Gravimagnetism, causality, and aberration of gravity in the gravitational light-ray deflection experiments

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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.