Gravitational two-body problem with acceleration-dependent spin terms (Q1819577)

We generalize our previous work [Phys. Rev. D 14, 861 ff. (1976)], on the gravitational two-body post-Newtonian Lagrangian with spin and parametrized post-Newtonian parameters \(\gamma\) and \(\beta\), by adding acceleration-dependent spin terms corresponding to an arbitrary spin supplementary condition. For the purpose of constructing the corresponding Hamiltonian we make use of our recently developed method of the double zero. Using this method, we remove the acceleration-dependent spin terms from the Lagrangian and, in the process, create new non- acceleration-dependent 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.