Gravitational two-body problem with acceleration-dependent spin terms

Abstract

We generalize our previous work, on the gravitational two-body post-Newtonian Lagrangian with spin and parametrized post-Newtonian parameters γ and β, by addingaccelerationdependent spin terms corresponding to anarbitrary spin supplementary condition. For the purpose of constructing the corresponding Hamiltonian we make use of our recently developedmethod of the double zero. Using this method, we remove the acceleration-dependent spin terms from the Lagrangian and, in the process, create new non-accelerationdependent terms. Use of this new Lagrangian enables us to construct the Hamiltonian corresponding to the arbitrary spin supplementary condition. Energy constants of the motion are also discussed.