A Geometric Derivation of the Einstein Equations from the Causal Action Principle

The causal action principle for causal fermion systems is analyzed for a minimizing measure whose support is assumed to have the structure of a smooth manifold $\tilde{M}$. The concept of osculating vacua is introduced. It is shown that the Lagrangian induces on $\tilde{M}$ a Lorentzian metric. More