The Motion of a Body in Newtonian Theories

@article{Weatherall2011TheMO,
  title={The Motion of a Body in Newtonian Theories},
  author={James Owen Weatherall},
  journal={Journal of Mathematical Physics},
  year={2011},
  volume={52},
  pages={032502-032502}
}
  • J. Weatherall
  • Published 3 October 2010
  • Physics, Mathematics
  • Journal of Mathematical Physics
A theorem due to Bob Geroch and Pong Soo Jang ["Motion of a Body in General Relativity." Journal of Mathematical Physics 16(1), (1975)] provides the sense in which the geodesic principle has the status of a theorem in General Relativity (GR). Here we show that a similar theorem holds in the context of geometrized Newtonian gravitation (often called Newton-Cartan theory). It follows that in Newtonian gravitation, as in GR, inertial motion can be derived from other central principles of the… 

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References

SHOWING 1-10 OF 25 REFERENCES
Covariant Newtonian limit of Lorentz space-times
The formulation of this limit given by Dautcourt [1] is slightly improved using the notions of Galilei manifold and Newtonian connection. It is then shown under what conditions the conservation
Topics in the Foundations of General Relativity and Newtonian Gravitation Theory
In "Topics in the Foundations of General Relativity and Newtonian Gravitation Theory", David B. Malament presents the basic logical-mathematical structure of general relativity and considers a number
The Gravitational equations and the problem of motion
Introduction. In this paper we investigate the fundamentally simple question of the extent to which the relativistic equations of gravitation determine the motion of ponderable bodies. Previous
ON THE GEODESIC HYPOTHESIS IN THE THEORY OF GRAVITATION.
  • T. Y. Thomas
  • Physics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1962
TAB = PWAWB PhAB, (AB = 0,1,2,3). (1) It is natural to interpret the scalar p in these equations as the material density. Also, the WA in (1) are the covariant components of the velocity, which is
Motion of a body in general relativity
A simple theorem, whose physical interpretation is that an isolated, gravitating body in general relativity moves approximately along a geodesic, is obtained.
Lectures on General Relativity
1. In dealing with physical problems, we are often interested in the solution of field equations with given sources, but with nothing known about initial conditions. Therefore, we cannot solve the
ON THOMAS' RESULT CONCERNING THE GEODESIC HYPOTHESIS.
  • A. Taub
  • Physics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1962
where po is the rest density, p the pressure, and e = E(p, po) the specific internal energy of the fluid as measured by an observer moving with it. The conservation of mass is then described by the
A covariant multipole formalism for extended test bodies in general relativity
SummaryA discussion and criticism is given of various forms that have been put forward for the multipole theory of an extended test body in curved space-time, and a new treatment is proposed, in
...
...