Quantum Gravity Theory (QGT): The Unified Mechanical Field, Relativistic Foundations, and Perturbative Axisymmetric Stellar Models

This paper presents the Quantum Gravity Theory (QGT) proposal in the structure and terminology of the original QGT manuscript, together with the subsequent mathematical development and computational checks. It expands the relativistic foundations required for a covariant theory: differential geometry, Einstein equations as benchmark equations, geodesic motion, weak-field limits, relativistic stellar structure, gravitational radiation, black-hole exterior geometry, and stability criteria. The original proposal describes gravity through a complex field ψ, with attractive quartic and repulsive sextic self-interactions, and interprets compact objects as non-singular, ultra-dense configurations. The later calculation program introduces an effective metric formulation, a self-interacting complex scalar action, a two-field extension for rotating configurations, and a perturbative treatment organized by spherical-harmonic sectors. We present the action and field equations, the potential and its stationary points, the Newtonian and orbital relations used in the original proposal, the standard relativistic benchmark equations, and the compact-object and photon-orbit framework. We then document the computed spherical background, the bound l = 1 mode, the l = 0 monopole response, the axial frame-dragging response, the even-parity l = 2 response, the Fredholm frequency correction, and the O(ε^3) mode corrections in the l = 1 and l = 3 channels. Numerical values are reported together with their domains of validity and residual checks. The assembled configuration is a perturbative reconstruction through the stated orders, not a completed fully nonlinear axisymmetric solution. In particular, the tested photon samples did not establish a polar-versus-equatorial escape-fraction difference, and the stationary scalar ansatz has no persistent radial Noether or energy flux. Claims concerning a universal derivation of G, a unique compressibility threshold, black-hole singularity resolution, or astrophysical jets therefore remain hypotheses requiring independent derivations and observational tests.