Constructing a Mass-current Radiation-reaction Force for Numerical Simulations

We present a new set of 3.5 Post-Newtonian equations in which Newtonian hydrodynamics is coupled to the nonconservative effects of gravitational radiation emission. Our formalism differs in two significant ways from a similar 3.5 Post-Newtonian approach proposed by Blanchet (1993, 1997). Firstly we concentrate only on the radiation-reaction effects produced by a time-varying mass-current quadrupole Sij . Secondly, we adopt a gauge in which the radiation-reaction force densities depend on the fourth time derivative of Sij , rather than on the fifth, as in Blanchet’s approach. This difference makes our formalism particularly well-suited to numerical implementation and could prove useful in performing fully numerical simulations of the recently discovered r-mode instability for rotating neutron stars subject to axial perturbations. Subject headings: relativity: Post-Newtonian approximation — gravitational radiation reaction — stars: neutron — stars: oscillations — instabilities.