Static Spherical Realization of a VGM Physical Response Law: Exterior Massive-Vector Sector, Metric Backreaction, and Observable Residuals

Abstract

This work develops a static, spherically symmetric realization of the VGM physical response framework, translating the general covariant response-law architecture into an explicit exterior field configuration. The analysis examines a massive-vector response sector, its induced metric backreaction, and the resulting departures from the corresponding general-relativistic background. Particular emphasis is placed on maintaining covariance, controlled asymptotic behavior, dimensional consistency, and a regular GR limit while identifying invariant residual structures that may ultimately be connected to observable quantities. The construction is presented as a conditional phenomenological realization rather than evidence for new physics: its purpose is to establish a mathematically explicit bridge between the abstract VGM response law and testable gravitational configurations, while retaining clear admissibility and falsifiability requirements.