The reduced Hamiltonian for next-to-leading-order spin-squared dynamics of general compact binaries

Within the post-Newtonian framework the fully reduced Hamiltonian (i.e. with eliminated spin supplementary condition) for the next-to-leading-order spin-squared dynamics of general compact binaries is presented. The Hamiltonian is applicable to the spin dynamics of all kinds of binaries with self-gravitating components such as black holes and/or neutron stars taking into account spin-induced quadrupolar deformation effects in second post-Newtonian order perturbation theory of Einstein's field equations. The corresponding equations of motion for spin, position and momentum variables are given in terms of canonical Poisson brackets. Comparison with a nonreduced potential calculated within the effective field theory approach is made.