The Informational Throughput Chain: From Energy Density to Einstein's Equations

This paper presents a compact informational framework connecting energy density to gravitational dynamics through a conserved informational throughput structure. Localized energy commits informational capacity, producing a load parameter that reduces the available throughput of spacetime. The remaining throughput determines signal velocity, gravitational acceleration, and potential gradients. From these relations Newtonian gravity and the Poisson equation arise as direct consequences. A relativistic generalization yields a throughput field equation sourced by the energy-momentum tensor. The resulting structure reproduces the weak-field scalar sector of Einstein’s equations and interprets spacetime curvature as redistribution of informational processing capacity. The fundamental informational area A₀ = ℓ_P² is derived from horizon consistency rather than assumed. Master Equation of the Framework κ = ρ_E V A₀ / ħc L(r) = 2κ/r χ² + L = 1 v = cχ g = −c² ∇χ/χ ∇²χ = −(4πG/c²)ρ □χ = −(4πG/c⁴)T These seven relations generate the full logical chain connecting energy density to the weak-field scalar sector of Einstein’s equations. Each step is derived explicitly in the sections that follow.