A Positive Mass Theorem Based on the Focusing and Retardation of Null Geodesics

TL;DR

This paper proves a new positive mass theorem in General Relativity using causal structure and null geodesic focusing, applicable in situations beyond previous theorems and potentially extendable to semi-classical gravity.

Contribution

It introduces a 4-dimensional proof based on causal structure and geodesic focusing, applicable beyond horizons and possibly extendable to semi-classical gravity.

Findings

Positive energy-density focuses null geodesics.

Negative total mass would retard null geodesics.

The theorem applies in situations not covered by previous positivity theorems.

Abstract

A positive mass theorem for General Relativity Theory is proved. The proof is 4-dimensional in nature, and relies completely on arguments pertaining to causal structure, the basic idea being that positive energy-density focuses null geodesics, and correspondingly retards them, whereas a negative total mass would advance them. Because it is not concerned with what lies behind horizons, this new theorem applies in some situations not covered by previous positivity theorems. Also, because geodesic focusing is a global condition, the proof might allow a generalisation to semi-classical gravity, even though quantum violations of local energy conditions can occur there.