Advances in Theoretical and Mathematical Physics

Volume 25 (2021)

Number 7

A positive mass theorem for static causal fermion systems

Pages: 1735 – 1818



Felix Finster (Fakultät für Mathematik, Universität Regensburg, Germany)

Andreas Platzer (Fakultät für Mathematik, Universität Regensburg, Germany)


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.

The authors are grateful for support by the German Science Foundation (DFG) within the research training group GRK 1692 “Curvature, Cycles, and Cohomology.”

Published 11 July 2022