Null cone computation of gravitational radiation

Isaacson, Richard A.; Welling, Joel; Winicour, Jeffrey

doi:10.1063/1.525904

Cited by 118 publications

(110 citation statements)

References 10 publications

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“…The formalism for the numerical evolution of Einstein's equations, in null cone coordinates, is well known [30,33,[37][38][39][40]. For the sake of completeness, we give a summary of those aspects of the formalism that will be used here.…”

Section: A the Bondi-sachs Metricmentioning

confidence: 99%

Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity

Reisswig¹,

Bishop²,

Pollney³

et al. 2010

Class. Quantum Grav.

146

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The accurate modeling of gravitational radiation is a key issue for gravitational wave astronomy. As simulation codes reach higher accuracy, systematic errors inherent in current numerical relativity waveextraction methods become evident, and may lead to a wrong astrophysical interpretation of the data. In this paper, we give a detailed description of the Cauchy-characteristic extraction technique applied to binary black hole inspiral and merger evolutions to obtain gravitational waveforms that are defined unambiguously, that is, at future null infinity. By this method we remove finite-radius approximations and the need to extrapolate data from the near zone. Further, we demonstrate that the method is free of gauge effects and thus is affected only by numerical error. Various consistency checks reveal that energy and angular momentum are conserved to high precision and agree very well with extrapolated data. In addition, we revisit the computation of the gravitational recoil and find that finite radius extrapolation very well approximates the result at J + . However, the (non-convergent) systematic differences to extrapolated data are of the same order of magnitude as the (convergent) discretisation error of the Cauchy evolution hence highlighting the need for correct wave-extraction.

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Section: A the Bondi-sachs Metricmentioning

confidence: 99%

Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity

Reisswig¹,

Bishop²,

Pollney³

et al. 2010

Class. Quantum Grav.

146

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“…The remaining gravitational variables (A and H A ) can be constructed from a subset of the evolution equations (17)(18) and constraint equations (19)(20). Different integration schemes can be designed depending on which two equations are chosen from (17-20) to solve for A and H A .…”

Section: Interior Domain: Cauchy Evolutionmentioning

confidence: 99%

“…In recent years, the characteristic initial value problem (cIVP) formulation of the Einstein equations in non-spherically symmetric configurations [18,15] has been explored, providing possible alternatives to the practical and theoretical problems introduced by the outer boundary conditions of the Cauchy initial value problem (CIVP). Based on the concept of combined Cauchy-characteristic evolution, a number of systems are currently under investigation.…”

Section: Introductionmentioning

confidence: 99%

Cauchy-characteristic evolution of Einstein-Klein-Gordon systems

et al. 1996

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A Cauchy-characteristic initial value problem for the Einstein-KleinGordon system with spherical symmetry is presented. Initial data are specified on the union of a space-like and null hypersurface. The development of the data is obtained with the combination of a constrained Cauchy evolution in the interior domain and a characteristic evolution in the exterior, asymptotically flat region. The matching interface between the space-like and characteristic foliations is constructed by imposing continuity conditions on metric, extrinsic curvature and scalar field variables, ensuring smoothness across the matching surface. The accuracy of the method is established for all ranges of M/R, most notably, with a detailed comparison of invariant observables against reference solutions obtained with a calibrated, global, null algorithm.

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“…[1] This algorithm is based upon the characteristic initial value problem for general relativity, using light cones as the evolution hypersurfaces, rather than the spacelike foliation used in traditional approaches based upon the Cauchy problem. The intimate use of characteristics has particular advantages for the description of gravitational radiation and black hole formation.…”

Section: Introductionmentioning

confidence: 99%

Null cone evolution of axisymmetric vacuum space–times

Gómez

Papadopoulos

Winicour

1994

Journal of Mathematical Physics

Self Cite

129

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We present the details of an algorithm for the global evolution of asymptotically flat, axisymmetric spacetimes, based upon a characteristic initial value formulation using null cones as evolution hypersurfaces. We identify a new static solution of the vacuum field equations which provides an important test bed for characteristic evolution codes. We also show how linearized solutions of the Bondi equations can be generated by solutions of the scalar wave equation, thus providing a complete set of test beds in the weak field regime. These tools are used to establish that the algorithm is second order accurate and stable, subject to a Courant-Friedrichs-Lewy condition. In addition, the numerical versions of the Bondi mass and news function, calculated at scri on a compactified grid, are shown to satisfy the Bondi mass loss equation to second order accuracy. This verifies that numerical evolution preserves the Bianchi identities. Results of numerical evolution confirm the theorem of Christodoulou and Klainerman that in vacuum, weak initial data evolve to a flat spacetime. For the class of asymptotically flat, axisymmetric vacuum spacetimes, for which no nonsingular analytic solutions are known, the algorithm provides highly accurate solutions throughout the regime in which neither caustics nor horizons form.

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Null cone computation of gravitational radiation

Cited by 118 publications

References 10 publications

Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity

Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity

Cauchy-characteristic evolution of Einstein-Klein-Gordon systems

Null cone evolution of axisymmetric vacuum space–times

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