Constructing a Mass-Current Radiation-Reaction Force For Numerical Simulations

TL;DR

This paper introduces a new 3.5 Post-Newtonian formalism focusing on mass-current quadrupole radiation-reaction effects, optimized for numerical simulations of neutron star instabilities, differing from previous approaches in gauge choice and derivative order.

Contribution

It presents a novel 3.5 Post-Newtonian framework that simplifies numerical implementation by focusing on mass-current quadrupole effects and using a different gauge.

Findings

Formalism is well-suited for numerical simulations.

Focuses on mass-current quadrupole radiation-reaction effects.

Uses a fourth time derivative, simplifying computations.

Abstract

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 $S_{ij}$. Secondly, 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 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.