Gravitational Radiation and Quadrupole Gravitational Waves in the Time-Field Theory (TFT)

Starting from the axiomatic framework of the Time-Field Theory (TFT) and the Lorentz-covariant d’Alembert equation, we present a full first-principles derivation of gravitational radiation. By means of the causal retarded potential and standard multipole expansion, we prove that monopole radiation is forbidden by mass conservation and dipole radiation is forbidden by center-of-mass conservation. The leading-order contribution is quadrupole gravitational radiation, which propagates in flat Euclidean spacetime exactly at the speed of light c. We derive the explicit expressions for the far-field perturbation, angular distribution, and total radiated power. TFT gravitational waves are not isotropic scalar breathing modes; instead, they are longitudinal scalar dynamical perturbations governed by the gradient nature of the time field, which is self-consistent and observationally compatible.