Informational Geodesics as the Origin of Spacetime Curvature: A Variational Principle for Emergent Metric Geometry in Viscous Time

We develop a variational principle in which spacetime curvature emerges from the preservation of informational identity along dynamical trajectories. The approach is motivated by the Viscous Time Theory (VTT) framework, where finite informational latency replaces an assumed geometric background. Instead of postulating a metric structure a priori, informational geodesics are defined as the paths that minimize a latency functional representing the local cost of identity reorganization in viscous time. The second-order structure of this action induces a symmetric bilinear form that behaves as an emergent metric tensor. Classical geodesic motion and the Einstein field equation are recovered in the limit of uniform latency density, showing that General Relativity arises as a special case of the more general informational action. The framework predicts curvature-like effects in regimes with negligible mass–energy but strong identity constraints, including coherent condensed-matter phases and entangled quantum systems. These predictions outline a testable research program connecting differential geometry with informational dynamics.