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arXiv · 0808.2510

Post-Newtonian Approximation in Maxwell-Like Form

Jeffrey D. Kaplan·David A. Nichols·Kip S. Thorne
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Abstract

The equations of the linearized first post-Newtonian approximation to general relativity are often written in "gravitoelectromagnetic" Maxwell-like form, since that facilitates physical intuition. Damour, Soffel and Xu (DSX) (as a side issue in their complex but elegant papers on relativistic celestial mechanics) have expressed the first post-Newtonian approximation, including all nonlinearities, in Maxwell-like form. This paper summarizes that DSX Maxwell-like formalism (which is not easily extracted from their celestial mechanics papers), and then extends it to include the post-Newtonian (Landau-Lifshitz-based) gravitational momentum density, momentum flux (i.e. gravitational stress tensor) and law of momentum conservation in Maxwell-like form. The authors and their colleagues have found these Maxwell-like momentum tools useful for developing physical intuition into numerical-relativity simulations of compact binaries with spin.

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Jeffrey D. Kaplan, David A. Nichols, Kip S. Thorne. 2009-09-11. Post-Newtonian Approximation in Maxwell-Like Form. https://doi.org/10.1103/physrevd.80.124014

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