Item

Abstract

In this work we complete the spin dependent conservative dynamics of
inspiralling compact binaries at the fourth post-Newtonian order, and in
particular the recent derivation of the next-to-next-to-leading order
spin-squared interaction potential. We derive the physical equations of motion
of the position and the spin from a direct variation of the action. Further, we
derive the quadratic in spin Hamiltonians, as well as their expressions in the
center of mass frame. We construct the conserved integrals of motion, which
form the Poincare algebra. This construction provided a consistency check for
the validity of our result, which is crucial in particular in the current
absence of another independent derivation of the next-to-next-to-leading order
spin-squared interaction. Finally, we provide here the complete gauge invariant
relations among the binding energy, angular momentum, and orbital frequency of
an inspiralling binary with generic compact spinning components to the fourth
post-Newtonian order. These high post-Newtonian orders, in particular taking
into account the spins of the binary constituents, will enable to gain more
accurate information on the constituents from even more sensitive gravitational
wave detections to come.