Constructing a mass-current radiation-reaction force for numerical simulations

We present a new set of 3.5 post-Newtonian equations in which Newtonian hyd rodynamics is coupled to the nonconservative effects of gravitational radia tion emission. Our formalism differs in two significant ways from a similar 3.5 post-Newtonian approach proposed by Blanchet. First, we concentrate on ly on the radiation-reaction effects produced by a time-varying mass-curren t quadrupole S-ij. Second, we adopt a gauge in which the radiation-reaction force densities depend on the fourth time derivative of S-ij, rather than on the fifth, as in Blanchet's approach. This difference makes our formalis m particularly well-suited to numerical implementation and could prove usef ul in performing fully numerical simulations of the recently discovered r-m ode instability for rotating neutron stars subject to axial perturbations.