Structural Differentiation Gravity and Black Hole Structure: A Non-Singular Interpretation within Structural Differentiation Cosmology

This work introduces Structural Differentiation Gravity (SDG), a minimal theoretical framework extending Structural Differentiation Cosmology (SDC) toward compact-object physics. Instead of interpreting gravity purely through spacetime curvature singularities, SDG describes gravitational behavior through gradients of a structural density field C(x,t). In this framework black holes are interpreted as regions of structural compression or structural saturation rather than singularities. The paper introduces a minimal formulation of structural gravity, derives the effective metric, geodesic equations, photon sphere condition, and gravitational lensing relations, and presents illustrative simulations of black hole shadow morphology. Eight figures illustrate structural density profiles, potentials, differentiation dynamics, photon orbit structure, and comparisons between classical GR black holes and SDG structural knots. This work represents a first exploratory step toward a structural interpretation of strong gravity and compact objects. Author: Koji Okino (Independent Researcher) Keywords: structural gravity, black holes, gravitational lensing, structural differentiation cosmology