The periodic standing-wave approximation: post-Minkowski computation

Abstract

The periodic standing wave method studies circular orbits of compact objects coupled to helically symmetric standing wave gravitational fields. From this solution an approximation is extracted for the strong field, slowly inspiralling motion of black holes and binary stars. Previous work on this model has dealt with nonlinear scalar models, and with linearized general relativity. Here we present the results of the method for the post-Minkowski (PM) approximation to general relativity, the first step beyond linearized gravity. We compute the PM approximation in two ways: first, via the standard approach of computing linearized gravitational fields and constructing from them quadratic driving sources for second-order fields, and second, by solving the second-order equations as an ``exact'' nonlinear system. The results of these computations have two distinct applications: (i) The computational infrastructure for the ``exact'' PM solution will be directly applicable to full general relativity. (ii) The results will allow us to begin supplying initial data to collaborators running general relativistic evolution codes.

19 pages, 3 figures, 1 table, RevTeX

References in corpus (18)

• Evolution of Binary Black Hole Spacetimes
• Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
• Gravitational wave extraction from an inspiraling configuration of merging black holes
• Maximum gravitational recoil
• Total recoil: the maximum kick from nonspinning black-hole binary inspiral
• Recoil Velocities from Equal-Mass Binary-Black-Hole Mergers
• Binary black hole merger dynamics and waveforms
• Getting a kick out of numerical relativity
• Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme
• Black Hole Mergers and Unstable Circular Orbits
• The last orbit of binary black holes
• Comparisons of binary black hole merger waveforms
• Accurate Evolution of Orbiting Binary Black Holes
• Quasi-stationary binary inspiral II: Radiation-balanced boundary conditions
• The Periodic Standing-Wave Approximation: Overview and Three Dimensional Scalar Models
• Radiation-balanced simulations for binary inspiral
• The periodic standing-wave approximation: eigenspectral computations for linear gravity and nonlinear toy models
• The periodic standing-wave approximation: nonlinear scalar fields, adapted coordinates, and the eigenspectral method

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• New code for equilibriums and quasiequilibrium initial data of compact objects. IV. Rotating relativistic stars with mixed poloidal and toroidal magnetic fields
• Thermodynamics of magnetized binary compact objects
• Multidomain Spectral Method for the Helically Reduced Wave Equation
• Two-timescale adiabatic expansion of a scalar field model
• Sparse spectral-tau method for the three-dimensional helically reduced wave equation on two-center domains
• The periodic standing-wave approximation: computations in full general relativity
• Standing waves in general relativity
• Numerical study of the Kerr solution in rotating coordinates