Other
Scientific paper
Jul 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985gregr..17..637n&link_type=abstract
General Relativity and Gravitation (ISSN 0001-7701), vol. 17, July 1985, p. 637-648.
Other
2
Gravitational Fields, Newton Theory, Reference Systems, Relativity, Rotation, Approximation, Einstein Equations, Equations Of Motion, Jacobi Integral, Space-Time Functions, Three Body Problem
Scientific paper
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.
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