Frame-Dragging and Gravitomagnetism:. Theory and Experiment

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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 derive 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 the Lense-Thirring effect by laser ranged satellites. A future accurate measurement of the Lense-Thirring effect, at the level of 1% accuracy, may include the LARES experiment to measure "frame-dragging" and to provide other basic tests of general relativity and gravitation. We describe the 1995-2001 measurement of Lense-Thirring effect obtained by analyzing the orbits of the two laser-ranged satellites LAGEOS and LAGEOS II; this method has provided a direct measurement of Earth's gravitomagnetism with accuracy of the order of 20 %.
Finally, we report the latest measurement of the Lense-Thirring effect, obtained in 2001 with the LAGEOS satellites over nearly 8 years of data. This 2001 result fully confirms and improves our previous measurements of the Earth frame-dragging: the Lense-Thirring effect exists and its experimental value is within ˜ 20% of what is predicted by Einstein's theory of general relativity.

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