Authors: László Árpád Gergely
Date: 28 May 2010
Abstract: We establish the evolution equations of the set of independent variables characterizing the 2PN rigorous conservative dynamics of a spinning compact binary, with the inclusion of the leading order spin-orbit, spin-spin and mass quadrupole - mass monopole effects, for generic (noncircular, nonspherical) orbits. More specifically, we give a closed system of first order ordinary differential equations for the orbital elements of the osculating ellipse and for the angles characterizing the spin orientations with respect to the osculating orbit. We also prove that (i) the relative angle of the spins stays constant for equal mass black holes, irrespective of their orientation, and (ii) the special configuration of equal mass black holes with equal, but anti-aligned spins, both laying in the plane of motion (leading to the largest recoil so far) is preserved during the inspiral at 2PN level of accuracy, with leading order spin-orbit, spin-spin and mass quadrupolar contributions included.
© M. Vallisneri 2012 — last modified on 2010/01/29
Tantum in modicis, quantum in maximis