Frame-Dragging and Gravitomagnetism

Dear Colleagues,

Gravitomagnetism and frame-dragging, in addition to gravitational waves, have been initially predicted by using the linear perturbation approach to the general theory of relativity. The wave solution in general relativity first appeared in the weak field approximation to Einstein’s field equations in 1916. In particular, the application of the weak-field limit to a rotating massive object by Lense and Thirring in 1918 pointed to a frame-dragging effect, so called the Lense-Thirring precession. Moreover, Thirring obtained Maxwell-like equations for gravity in the weak-field approach, suggesting the presence of magnetic-type fields in gravity, so later called gravitomagnetism by Thorne in 1980s.

Our understanding of gravitomagnetism has been further deepened by the 1960s development of the 1+3 covariant approach to general relativity, where the Newtonian tidal gravity is prescribed by the electric part of the Weyl curvature, so called the gravitoelectric field. We notice that the magnetic part of the Weyl tensor offers an additional field, the gravitomagnetic field, associated with the non-local nature of gravity that is generated by the angular momentum of a rotating massive body. The 1+3 decomposition of the Bianchi identities in terms of the electric and magnetic components of the Weyl tensor provided some dynamical constraints for the gravitoelectric and gravitomagnetic fields, which are analogous to Maxwell’s equations in electromagnetism. Both the gravitoelectric and gravitomagnetic fields were found to have a fundamental role in supporting long-range gravitational waves in empty space.

Moreover, it has been demonstrated by Cohen and other people in the framework of the parameterized post-Newtonian approximation that the gravitomagnetic field of a rotating massive body can influence the proper time of a clock in a test particle orbiting around, so called the gravitomagnetic clock effect. It follows that the clock of equatorial particles prograding are slower than the clock of equatorial particles retrograding the rotation direction of the spinning massive body. This effect implies that the local time of the artificial satellites around the Earth should be slightly different because of the gravitomagnetic perturbation generated by the rotation of the Earth. Similarly, we expect that a spinning black hole affects the local time of prograding and retrograding particles in equatorial orbits around its event horizon, so the gravitomagnetic clock effect should be observable on electromagnetic radiations passing nearby spinning black holes as surrounding twisted light spectra.

Several space-based experiments aiming at detecting frame-dragging effects around the Earth, including Gravity Probe B and LAGEOS, and other scenarios in our Solar system (Sun and Mercury, probes around Mars, Juno at Jupiter) have been proposed and conducted so far. Although the gravitomagnetic field around the Earth is extremely weak and very difficult to be detected, the gravitomagnetic field of a spinning massive compact object such as a black hole is predicted to be very large near its event horizon. The gravitomagnetic field and frame-dragging effects are expected to be observable in quasars and active galactic nuclei, where spinning supermassive black holes are resident. Contemporaneity high energy X-ray observations revealed the presence of compact relativistic outflows launched near supermassive black holes, which could be related to less understood physics of gravitomagnetism. In 1971, Penrose theorized the extraction of rotational energy from a rotating black hole in the Kerr spacetime that yields the first theoretical explanation for relativistic jets nearby black holes based on the general-relativistic non-Newtonian field generated by rotating black holes. While the presence of gravitational waves have been confirmed through the recent LIGO and Virgo detection in 2016, experimental and observational tests of gravitomagnetism and frame-dragging will definitely validate the general theory of relativity, and it will help us understand better the quantum nature of gravity.

The main aim of this Special Issue is to review the recent developments in theatrical studies of frame-dragging and gravitomagnetism in the general theory of relativity, as well as observational evidence for the gravitomagnetic field in astrophysics and cosmology.

Some relevant references:

1. Iorio et al., Astrophysics and Space Science, Volume 331, Issue 2, pp.351-395, 2011
2. Renzetti, Central European Journal of Physics, Volume 11, Issue 5, pp.531-544, 2013
3. Will, Living Reviews in Relativity, Volume 17, No. 4, 2014
4. Tamburini et al. Nature Physics, Volume 7, Issue 3, pp. 195-197, 2011
5. Ciufolini & Wheeler, Gravitation and Inertia, Princeton University Press, 1995
6. Thorne ‎et al., Black Holes: The Membrane Paradigm, Yale University Press, 1986
7. Lämmerzahl et al. Gyros, Clocks, Interferometers...: Testing Relativistic Gravity in Space, Springer Science, 2001

Prof. Dr. Lorenzo Iorio
Dr. Ashkbiz Danehkar
Guest Editors

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