As in the case of the Liénard–Wiechert potentials for electromagnetic effects and waves, the static potentials from a moving gravitational mass (i.e., its simple gravitational field, also known as gravitostatic field) are "updated," so that they point to the mass's actual position at constant velocity, with no retardation effects. This happens also for static electric and magnetic effects and is required by Lorentz symmetry, since any mass or charge moving with constant velocity at a great distance, could be replaced by a moving observer at the same distance, with the object now at "rest."
This concept parallels the Liénard–Wiechert potentials for electromagnetic effects and waves, where the static gravitational field from a moving mass is updated to reflect its current position while it moves at a constant velocity without acceleration. This adjustment also applies to static electric and magnetic fields and is mandated by Lorentz symmetry, as an object in motion could be equivalent to a stationary observer at the same distance.