Gravitomagnetism and the Speed of Gravity

TL;DR

This paper discusses how measuring the extrinsic gravitomagnetic field generated by moving matter can test the Lorentz invariance of gravity, using observations of gravitational light deflection and relativistic time delay.

Contribution

It demonstrates that the extrinsic gravitomagnetic field can be measured via relativistic time delay and clarifies the interpretation of Jovian deflection experiments in testing gravity's Lorentz invariance.

Findings

Jovian deflection experiment confirms the extrinsic gravitomagnetic field with 20% accuracy.

Measuring gravitational light deflection by the Sun can further test the aberration of gravity.

The experiment supports the Lorentz invariance of the gravitational field.

Abstract

Experimental discovery of the gravitomagnetic fields generated by translational and/or rotational currents of matter is one of primary goals of modern gravitational physics. The rotational (intrinsic) gravitomagnetic field of the Earth is currently measured by the Gravity Probe B. The present paper makes use of a parametrized post-Newtonian (PN) expansion of the Einstein equations to demonstrate how the extrinsic gravitomagnetic field generated by the translational current of matter can be measured by observing the relativistic time delay caused by a moving gravitational lens. We prove that measuring the extrinsic gravitomagnetic field is equivalent to testing relativistic effect of the aberration of gravity caused by the Lorentz transformation of the gravitational field. We unfold that the recent Jovian deflection experiment is a null-type experiment testing the Lorentz invariance of the gravitational field (aberration of gravity), thus, confirming existence of the extrinsic gravitomagnetic field associated with orbital motion of Jupiter with accuracy 20%. We comment on erroneous interpretations of the Jovian deflection experiment given by a number of researchers who are not familiar with modern VLBI technique and subtleties of JPL ephemeris. We propose to measure the aberration of gravity effect more accurately by observing gravitational deflection of light by the Sun and processing VLBI observations in the geocentric frame with respect to which the Sun is moving with velocity 30 km/s.