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The perihelion of Mercury advance and the light bending calculated in (enhanced) Newton's theory

Journal article
Authors Marek A Abramowicz
G. F. R. Ellis
J. Horák
M. Wielgus
Published in General Relativity and Gravitation
Volume 46
Issue 1
Pages artikel nr 1630
ISSN 0001-7701
Publication year 2014
Published at Department of Physics (GU)
Pages artikel nr 1630
Language en
Links dx.doi.org/10.1007/s10714-013-1630-...
Keywords Newton's gravity, Perihelion advance, Space curvature
Subject categories Physical Sciences

Abstract

We show that results of a simple dynamical gedanken experiment interpreted according to standard Newton's gravitational theory, may reveal that threedimensional space is curved. The experiment may be used to reconstruct the curved geometry of space, i.e. its non-Euclidean metric 3gik. The perihelion of Mercury advance and the light bending calculated from the Poisson equation 3gik∇i∇kΦ = -4πGρ and the equation of motion Fi = mai in the curved geometry 3gik have the correct (observed) values. Independently, we also show that Newtonian gravity theory may be enhanced to incorporate the curvature of three dimensional space by adding an extra equation which links the Ricci scalar 3R with the density of matter ρ. Like in Einstein's general relativity, matter is the source of curvature. In the spherically symmetric (vacuum) case, the metric of space 3gik that follows from this extra equation agrees, to the expected accuracy, with the metric measured by the Newtonian gedanken experiment mentioned above. © 2013 The Author(s).

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