Non-linear effects in the post-Newtonian approximation of a spherically symmetric field



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Gambi, J.M. and Romero Pérez, Mª Pilar and Zamorano, P. and García del Pino, M.L. (2000) Non-linear effects in the post-Newtonian approximation of a spherically symmetric field. Il Nuovo Cimento della Società Italiana di Fisica - B: General Physics, Relativity, Astronomy and Mathematical Physics and Methods, 115 (2). pp. 165-178. ISSN 1594-9982

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Conditions for the compatibility of the exterior metric of a spherically symmetric object with the field equations for the empty space and equations of motion and of trajectories for test particles, written in polar Gaussian and Fermi coordinates, are obtained to show that, although their explicit exact solutions cannot be derived in these coordinates, the post-Newtonian limits of these solutions can, nevertheless, be obtained. With these limits, it is next shown that the cited post-Newtonian equations do not fit into the standard post-Newtonian approximation either. It is then shown that these coordinates can, nevertheless, be included in a more general formalism together with the usual post-Newtonian (standard, harmonic, Painleve and isotropic) coordinates so that their respective equations of motion may be compared to each other and, finally, it is demonstrated that the only non-linear term taken in the Christoffel symbols with these usual coordinates in the standard post-Newtonian equations of motion to explain some known perturbations is not needed when polar Gaussian or Fermi coordinates are used to explain also those perturbations. In fact, it is demonstrated that these are the only coordinates for which that term becomes zero.

Item Type:Article
Subjects:Sciences > Physics > Astronomy
ID Code:19925
Deposited On:12 Feb 2013 16:56
Last Modified:12 Feb 2013 16:59

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