski, J. Kijowski in 1987 (Positivity of total energy in general relativity, Physical Review D {\bf 36} (1987), 1041-4). We summarize these results briefly and present a new foliation gauge.