Spin supplementary conditions for spinning compact binaries

Abstract

We consider different spin supplementary conditions (SSC) for a spinning compact binary with the leading-order spin-orbit (SO) interaction. The Lagrangian of the binary system can be constructed but it is acceleration-dependent in two cases of SSC. We rewrite the generalized Hamiltonian formalism proposed by Ostrogradsky and compute the conserved quantities and the dissipative part of relative motion during the gravitational radiation of each SSC. We give the orbital elements and observed quantities of the SO dynamics, for instance the energy and the orbital angular momentum losses and waveforms and discuss their SSC dependence.

15 two-column pages, 3 figures, 1 tables; corrected version, a new subsection 3.A ('Canonical structure') and some references added

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• Spin and quadrupolar effects in the secular evolution of precessing compact binaries with black hole, neutron star, gravastar, or boson star components
• Tidal deformations of compact objects and gravitational wave emission
• Spin precession of binary neutron stars with magnetic dipole moments