A moving particle's momentum field is required for gravitomagnetism, and for compatibility with QM (which has a corresponding momentum probability field). It is also required for classical theory, because if a moving particle's mass is distributed across space as its mass-field, it would be perverse if the associated momentum was not distributed similarly.

However, GR1916's SR foundation requires momentum fields not to exist, because a momentum field means that a moving particle drags light and distorts the light-metric away from flatness, and away from the flat Lorentz-Einstein-Minkowski (LEM) description.

Relativistic momentum exchange gives us relativistic light-dragging and Hertzian rather than Lorentzian relativity. And Hertzian and and Lorentzian relativity (dynamically curved spacetime and fixed spacetime) generate different equations.

So modern SR-based gravitational theory both MUST include momentum-fields (to support a range of principles) and MUST NOT include momentum fields (to avoid contradicting SR). How do modern theorists get around this apparently irreconcilable contradiction? What gives?