Table of Contents
ISRN Mathematical Physics
Volume 2012 (2012), Article ID 260951, 15 pages
http://dx.doi.org/10.5402/2012/260951
Research Article

Mimicking General Relativity with Newtonian Dynamics

Instituto de Cosmologia Relatividade Astrofisica (ICRA-Brasil/CBPF) Rua Dr. Xavier Sigaud, 150, 22290-180 Rio de Janeiro, RJ, Brazil

Received 4 August 2011; Accepted 21 September 2011

Academic Editors: I. Radinschi, W. Sabra, and D. Singleton

Copyright © 2012 E. Goulart. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The aim of this paper is twofolded. (1) Showing that Newtonian mechanics of point particles in static potentials admits an alternative description in terms of effective riemannian spacetimes. (2) Using the above geometrization scheme to investigate aspects of the gravitational field as it appears in the Einstein theory. It is shown that the mechanical (3 + 1) effective metrics are quite similar to Gordon's metric, as it is suggested by the well-known optical-mechanical analogy. Some special potentials are worked out.