Gravimagnetism, Causality, and Aberration of Gravity in the Gravitational Light-Ray Deflection Experiments

Experimental verification of the existence of gravimagnetic fields generated by currents of matter is important for a complete understanding and formulation of gravitational physics. Although the rotational `intrinsic' gravimagnetic field has been extensively studied and is now being measured by the Gravity Probe B, the `extrinsic' gravimagnetic field generated by the translational current of matter is less well studied. The present paper uses the post-Newtonian parametrized Einstein and light geodesics equations to show that the `extrinsic' gravimagnetic field generated by the translational current of matter can be measured by observing the relativistic time delay and/or light deflection caused by the moving mass. We prove that the `extrinsic' gravimagnetic field is generated by the relativistic effect of the aberration of the gravity force caused by the Lorentz transformation of the metric tensor and the Levi-Civita connection. We show that the Lorentz transformation of the gravity field variables is equivalent to the technique of the retarded Lienard-Wiechert gravitational potentials predicting that a light particle is deflected by gravitational field of a moving body from its retarded position so that both general-relativistic phenomena -- the aberration and the retardation of gravity -- are tightly connected and observing the aberration of gravity proves that gravity has a causal nature. We explain in this framework the 2002 deflection experiment of a quasar by Jupiter where the aberration of gravity from its orbital motion was measured with accuracy 20%. We describe a theory of VLBI experiment to measure the gravitational deflection of radio waves from a quasar by the Sun, as viewed by a moving observer from the geocentric frame, to improve the measurement accuracy of the aberration of gravity to a few percent.