Gravitomagnetic forces and quadrupole gravitational radiation from special relativity

Abstract

The mere principle of relativity and Lorentz transformations for the mass current predict, in close analogy to electromagnetism, the existence of gravitomagnetic fields. With the reasonable assumption of the non existence of a gravitomagnetic mass, a parameter-free set of equations for "effective" vector gravitoelectromagnetism results. As a consequence gravity propagates at the speed of light in a flat Minkowski space and quadrupole gravitational radiation, consistent with energy balance, is predicted with the same value of GR. Heuristic considerations relate gravitational radiation to the strong field parameter $\frac {GM}{c^2 r}$, suggesting the complete evaporation of a black hole at the Planck scale.