A Positive Mass Theorem for Static Causal Fermion Systems

TL;DR

This paper introduces a new definition of total mass for asymptotically flat static causal fermion systems, proving a positive mass theorem that applies even to singular or quantum spacetimes, thus linking gravity effects to the causal action principle.

Contribution

It defines a mass concept for static causal fermion systems without regularity assumptions and proves a positive mass theorem, extending gravitational insights to quantum and singular spacetimes.

Findings

Positive mass theorem proven for static causal fermion systems.

Mass definition applicable to singular or quantum spacetimes.

Method links causal action principle to nonlinear gravity effects.

Abstract

Asymptotically flat static causal fermion systems are introduced. Their total mass is defined as a limit of surface layer integrals which compare the measures describing the asymptotically flat spacetime and a vacuum spacetime near spatial infinity. Our definition does not involve any regularity assumptions; it even applies to singular or generalized "quantum" spacetimes. A positive mass theorem is proven. Our methods and results explain why and how the causal action principle incorporates the nonlinear effects of gravity for static systems.