Angular velocity of rotation of extended bodies in general relativity

Abstract

Abstract. We consider rotational motion of an arbitrarily composed and shaped, deformable weakly self-gravitating body being a member of a system of Ν arbitrarily composed and shaped, deformable weakly selfgravitating bodies in the post-Newtonian approximation of general relativity. Considering importance of the notion of angular velocity of the body (Earth, pulsar) for adequate modelling of modern astronomical observations, we are aimed at introducing a post-Newtonian-accurate definition of angular velocity. Not attempting to introduce a relativistic notion of rigid body (which is well known to be ill-defined even at the first post-Newtonian approximation) we consider bodies to be deformable and introduce the postNewtonian generalizations of the Tisserand axes and the principal axes of inertia.

A Universal Tool for Determining the Time Delay and the Frequency Shift of Light: Synge's World function

“…(89) is the well-known Shapiro time delay [16]. Equations (90) and (91) extend results previously found for γ = 1 and α 1 = 0 [1]. However, our derivation is more straightforward and yields formulae which are more convenient to calculate the frequency shifts.…”

“…In practically all of the previous studies, the explicit expressions of such travel times and frequency shifts as predicted by various metric theories of gravity are derived from an integration of the null geodesic differential equations. This method works quite well within the first post-Minkowskian approximation, as it is shown by the results obtained, e.g., in [1][2][3][4][5]. Of course, it works also within the post-Newtonian approximation, especially in the case of a static, spherically symmetric space-time treated up to order 1/c 3 [6,7].…”

Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers

“…Most notably, Crosta and Mignard [30] proposed to measure the deflection-of-light term associated with the axisymmetric (quadrupolar) part of Jupiter's gravitational field [31,32]. Their work is aimed at converting the earlier theoretical calculations [33][34][35] of light bending by gravitational multipoles into a practical algorithm for Gaia, thus, extending the relativistic techniques of astrometric data reduction worked out in a number of previous papers [9,10,36 -39]. Detection and precise measurement of the quadrupolar deflection of light in the solar system is important for providing an independent experimental support for the theory of gravitational lensing by clusters of galaxies.…”

Time transfer and frequency shift to the order1/c4in the field of an axisymmetric rotating body

“…For the time transfer, the main relativistic correction of order 1/c 3 is the well-known Shapiro time delay [4]. Other corrections due to the quadrupole moment and to the intrinsic angular momentum have been studied by several authors [5]. Gravitational corrections of order 1/c 2 in the frequency transfers were theoretically determined and experimentally checked a long time ago [6].…”

“…The method generally employed to study the questions related to the propagation of light in a gravitational field is based on the solution of the null geodesic equations (see, e.g., [5,10,11,12,13] for investigations in the linearized, weak-field limit of general relativity). However, the theory of the world-function developed by Synge [14] presents the great advantage to spare the trouble of integrating the geodesic equations.…”