A Positive Mass Theorem for Static Causal Fermion Systems

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.

57 pages, LaTeX, 3 figures, sign errors in (6.5) and (6.9) corrected, footnote on page 43 added

References in corpus (3)

• Banach Manifold Structure and Infinite-Dimensional Analysis for Causal Fermion Systems
• Fermionic Fock Spaces and Quantum States for Causal Fermion Systems
• Two-Dimensional Area and Matter Flux in the Theory of Causal Fermion Systems

Cited by in corpus (4)

• Causal Fermion Systems: Classical Gravity and Beyond
• Elliptic Methods for Solving the Linearized Field Equations of Causal Variational Principles
• A Positive Quasilocal Mass for Causal Variational Principles
• A Canonical Construction of the Extended Hilbert Space for Causal Fermion Systems