Orbital effects due to gravitational induction

Abstract

We study the motion of test particles in the metric of a localized and slowly rotating astronomical source, within the framework of linear gravitoelectromagnetism, grounded on a Post-Minkowskian approximation of general relativity. Special attention is paid to gravitational inductive effects due to time-varying gravitomagnetic fields. We show that, within the limits of the approximation mentioned above, there are cumulative effects on the orbit of the particles either for planetary sources or for binary systems. They turn out to be negligible.

Fluid statics of a self-gravitating perfect-gas isothermal sphere

“…2.5), we call the reader's attention to an important detail: the density values attained at sphere center and shell internal wall are unequivocally determined by the integration of Eqs. (42); no knowledge of those values is required before integration. Figure 3 shows the corresponding profiles of the gravitational field inside the gas sphere.…”

“…( 42) exists beyond the upper bound N m and, therefore, no fluid-static field can exist in the gas if N > N m ; with numerical accuracy preset to eight significant digits, we obtained N m = 2.51755148 (rounded off to 2.5175 in the figures) as the greatest value for which it was possible to obtain a solution of Eqs. (42). Characteristic values corresponding to N m can be read off from Figs.…”

“…(41) and Eqs. (42)] based on Eq. ( 40): it includes boundary conditions whose physical legitimization is unambiguous; it is governed by one single, clearly identified physical characteristic number, the gravitational number N ; it involves nondimensional variables scaled with factors constructed with variables characterizing the physical system, known a priori and as precisely controllable as the gravitational number is.…”

Gravitomagnetic effects in the Kerr-Newman spacetime

“…This effect, called the Lense-Thirring effect, was verified by the GP-B experiment with an accuracy of 19% [6]. In recent years, several aspects of gravitomagnetism have been studied, taking into account effects produced by the gravitational field of rotating astronomical sources [13,2,10].…”

Gravitomagnetism due to a rotating charged body in Brans-Dicke theory

“…In this way, one defines the gravitomagnetic field in the context of the Kerr metric, which describes the curved spacetime geometry around a rotating mass [6]. The gravitomagnetism has been studied taking into account effects produced by the gravitational field of rotating astronomical sources [11,4,9]. In relation to the Earth, it produces a gravitomagnetic field that causes a precession in gyroscopes orbiting around the planet; this is the Lense-Thirring effect, which was verified by the GP-B experiment with an accuracy of 19% [7].…”