Theoretical analysis demonstrates gravitational light bending via an effective optical action, indicating potential regular saturated cores in strong gravitational fields.
We propose an Evoltropic formulation in which the local rate of physical evolution is represented by a dimensionless Evolution Rate Field E(x) satisfying 0 < E ≤ 1. Rather than treating gravitational light bending exclusively as a consequence of spacetime curvature, we investigate an effective optical action in which light trajectories are stationary underSE[γ] = ZγdsE(x).The reciprocal nE = 1/E acts as an effective Evolution-optical index. In the weak-field regime, the identification E ≃ 1 + 2Φ/c2, with Φ = −GM/r, gives nE ≃ 1 + 2GM/(c2r)and yields the standard leading-order gravitational deflection α = 4GM/(bc2). We thenshow that an exact Evolution field can be constructed from the Schwarzschild optical metric in isotropic coordinates, reproducing the Schwarzschild null trajectories and photon sphere. This construction is distinguished from an independent derivation: the exact Schwarzschild-compatible E profile is presently a reconstruction, not a consequence of the provisional Evoltropic field equation. We further introduce the hypothesis of a nonzero minimum Evolution rate Emin > 0, which replaces the divergent optical index of the classical Schwarzschild interior by a bounded value nmax = 1/Emin. A provisional scalar–tensor action is developed to make E dynamical, and the requirements for a regular saturated core are analyzed. The paper therefore establishes a variational framework and several consistency tests while identifying the coupled strong-field boundary-value problem as the decisive unresolved test.
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Amar Naik (2026) studied this question.