Light Propagation in the Gravitational Field of Moving Bodies by means of Lorentz Transformation. I. Mass monopoles moving with constant velocities

We show how to derive the equations of light propagation in the gravitational field of uniformly moving mass monopoles without formulating and integrating the differential equations of light propagation in that field. The well-known equations of light propagation in the gravitational field of a motionless mass monopole are combined with a suitable Lorentz transformation. The possibility to generalize this technique for the more complicated case of uniformly moving body of arbitrary multipole structure is discussed.Comment: 10 page

Post-Newtonian limitations on measurement of the PPN parameters caused by motion of gravitating bodies

We derive explicit Lorentz-invariant solution of the Einstein and null geodesic equations for data processing of the time delay and ranging experiments in gravitational field of moving gravitating bodies of the solar system - the Sun and major planets. We discuss general-relativistic interpretation of these experiments and the limitations imposed by motion of the massive bodies on measurement of the parameters gamma_{PPN}, beta_{PPN} and delta_{PPN} of the parameterized post-Newtonian formalism.Comment: 17 pages, 1 figure; accepted for publication to MNRA

Comment on 'Model-dependence of Shapiro time delay and the "speed of gravity/speed of light" controversy'

In a recent paper published in Classical and Quantum Gravity, 2004, vol. 21, p. 3803 Carlip used a vector-tensor theory of gravity to calculate the Shapiro time delay by a moving gravitational lens. He claimed that the relativistic correction of the order of v/c beyond the static part of the Shapiro delay depends on the speed of light c and, hence, the Fomalont-Kopeikin experiment is not sensitive to the speed of gravity c_g. In this letter we analyze Carlip's calculation and demonstrate that it implies a gravitodynamic (non-metric) system of units based on the principle of the constancy of the speed of gravity but it is disconnected from the practical method of measurement of astronomical distances based on the principle of the constancy of the speed of light and the SI metric (electrodynamic) system of units. Re-adjustment of theoretically-admissible but practically unmeasurable Carlip's coordinates to the SI metric system of units used in JPL ephemeris, reveals that the velocity-dependent correction to the static part of the Shapiro time delay does depend on the speed of gravity c_g as shown by Kopeikin in Classical and Quantum Gravity, 2004, vol. 21, p. 1. This analysis elucidates the importance of employing the metric system of units for physically meaningful interpretation of gravitational experiments.Comment: 8 pages, no figures, accepted to Classical and Quantum Gravit

Reply to ``Comment on Model-dependence of Shapiro time delay and the `speed of gravity/speed of light' controversy''

To determine whether the Shapiro time delay of light passing near a moving object depends on the ``speed of gravity'' or the ``speed of light,'' one must analyze observations in a bimetric framework in which these two speeds can be different. In a recent comment (gr-qc/0510048), Kopeikin has argued that such a computation -- described in gr-qc/0403060 -- missed a hidden dependence on the speed of gravity. By analyzing the observables in the relevant bimetric model, I show that this claim is incorrect, and that the conclusions of gr-qc/0403060 stand.Comment: 3 page reply to gr-qc/051004

Radio Tests of GR

Since VLBI techniques give microarcsecond position accuracy of celestial objects, tests of GR using radio sources as probes of a gravitational field have been made. We present the results from two recent tests using the VLBA: In 2005, the measurement of the classical solar deflection; and in 2002, the measurement of the retarded gravitational deflection associated with Jupiter. The deflection experiment measured PPN-gamma to an accuracy of 0.0003; the Jupiter experiment measured the retarded term to 20% accuracy. The controversy over the interpretation of the retarded term is summarized.Comment: 4 pages: IAU24

Retardation of Gravity in Binary Pulsars

We study the effect of retardation of gravity in binary pulsars. It appears in pulsar timing formula as a periodic excess time delay to the Shapiro effect. The retardation of gravity effect can be large enough for observation in binary pulsars with the nearly edgewise orbits and relatively large ratio of the projected semimajor axis to the orbital period of the pulsar. If one succeeds in measuring the retardation of gravity it will give further experimental evidence in favor of General Relativity

Post-Newtonian Treatment of the VLBI Experiment on September 8, 2002

Gravitational physics of VLBI experiment conducted on September 8, 2002 and dedicated to measure the speed of gravity is treated in the first post-Newtonian approximation. Explicit speed-of-gravity parameterization is introduced to the Einstein equations to single out the retardation effect associated with the finite speed of gravity in the relativistic time delay of light propagating in the gravitational field of moving Jupiter. Velocity-dependent 1.5 post-Newtonian correction to the Shapiro time delay is derived and compared with our previous result obtained by making use of the post-Minkowskian approximation. We prove that the 1.5 post-Newtonian correction to the Shapiro delay depends on the speed of propagation of gravity c_g that is a directly measurable parameter in the VLBI experiment

Gravitomagnetism and the Speed of Gravity

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.Comment: 16 pages, no figure

Shapiro Effect as a Possible Cause of the Low-Frequency Pulsar Timing Noise in Globular Clusters

A prolonged timing of millisecond pulsars has revealed low-frequency uncorrelated noise, presumably of astrophysical origin, in the pulse arrival time (PAT) residuals for some of them. In most cases, pulsars in globular clusters show a low-frequency modulation of their rotational phase and spin rate. The relativistic time delay of the pulsar signal in the curved space time of randomly distributed and moving globular cluster stars (the Shapiro effect) is suggested as a possible cause of this modulation. Given the smallness of the aberration corrections that arise from the nonstationarity of the gravitational field of the randomly distributed ensemble of stars under consideration, a formula is derived for the Shapiro effect for a pulsar in a globular cluster. The derived formula is used to calculate the autocorrelation function of the low-frequency pulsar noise, the slope of its power spectrum, and the behavior of the $\sigma_z$ statistic that characterizes the spectral properties of this noise in the form of a time function. The Shapiro effect under discussion is shown to manifest itself for large impact parameters as a low-frequency noise of the pulsar spin rate with a spectral index of n=-1.8 that depends weakly on the specific model distribution of stars in the globular cluster. For small impact parameters, the spectral index of the noise is n=-1.5.Comment: 23 pages, 6 figure