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

TL;DR

This paper introduces concepts of area and matter flux in causal fermion systems and shows a relation between area change and matter flux that generalizes a classical GR equation.

Contribution

It extends classical general relativity concepts to causal fermion systems, establishing a new relation between area change and matter flux for critical points.

Findings

Area change under Killing flow is proportional to matter flux.

Generalizes Jacobson's equation from classical GR.

Applicable to critical points of the causal action.

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.