1654-9163 (print) ISSN 2001-7235 (online)
The Abraham Zelmanov Journal
The journal for General Relativity, gravitation and cosmology
Gravitational Fields Exterior to Homogeneous Spheroidal Masses
General relativistic mechanics in gravitational fields exterior to homogeneous spheroidal masses is developed using our new approach. Einstein's field equations in the gravitational field exterior to a static homogeneous prolate spheroid are derived and a solution for the first field equations constructed. Our derived field equations exterior to the mass distribution have only one unknown function determined by the mass or pressure distribution. The obtained solutions yield the unknown function as generalizations of Newton's gravitational scalar potential. Remarkably, our solution puts Einstein's geometrical theory of gravity on same footing with Newton's dynamical theory; with the dependence of the field on one and only one unknown function comparable to Newton's gravitational scalar potential. The consequences of the homogeneous spheroidal gravitational field on the motion of test particles have been theoretically investigated. The effect of the oblate nature of the Sun and planets on some gravitational phenomena has been examined. These are gravitational time dilation, gravitational length contraction and gravitational spectral shift of light. Our obtained theoretical value for the Pound-Rebka experiment on gravitational spectra shift (2.578×10-15) agrees satisfactorily with the experimental value of 2.45×10-15. Expressions for the conservation of energy and angular momentum are obtained. Planetary equations of motion and equations of motion of photons in the vicinity of spheroids are derived; having additional spheroidal terms not found in Schwarzschild's space-time.
Ref: The Abraham Zelmanov Journal, 2012, volume 5, pages 31-67
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The Abraham Zelmanov Journal is an annually issue scientific journal registered with the Royal National Library of Sweden.