Physically Acceptable Solution of Einstein's Equation for Many-Body System
Open Access
- 1 August 1973
- journal article
- Published by Oxford University Press (OUP) in Progress of Theoretical Physics
- Vol. 50 (2) , 492-514
- https://doi.org/10.1143/ptp.50.492
Abstract
Einstein’s gravitational equation for slowly moving particles is solved up to the order of the post-post-Newtonian approximation. Though in this order the metric tensor diverges at spatial infinity when de Donder’s coordinate condition is employed, it is shown that there exist a class of coordinate systems in which the metric tensor is Minkowskian at infinity. We get solutions for the metric tensor up to the order of c-6. Using these solutions, we obtain, in the post-Newtonian order, the most general Hamiltonian for many-body system. The G·v4-part of the potential in the post-post-Newtonian order is also given.Keywords
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