“Gravitomagnetism” is just one formalism for understanding General Relativity. In GR, the density and flow of energy and momentum (expressed as the energy-momentum-stress tensor) is what causes spacetime curvature and affects the motion of particles. Whether you are talking about massive or massless particles, their motion helps determine the gravity they cause.

If you want to see how the velocity of two massive particles affects their mutual gravitational accelerations, look at the Einstein-Infeld-Hoffmann equations. I have not seen analogous equations for massless particles, but they probably exist.

“Gravitomagnetism” is just one formalism for understanding General Relativity. In GR, the density and flow of energy and momentum (expressed as the energy-momentum-stress tensor) is what causes spacetime curvature and affects the motion of particles. Whether you are talking about massive or massless particles, their motion helps determine the gravity they cause.

If you want to see how the velocities and accelerations of two massive particles affects their mutual gravitational accelerations, look at the Einstein-Infeld-Hoffmann equations. I have not seen analogous equations for massless particles, but they probably exist.