Simple Gravity III: Internal Phase Dynamics and an Additional Radiative Channel

We present Simple Gravity III, an extension of a nonlinear scalar gravitational framework through the introduction of an internal dynamical phase sector. The theory preserves the previously established static field, strong-field regime, and principal radiative sector of Simple Gravity I–II, while adding a new scalar degree of freedom that is excited only by time-dependent source dynamics. The internal phase field generates an additional radiative channel that contributes a higher-order dissipative correction to compact binary inspirals. We derive the far-zone solution, energy flux, total emitted power, and the resulting correction to the frequency-domain gravitational-wave phase. The theory predicts a fixed, parameter-free phase correction of the form Δψ(f) = −(5/32)(πMf)^{1/3}, corresponding to a distinct non-GR signature. The magnitude of this effect lies within the sensitivity range of current gravitational-wave detectors, making the theory directly testable with existing observational data. This work provides a consistent dynamical extension of the Simple Gravity framework and suggests the existence of an internal phase structure in the gravitational field. This work extends Simple Gravity I–II by introducing an internal dynamical phase sector while preserving previously established results.