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Post-Newtonian Gravitation

In: Mathematical and Computational Approaches in Advancing Modern Science and Engineering

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  • Erik I. Verriest

    (Georgia Institute of Technology)

Abstract

Einstein’s field equations relate space-time geometry to matter and energy distribution. These tensorial equations are so unwieldy that solutions are only known in some very specific cases. A semi-relativistic approximation is desirable: One where space-time may still be considered as flat, but where Newton’s equations (where gravity acts instantaneously) are replaced by a post-Newtonian theory, involving propagation of gravity at the speed of light. As this retardation depends on the geometry of the point masses, a dynamical system with state dependent delay results, where delay and state are implicitly related. We investigate several cases with Lagrange’s inversion technique and perturbation expansions. Interesting phenomena (entrainment, dynamic friction, fission and orbital speeds) emerge.

Suggested Citation

  • Erik I. Verriest, 2016. "Post-Newtonian Gravitation," Springer Books, in: Jacques Bélair & Ian A. Frigaard & Herb Kunze & Roman Makarov & Roderick Melnik & Raymond J. Spiteri (ed.), Mathematical and Computational Approaches in Advancing Modern Science and Engineering, pages 153-164, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-30379-6_15
    DOI: 10.1007/978-3-319-30379-6_15
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