Journal ArticleDOI
Numerical relativity. II. Numerical methods for the characteristic initial value problem and the evolution of the vacuum field equations for space‒times with two Killing vectors
R. W. Corkill,J. M. Stewart +1 more
TLDR
In this article, a sequence of papers on the numerical solution of the characteristic initial value problem in general relativity is presented, where the equations to be integrated have regular coefficients, but the nonlinearity leads to the occurrence of singularities after a finite evolution time.Abstract:
This is the second of a sequence of papers on the numerical solution of the characteristic initial value problem in general relativity. Although the equations to be integrated have regular coefficients, the nonlinearity leads to the occurrence of singularities after a finite evolution time. In this paper we first discuss some novel techniques for integrating the equations right up to the singularities. The second half of the paper presents as examples the numerical evolution of the Schwarzschild and certain colliding plane wave space-times.read more
Citations
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Journal ArticleDOI
Reduction of the characteristic initial value problem to the Cauchy problem and its applications to the Einstein equations
TL;DR: In this article, it is shown that the characteristic initial value problem for the Einstein equations in vacuum or with perfect fluid source is well posed when data are given on two transversely intersecting null hypersurfaces.
Journal ArticleDOI
Characteristic Evolution and Matching
TL;DR: The development of numerical evolution codes for general relativity based upon the characteristic initial-value problem is reviewed and the ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching.
Journal ArticleDOI
Extraction of gravitational waves in numerical relativity
Nigel T. Bishop,Luciano Rezzolla +1 more
TL;DR: A number of methods have been developed over the years to extract the radiative part of the solution from a numerical simulation and these include: quadrupole formulas, gauge-invariant metric perturbations, Weyl scalars, and characteristic extraction as discussed by the authors.
Journal ArticleDOI
On the stability and the numerical solution of the unsteady interactive boundary-layer equation
O. R. Tutty,S. J. Cowley +1 more
TL;DR: In this paper, it was shown that Rayleigh instability is possible within the interactive boundary-layer formulation and that the presence of Rayleigh modes often leads to accuracy problems which cannot be overcome by simple grid refinement.
Journal ArticleDOI
A scheme to numerically evolve data for the conformal Einstein equation
TL;DR: The second- and the fourth-order discretizations, which are used for the construction of the complete data set and for the numerical integration of the time evolution equations, are described and their efficiencies are compared.
References
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Journal ArticleDOI
Difference Methods for Initial-Value Problems.
Difference methods for initial-value problems
Robert D. Richtmyer,K. W. Morton +1 more
TL;DR: In this article, differentielles and stabilite were used for differentiable transport in the context of transfert de chaleur and ondes Reference Record created on 2005-11-18, modified on 2016-08-08
Journal ArticleDOI
Scattering of two impulsive gravitational plane waves.
TL;DR: Werner10 has presented a plausible case for believing that his detectors may indeed have monitored frequent and sharply pulsed gravitational waves, which seem to be emanating from the centre of the authors' galaxy.
Journal ArticleDOI
Characteristic Initial Data and Wavefront Singularities in General Relativity
H. Friedrich,J. M. Stewart +1 more
TL;DR: In this article, the structure of singularities (caustics), self-intersections of wavefronts and wavefront families in arbitrary space-times is discussed in detail and illustrated by explicit examples of stable wavefront singularities in Minkowski space.
Journal ArticleDOI
Numerical Relativity. I. The Characteristic Initial Value Problem
J. M. Stewart,H. Friedrich +1 more
TL;DR: The first of a series of papers on numerical relativity, the characteristic initial value problem is posed in a form suitable for numerical integration as mentioned in this paper, which can be reduced to the solution of two initial value problems for sets of ordinary differential equations on the initial surfaces.
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Characteristic Initial Data and Wavefront Singularities in General Relativity
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