General Relativity and Gravitation

, Volume 17, Issue 7, pp 637–648 | Cite as

Post-Newtonian approximation for a rotating frame of reference

  • Robert A. Nelson
Research Articles
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Abstract

The field equations of general relativity are solved to post-Newtonian order for a rotating frame of reference. A new method of approximation is used based on a 3+1 decomposition of the equations. The results are expressed explicitly in terms of the gravitational potentials. The space-time is asymptotically flat but not locally flat. The space-time metric contains gravitational terms, inertial terms, and coupled gravitational-inertial terms. The inertial terms in the equation of motion are in agreement with terms obtained by other authors using kinematic methods. The metric and equation of motion reduce to those for an inertial frame of reference under a simple coordinate transformation. The total energy of a particle is given. For the restricted three-body problem this represents the relativistic extension of Jacobi's integral to post-Newtonian order.

Keywords

Total Energy General Relativity Field Equation Differential Geometry Coordinate Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • Robert A. Nelson
    • 1
  1. 1.Department of Physics and AstronomyUniversity of MarylandMaryland

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