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Published December 2009 | Published
Journal Article Open

Post-Newtonian approximation in Maxwell-like form


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.

Additional Information

© 2009 The American Physical Society. Received 18 August 2008; revised 25 February 2009; published 10 December 2009. For helpful discussions we thank Yanbei Chen and Drew Keppel. We also thank Luc Blanchet for bringing references [16,27] to our attention, and anonymous referees for helpful critiques and suggestions. This research was supported in part by NSF Grant Nos. PHY-0601459 and PHY-0653653.

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August 19, 2023
October 19, 2023