Two-Dimensional Area and Matter Flux in the Theory of Causal Fermion Systems

Abstract

The notions of two-dimensional area, Killing fields and matter flux are introduced in the setting of causal fermion systems. It is shown that for critical points of the causal action, the area change of two-dimensional surfaces under a Killing flow in null directions is proportional to the matter flux through these surfaces. This relation generalizes an equation in classical general relativity due to Ted Jacobson to the setting of causal fermion systems.

21 pages, LaTeX, 4 figures, small improvements (published version)

References in corpus (2)

• Causal Fermion Systems: An Elementary Introduction to Physical Ideas and Mathematical Concepts
• A Gauge Fixing Procedure for Causal Fermion Systems

Cited by in corpus (8)

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• Causal Fermion Systems: Classical Gravity and Beyond
• From Quantum Relative Entropy to the Semiclassical Einstein Equations
• A Positive Mass Theorem for Static Causal Fermion Systems
• Hyperbolic space in the Newtonian limit: the cosmological constant
• Notions of Fermionic Entropies of a Causal Fermion System
• A Positive Quasilocal Mass for Causal Variational Principles
• A Canonical Construction of the Extended Hilbert Space for Causal Fermion Systems