Ultra--cold gases and the detection of the Earth's rotation: Bogoliubov space and gravitomagnetism

The present work analyzes the consequences of the gravitomagnetic effect of the Earth upon a bosonic gas in which the corresponding atoms have a non--vanishing orbital angular momentum. Concerning the ground state of the Bogoliubov space of this system we deduce the consequences, on the pressure and on the speed of sound, of the gravitomagnetic effect. We prove that the effect on a single atom is very small, but we also show that for some thermodynamical properties the consequences scale as a non--trivial function of the number of particles.Comment: 4 page

Beyond Gravitoelectromagnetism: Critical Speed in Gravitational Motion

A null ray approaching a distant astronomical source appears to slow down, while a massive particle speeds up in accordance with Newtonian gravitation. The integration of these apparently incompatible aspects of motion in general relativity is due to the existence of a critical speed. Dynamics of particles moving faster than the critical speed could then be contrary to Newtonian expectations. Working within the framework of gravitoelectromagnetism, the implications of the existence of a critical speed are explored. The results are expected to be significant for high energy astrophysics.Comment: 13 pages, to appear in the Special December 2005 Issue of Int. J. Mod. Phys.

About Gravitomagnetism

The gravitomagnetic field is the force exerted by a moving body on the basis of the intriguing interplay between geometry and dynamics which is the analog to the magnetic field of a moving charged body in electromagnetism. The existence of such a field has been demonstrated based on special relativity approach and also by special relativity plus the gravitational time dilation for two different cases, a moving infinite line and a uniformly moving point mass, respectively. We treat these two approaches when the applied cases are switched while appropriate key points are employed. Thus, we demonstrate that the strength of the resulted gravitomagnetic field in the latter approach is twice the former. Then, we also discuss the full linearized general relativity and show that it should give the same strength for gravitomagnetic field as the latter approach. Hence, through an exact analogy with the electrodynamic equations, we present an argument in order to indicate the best definition amongst those considered in this issue in the literature. Finally, we investigate the gravitomagnetic effects and consequences of different definitions on the geodesic equation including the second order approximation terms.Comment: 16 pages, a few amendments have been performed and a new section has been adde

Gravitomagnetism and the Clock Effect

The main theoretical aspects of gravitomagnetism are reviewed. It is shown that the gravitomagnetic precession of a gyroscope is intimately connected with the special temporal structure around a rotating mass that is revealed by the gravitomagnetic clock effect. This remarkable effect, which involves the difference in the proper periods of a standard clock in prograde and retrograde circular geodesic orbits around a rotating mass, is discussed in detail. The implications of this effect for the notion of ``inertial dragging'' in the general theory of relativity are presented. The theory of the clock effect is developed within the PPN framework and the possibility of measuring it via spaceborne clocks is examined.Comment: 27 pages, LaTeX, submitted to Proc. Bad Honnef Meeting on: GYROS, CLOCKS, AND INTERFEROMETERS: TESTING GENERAL RELATIVITY IN SPACE (22 - 27 August 1999; Bad Honnef, Germany

Gravitomagnetism in teleparallel gravity

The assumption that matter charges and currents could generate fields, which are called, by analogy with electromagnetism, gravitoeletric and gravitomagnetic fields, dates from the origins of General Relativity (GR). On the other hand, the Teleparallel Equivalent of GR (TEGR), as a gauge theory, seems to be the ideal scenario to define these fields, based on the gauge field strength components. The purpose of the present work is to investigate the nature of the gravitational electric and magnetic fields in the context of the TEGR, where the tetrad formalism behind it seems to be more appropriated to deal with phenomena related to observers. As our main results, we have obtained, for the first time, the exact expressions for the gravito-electromagnetic fields for the Schwarzschild solution that in the linear approximation become the usual expected ones. To improve our understanding about these fields, we have also studied the geometry produced by a spherical rotating shell in slow motion and weak field regime. Again, the expressions obtained are in complete agreement with those of electromagnetism.Comment: 25 pages. Submitted to International Journal of Modern Physics D. Version 2: some new discussions, references adde

Phenomenology of the Lense-Thirring effect in the Solar System

Recent years have seen increasing efforts to directly measure some aspects of the general relativistic gravitomagnetic interaction in several astronomical scenarios in the solar system. After briefly overviewing the concept of gravitomagnetism from a theoretical point of view, we review the performed or proposed attempts to detect the Lense-Thirring effect affecting the orbital motions of natural and artificial bodies in the gravitational fields of the Sun, Earth, Mars and Jupiter. In particular, we will focus on the evaluation of the impact of several sources of systematic uncertainties of dynamical origin to realistically elucidate the present and future perspectives in directly measuring such an elusive relativistic effect.Comment: LaTex, 51 pages, 14 figures, 22 tables. Invited review, to appear in Astrophysics and Space Science (ApSS). Some uncited references in the text now correctly quoted. One reference added. A footnote adde