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

L. Rezzolla·M. Shibata·H. Asada·T. W. Baumgarte·S. L. Shapiro
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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.

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L. Rezzolla, M. Shibata, H. Asada, T. W. Baumgarte, S. L. Shapiro. 1999-05-08. Constructing a Mass-Current Radiation-Reaction Force For Numerical Simulations. https://doi.org/10.1086/307942

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