Weak Gravitation in the 4+1 Formalism

The 4+1 formalism in general relativity (GR) prescribes field equations for the spacetime metric γμνx,τ which is local coordinates x and evolves according to an external “worldtime” τ. This extends GR Stueckelberg Horwitz Piron (SHP) framework, developed address various issues known as problem of time they appear electrodynamics. SHP theories exhibit a formal 5D symmetry on (x,τ) that strategically broken representations Lorentz group, resulting manifestly covariant canonical describing τ-evolution structures initial value problem. Einstein are found by constructing pseudo-manifold (combining 4D geometry τ-dynamics) performing natural foliation under symmetry. paper discusses weak gravitation formalism, demonstrating decomposition into first-order evolution unconstrained metric, propagation constraints associated with Bianchi identity.