Radiation-balanced simulations for binary inspiral

Beetle, Christopher; Landry, Walter; Price, Richard H.

doi:10.1088/0264-9381/19/7/307

Cited by 21 publications

(58 citation statements)

References 13 publications

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“…(32) [29,[37][38][39][40][41]. A serious fault with such spacetimes is that they cannot be asymptotically flat since they contain a balancing amount of incoming and outgoing radiation for all time.…”

Section: Corotating and Nonspinning Black-hole Binariesmentioning

confidence: 99%

Circular orbits and spin in black-hole initial data

et al. 2006

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The construction of initial data for black-hole binaries usually involves the choice of free parameters that define the spins of the black holes and essentially the eccentricity of the orbit. Such parameters must be chosen carefully to yield initial data with the desired physical properties. In this paper, we examine these choices in detail for the quasiequilibrium method coupled to apparent-horizon/quasiequilibrium boundary conditions. First, we compare two independent criteria for choosing the orbital frequency, the ''Komar-mass condition'' and the ''effective-potential method,'' and find excellent agreement. Second, we implement quasilocal measures of the spin of the individual holes, calibrate these with corotating binaries, and revisit the construction of nonspinning black-hole binaries. Higher-order effects, beyond those considered in earlier work, turn out to be important. Without those, supposedly nonspinning black holes have appreciable quasilocal spin; furthermore, the Komar-mass condition and effective-potential method agree only when these higher-order effects are taken into account. We compute a new sequence of quasicircular orbits for nonspinning black-hole binaries, and determine the innermost stable circular orbit of this sequence.

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Section: Corotating and Nonspinning Black-hole Binariesmentioning

confidence: 99%

Circular orbits and spin in black-hole initial data

et al. 2006

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“…Independently varying the metric variables, {δα, δβ a , δγ ab , δπ ab }, gives the field equations, 18) and the relation,…”

Section: Formulation a 3+1 Formalismmentioning

confidence: 99%

Erratum: Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits [Phys. Rev. D70, 044044 (2004)]

Shibata¹,

Uryū²,

Friedman³

2004

Phys. Rev. D

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Two relations, the virial relation MADM = MK and the first law in the form δMADM = ΩδJ, should be satisfied by a solution and a sequence of solutions describing binary compact objects in quasiequilibrium circular orbits. Here, MADM, MK, J, and Ω are the ADM mass, Komar mass, angular momentum, and orbital angular velocity, respectively. δ denotes an Eulerian variation. These two conditions restrict the allowed formulations that we may adopt. First, we derive relations between MADM and MK and between δMADM and ΩδJ for general asymptotically flat spacetimes. Then, to obtain solutions that satisfy the virial relation and sequences of solutions that satisfy the first law at least approximately, we propose a formulation for computation of quasiequilibrium binary neutron stars in general relativity. In contrast to previous approaches in which a part of the Einstein equation is solved, in the new formulation, the full Einstein equation is solved with maximal slicing and in a transverse gauge for the conformal three-metric. Helical symmetry is imposed in the near zone, while in the distant zone, a waveless condition is assumed. We expect the solutions obtained in this formulation to be excellent quasiequilibria as well as initial data for numerical simulations of binary neutron star mergers.

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“…For fields other than gravity one could invoke a force, some deux ex machina, to keep the orbits unchanging, and have that force not couple to the field being studied. This certainly can be, and has been done in model problems [8,9,10,11,12] but, in principle, cannot be done in general relativity. In Einstein's gravitation all forces couple to gravity.…”

Section: Periodic Standing Wave (Psw) Approximationmentioning

confidence: 99%

“…This method, in effect, keeps only the features of the solution that are most important to the structure of the near-source fields and to the radiation, and has been used so far to study nonlinear toy models [8,9,12], linearized general relativity [18], and the post-Minkowski extension of linearized gravity [19]. This method is remarkable for its simplicity in giving approximate solutions, but is ill suited to the high accuracy needed for several purposes.…”

Section: Periodic Standing Wave (Psw) Approximationmentioning

confidence: 99%

See 1 more Smart Citation

Multidomain spectral method for the helically reduced wave equation

Lau

Price²

2007

Journal of Computational Physics

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We consider the 2+1 and 3+1 scalar wave equations reduced via a helical Killing field, respectively referred to as the 2-dimensional and 3-dimensional helically reduced wave equation (HRWE). The HRWE serves as the fundamental model for the mixed-type PDE arising in the periodic standing wave (PSW) approximation to binary inspiral. We present a method for solving the equation based on domain decomposition and spectral approximation. Beyond describing such a numerical method for solving strictly linear HRWE, we also present results for a nonlinear scalar model of binary inspiral. The PSW approximation has already been theoretically and numerically studied in the context of the post-Minkowskian gravitational field, with numerical simulations carried out via the "eigenspectral method." Despite its name, the eigenspectral technique does feature a finite-difference component, and is lower-order accurate. We intend to apply the numerical method described here to the theoretically well-developed post-Minkowski PSW formalism with the twin goals of spectral accuracy and the coordinate flexibility afforded by global spectral interpolation.

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Radiation-balanced simulations for binary inspiral

Cited by 21 publications

References 13 publications

Circular orbits and spin in black-hole initial data

Circular orbits and spin in black-hole initial data

Erratum: Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits [Phys. Rev. D70, 044044 (2004)]

Multidomain spectral method for the helically reduced wave equation

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