NUVO Metric and Geodesic Derivations - Part 3 of the NUVO Theory Series

NUVO theory introduces a flat-space conformal framework for gravitation and motion in which spacetime is modulated by the scalar field λ(t, r, v), derived from a test particle’s normalized instantaneous energy state. This conformal factor adjusts the local metric based on instantaneous velocity and gravitational context, replacing the need for curvature with dynamic scaling. In this second paper of the NUVO series, we develop the geodesic structure implied by this conformal transformation, deriving the NUVO metric, its Christoffel symbols, and the resulting equations of motion. Underlying this structure is a refined concept of inertia, decomposed into two distinct forms: pinertia, the coupling of a particle to space; and sinertia, the reciprocal coupling of space to the particle. These couplings exist independently of energy terms and govern the mutual relationship between geometry and matter. A key conceptual advancement in this work is the reinterpretation of Special Relativity (SR) as a special case of NUVO, arising only when the theory is violated by substituting relative velocity for the required instantaneous velocity. In that limit, inertial frames emerge, and SR’s apparent effects—such as time dilation and length contraction— arise as observational illusions, not physical modulations. NUVO maintains that only when acceleration is present does true modulation of space occur, leading to measurable differences. This distinction becomes physically measurable in systems like GPS satellites, where relativistic clock offsets arise not merely from velocity, but from the asymmetric gravitational potential and acceleration. This work lays the mathematical and conceptual foundation for interpreting gravitational and relativistic behavior as smooth outcomes of field-modulated flat space, rather than curved spacetime. This paper builds directly on the scalar field derived in Series 1 and provides the geometric foundation for observational predictions in Series 3.