**Authors**: Sylvain Marsat, Alejandro Bohe, Guillaume Faye, Luc Blanchet

**Date**: 15 Oct 2012

**Abstract**: We compute next-to-next-to-leading order spin contributions to the post-Newtonian equations of motion for binaries of compact objects, such as black holes or neutron stars. For maximally spinning black holes, those contributions are of third-and-a-half post-Newtonian (3.5PN) order, improving our knowledge of the equations of motion, already known for non-spinning objects up to this order. Building on previous work, we represent the rotation of the two bodies using a pole-dipole matter stress-energy tensor, and iterate Einstein's field equations for a set of potentials parametrizing the metric in harmonic coordinates. Checks of the result include the existence of a conserved energy, the approximate global Lorentz invariance of the equations of motion in harmonic coordinates, and the recovery of the motion of a spinning object on a Kerr background in the test-mass limit. We verified the existence of a contact transformation, together with a redefinition of the spin variables that makes our result equivalent to a previously published reduced Hamiltonian, obtained from the Arnowitt-Deser-Misner (ADM) formalism.

1210.4143
(/preprints)

2012-10-15, 22:33
**[edit]**

© M. Vallisneri 2012 — last modified on 2010/01/29

*Tantum in modicis, quantum in maximis*