Gravitational Flux Area and the Self-Reinforcing Feedback Principle: A Framework Beyond Newtonian Gravity and General Relativity (v2)

This paper proposes two complementary principles to explain flat galactic rotation curves without dark matter. Principle I (Gravitational Flux Area): The effective area Aₑff (r) through which gravitational flux propagates is determined by the geometry of the matter distribution, not universally equal to 4πr². For a thin galactic disk of scale height H, flux propagates cylindrically with Aₑff = 4πHr, yielding g ∝ 1/r and flat circular velocity without invoking dark matter. Principle II (Self-Reinforcing Feedback): Gravitational flux concentrates toward mass overdensities, drawing more matter in, which deepens the overdensity and further concentrates the flux. This feedback — analogous to water carving a river channel — drives matter into disk configurations that produce cylindrical flux geometry, and self-consistently maintains those configurations. This version adds four major results not present in the previous version: Variational proof of disk stability — The flat disk is proven to be the unique stable attractor of the feedback dynamics for systems with non-zero angular momentum, via minimization of the flux concentration functional subject to fixed mass and angular momentum constraints. Derivation of the feedback threshold — The critical mass fraction fcrit=H/R (disk aspect ratio) is derived from first principles as a purely geometric, parameter-free condition separating feedback-active from feedback-inactive systems. Verified across all major system types: solar system, globular clusters, dwarf galaxies, spiral galaxies, elliptical galaxies. Numerical verification of H (r) ≈ const — The effective disk thickness H (r) is derived from the Miyamoto-Nagai potential and shown to vary by only 4. 2% across galactic radii, confirming that the constant-H approximation is a consequence of disk structure, not an assumption. Gravitational lensing predictions — Two new lensing mechanisms are proposed: (a) disk-plane lensing amplification by a factor r/H, with a viewing-angle anisotropy testable with Euclid; (b) Void-Anchored Lensing (VAL), in which cosmic voids act as boundary conditions that focus light paths toward filaments and clusters — naturally explaining the mass-centroid offset observed in merging clusters such as the Bullet Cluster without dark matter. The two core principles remain unchanged from v1: (I) gravitational flux propagates through an effective area determined by matter geometry, not universally 4πr²; (II) a self-reinforcing feedback between flux concentration and matter accumulation drives stable structures toward flat disks, filaments, and voids.