Asymptotically Flat Initial Data¶with Prescribed Regularity at Infinity

Dain, Sergio; Friedrich, Helmut

doi:10.1007/s002200100524

Cited by 78 publications

(211 citation statements)

References 33 publications

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“…The initial data are constructed applying the "puncture" method [31,32,33,34] as described in [35]. We have considered four different sequences labelled as "r", "s," "t", and "u" along straight lines in the (a 1 , a 2 ) parameter space, also referred to as the "spin diagram".…”

Section: Numerical Setup and Initial Datamentioning

confidence: 99%

Gravitational-wave detectability of equal-mass black-hole binaries with aligned spins

et al. 2009

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Binary black-hole systems with spins aligned or anti-aligned to the orbital angular momentum, and which therefore do not exhibit precession effects, provide the natural ground to start detailed studies of the influence of strong-field spin effects on gravitational wave observations of coalescing binaries. Furthermore, such systems may be the preferred end-state of the inspiral of generic supermassive binary black-hole systems. In view of this, we have computed the inspiral and merger of a large set of binary systems of equal-mass black holes with spins parallel to the orbital angular momentum but otherwise arbitrary. Our attention is particularly focused on the gravitational-wave emission so as to quantify how much spin effects contribute to the signal-to-noise ratio, to the horizon distances, and to the relative event rates for the representative ranges in masses and detectors. As expected, the signal-to-noise ratio increases with the projection of the total black hole spin in the direction of the orbital momentum. We find that equal-spin binaries with maximum spin aligned with the orbital angular momentum are more than "three times as loud" as the corresponding binaries with anti-aligned spins, thus corresponding to event rates up to 30 times larger. We also consider the waveform mismatch between the different spinning configurations and find that, within our numerical accuracy, binaries with opposite spins S1 = −S2 cannot be distinguished whereas binaries with spin S1 = S2 have clearly distinct gravitationalwave emissions. Finally, we derive a simple expression for the energy radiated in gravitational waves and find that the binaries always have efficiencies E rad /M 3.6%, which can become as large as E rad /M ≃ 10% for maximally spinning binaries with spins aligned with the orbital angular momentum. These binaries are therefore among the most efficient sources of energy in the Universe.

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Section: Numerical Setup and Initial Datamentioning

confidence: 99%

Gravitational-wave detectability of equal-mass black-hole binaries with aligned spins

et al. 2009

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“…Bowen-York puncture data were first constructed long before stable numerical simulations of black-hole binaries were possible, and were useful in both mathematical relativity [35][36][37] and in studies of initial data [14,[38][39][40][41]. However, with the advent of the moving-puncture method [2,3] it was found that wormholes may not be the most suitable topology for black-hole initial data.…”

Section: B Trumpet-puncture Datamentioning

confidence: 99%

Bowen-York trumpet data and black-hole simulations

2009

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Type of publicationArticle (peer-reviewed) The most popular method to construct initial data for black-hole-binary simulations is the puncture method, in which compactified wormholes are given linear and angular momentum via the Bowen-York extrinsic curvature. When these data are evolved, they quickly approach a trumpet topology, suggesting that it would be preferable to use data that are in trumpet form from the outset. To achieve this, we extend the puncture method to allow the construction of Bowen-York trumpets, including an outline of an existence and uniqueness proof of the solutions. We construct boosted, spinning and binary Bowen-York puncture trumpets using a single-domain pseudospectral elliptic solver, and evolve the binary data and compare with standard wormhole-data results. We also show that for boosted trumpets the black-hole mass can be prescribed a priori, without recourse to the iterative procedure that is necessary for wormhole data.

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“…Solutions to this problem have been discussed by Corvino [5], utilizing a "gluing" technique in order to obtain initial data which are exact Schwarzschild data near spatial infinity, and more generally by Dain and Friedrich [6]. Note that, on the other hand, there are specific conditions which guarantee the regularity at I of initial data on hyperboloidal slices [1,2].…”

Section: The Wave Equationmentioning

confidence: 99%

A Fully Pseudospectral Scheme for Solving Singular Hyperbolic Equations on Conformally Compactified Space-Times

Hennig

Ansorg

2009

J. Hyper. Differential Equations

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Abstract. With the example of the spherically symmetric scalar wave equation on Minkowski space-time we demonstrate that a fully pseudospectral scheme (i.e. spectral with respect to both spatial and time directions) can be applied for solving hyperbolic equations. The calculations are carried out within the framework of conformally compactified space-times. In our formulation, the equation becomes singular at null infinity and yields regular boundary conditions there. In this manner it becomes possible to avoid "artificial" conditions at some numerical outer boundary at a finite distance. We obtain highly accurate numerical solutions possessing exponential spectral convergence, a feature known from solving elliptic PDEs with spectral methods. Our investigations are meant as a first step towards the goal of treating time evolution problems in General Relativity with spectral methods in space and time.

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Asymptotically Flat Initial Data¶with Prescribed Regularity at Infinity

Abstract: We prove the existence of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate.

Cited by 78 publications

References 33 publications

Gravitational-wave detectability of equal-mass black-hole binaries with aligned spins

Gravitational-wave detectability of equal-mass black-hole binaries with aligned spins

Bowen-York trumpet data and black-hole simulations

A Fully Pseudospectral Scheme for Solving Singular Hyperbolic Equations on Conformally Compactified Space-Times

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