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

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.

17 pages, Latex2e, emulateapj.sty. To appear in ApJ

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Cited by in corpus (23)

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• Gravitational waves from instabilities in relativistic stars
• Nonlinear mode coupling in rotating stars and the r-mode instability in neutron stars
• General relativistic hydrodynamics with viscosity: contraction, catastrophic collapse, and disk formation in hypermassive neutron stars
• Extraction of Gravitational Waves in Numerical Relativity
• Quasi-periodic accretion and gravitational waves from oscillating "toroidal neutron stars" around a Schwarzschild black hole
• Non-Linear Evolution of the r-Modes in Neutron Stars
• Nonlinear r-modes in Rapidly Rotating Relativistic Stars
• Nonlinear r-Modes in Neutron Stars: Instability of an unstable mode
• Nonlinear r-modes in a spherical shell: issues of principle
• Numerical evolutions of nonlinear r-modes in neutron stars
• Delay Equations and Radiation Damping
• Time evolution of the linear perturbations of a rotating Newtonian polytrope
• Differential rotation of the unstable nonlinear r-modes
• Inertial modes in slowly rotating stars : an evolutionary description
• Gravitational Radiation Theory and Light Propagation
• Optimizing the third-and-a-half post-Newtonian gravitational radiation-reaction force for numerical simulations
• Limits on Magnetic Field Amplification from the r-Mode Instability
• A Post-Newtonian approach to black hole-fluid systems
• The r-mode instability: Analytical solution with gravitational radiation reaction
• Long-term impact of the magnetic-field strength on the evolution and electromagnetic emission by neutron-star merger remnants
• Quantum gravitomagnetic interaction
• Repulsive quantum gravitoelectric-gravitomagnetic interaction