%0 Journal Article
%T The Erez每Rosen Solution Versus the Hartle每Thorne Solution
%J Symmetry | An Open Access Journal from MDPI
%D 2019
%R https://doi.org/10.3390/sym11101324
%X In this work, we investigate the correspondence between the Erez每Rosen and Hartle每Thorne solutions. We explicitly show how to establish the relationship and find the coordinate transformations between the two metrics. For this purpose the two metrics must have the same approximation and describe the gravitational field of static objects. Since both the Erez每Rosen and the Hartle每Thorne solutions are particular solutions of a more general solution, the Zipoy每Voorhees transformation is applied to the exact Erez每Rosen metric in order to obtain a generalized solution in terms of the Zipoy每Voorhees parameter 汛 = 1 + s q . The Geroch每Hansen multipole moments of the generalized Erez每Rosen metric are calculated to find the definition of the total mass and quadrupole moment in terms of the mass m, quadrupole q and Zipoy每Voorhees 汛 parameters. The coordinate transformations between the metrics are found in the approximation of ‵q. It is shown that the Zipoy每Voorhees parameter is equal to 汛 = 1 ˋ q with s = ˋ 1 . This result is in agreement with previous results in the literature. View Full-Tex
%U https://www.mdpi.com/2073-8994/11/10/1324