GRAVITOMAGNETISM AND FRAME-DRAGGING: THEORY AND MEASUREMENT

After a brief introduction on frame-dragging and gravitomagnetic field, including an invariant characterization of gravitomagnetism, we describe the phenomena due to spin on test gyroscopes, test particles, clocks and photons. In particular we show that when different light beams are deflected by the mass of a rotating object, with angular momentum J, and then, by gravitational lensing, observed at a far point as different images of the same source with different angular positions, there may be a significant time delay between the different images due to the spin of the deflecting body. We then discuss the time delay in the travel time of photons propagating inside a massive rotating shell. We apply this time delay, due to the spin of the shell, to the case of gravitational lensing and we show that there may be an appreciable time delay between the arrival of different images at Earth. We then consider some astrophysical configurations: a typical rotating galaxy and a typical rotating cluster, or super-cluster, of galaxies; the spin-time-delay might be large enough to be detected at Earth. This phenomenon should then be taken into account in the modeling of the time delay of different images by gravitational lensing and might be measurable in some gravitational lensing images. The spin-time-delay might give a new observable in the study of the dark matter content in rotating galaxies and clusters.

We then describe the latest results in the measurement of gravitomagnetism of Earth and Lense-Thirring effect by laser ranged satellites. Gravity Probe-B, launched by NASA on April 20 2004, will try to measure the Earth frame-dragging with accuracy of 1 % or better. A future accurate determination of the Lense-Thirring effect, at the level of 1 % accuracy, may be provided by the LARES/WEBER-SAT experiment to measure “frame-dragging” and to give other basic tests of fundamental physics and general relativity. Here we describe the 1995-2004 measurement of Lense-Thirring effect obtained by analyzing the orbits of the two laser-ranged satellites LAGEOS and LAGEOS II; this method has provided in 2004 a direct measurement of Earth's gravitomagnetism with accuracy of the order of 10 %. We first report the measurement of the Lense-Thirring effect, obtained in 2001 over nearly 8 years of data using the nodes of the LAGEOS satellites and the perigee of LAGEOS II: it fully agrees with the previous 1998 result over a period of 4 years only. Finally, we describe the 2004 determinations of Earth's frame-dragging, using the recently released Earth's gravity field models, generated by the space mission GRACE, and analyzing about 11 years of data of the nodes, only, of the LAGEOS satellites. This new analysis agrees with our previous measurements of the Lense–Thirring effect using the LAGEOS satellites and obtained with the JGM-3 and EGM96 Earth's models. However, this new determination is much more accurate and, especially, more robust than our previous measurements. Indeed, the present analysis uses the nodal rates of the two satellites only, making no use of the perigee rate, as in our previous analyses. By using the Earth model EIGEN-GRACE02S, we obtain a relative error of the order of 4 % to 8 % of the Lense-Thirring effect due to the uncertainties in the Earth static gravity field and a total root-sum-square error budget of about 5 % to 10 % due to all the error sources. Specifically, by using EIGEN-GRACE02S, we obtain: μ = 0.99 ± 0.1. This 2004 results fully confirm and improve our previous measurements of the Earth frame-dragging: the Lense-Thirring effect exists and its experimental value is within ~ 10 % of what is predicted by Einstein's theory of general relativity.