English

Post-Newtonian Approximation in Maxwell-Like Form

General Relativity and Quantum Cosmology 2012-12-13 v4

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.

Keywords

Cite

@article{arxiv.0808.2510,
  title  = {Post-Newtonian Approximation in Maxwell-Like Form},
  author = {Jeffrey D. Kaplan and David A. Nichols and Kip S. Thorne},
  journal= {arXiv preprint arXiv:0808.2510},
  year   = {2012}
}

Comments

v4: Revised for resubmission to Phys Rev D, 6 pages. v3: Reformulated in terms of DSX papers. Submitted to Phys Rev D, 6 pages. v2: Added references. Changed definitions & conventions

R2 v1 2026-06-21T11:11:47.027Z