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International Journal of Modern Physics C, 1994
The present status of numerical relativity is reviewed. There are five closely interconnected aspects of numerical relativity: (1) Formulation. The general covariant Einstein equations are reformulated in a way suitable for numerical study by separating the 4-dimensional spacetime into a 3-dimensional space evolving in time. (2) Techniques.
Seidel, Edward, Suen, Wai-Mo
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The present status of numerical relativity is reviewed. There are five closely interconnected aspects of numerical relativity: (1) Formulation. The general covariant Einstein equations are reformulated in a way suitable for numerical study by separating the 4-dimensional spacetime into a 3-dimensional space evolving in time. (2) Techniques.
Seidel, Edward, Suen, Wai-Mo
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NUMERICAL RELATIVITY: EVOLVING SPACETIME
International Journal of Modern Physics C, 1993The construction of numerical solutions of Einstein's General Relativity equations is formulated as an initial-value problem. The space-plus-time (3 + 1) decomposition of the spacetime metric tensor is used to discuss the structure of the field equations. The resulting evolution system is shown to depend in a crucial way on the coordinate gauge.
Bona, C., Massó, J.
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2010
Aimed at students and researchers entering the field, this pedagogical introduction to numerical relativity will also interest scientists seeking a broad survey of its challenges and achievements. Assuming only a basic knowledge of classical general relativity, the book develops the mathematical formalism from first principles, and then highlights some
Thomas W. Baumgarte, Stuart L. Shapiro
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Aimed at students and researchers entering the field, this pedagogical introduction to numerical relativity will also interest scientists seeking a broad survey of its challenges and achievements. Assuming only a basic knowledge of classical general relativity, the book develops the mathematical formalism from first principles, and then highlights some
Thomas W. Baumgarte, Stuart L. Shapiro
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Non-astrophysical numerical relativity
Classical and Quantum Gravity, 2012Numerical relativity is a powerful tool for astrophysical applications where gravity is strong, as shown dramatically by numerical studies of compact binary systems. However, as a fundamental theory of space, time and gravity, general relativity has many non-astrophysical aspects, and numerical techniques can also be used to great advantage in these ...
David Garfinkle, Luis Lehner
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Numerical Relativity beyond General Relativity
2019Einstein’s theory of general relativity has passed all precision tests to date. At some length scale, however, general relativity (GR) must break down and be reconciled with quantum mechanics in a quantum theory of gravity (a beyond-GR theory). Binary black hole mergers probe the non-linear, highly dynamical regime of gravity, and gravitational waves ...
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Semi-numerical relative orientation
Cartography, 1962After recapitulating the basic principles of relative orientation a theory is given for the semi-numerical orientation using rotations only. The method has many of the advantages of a least squares solution and is suitable for application in an instrument with graduated scales only on the omega-elements, such as the Wild B-8.
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Status of numerical relativity
Pramana, 2004I describe the current status of numerical relativity from my personal point of view. Here, I focus mainly on explaining the numerical implementations necessary for simulating general relativistic phenomena such as the merger of compact binaries and stellar collapse, emphasizing the well-developed current status of such implementations that enable ...
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Numerical Relativity and Cosmology
1988We discuss two schemes for general relativistic numerical cosmological solutions. The scheme are based on the 3+1 ADM formalism and on the 3+1 Regge Calculus and they are designed for a full three dimensional time dependent solution of the Einstein equations.
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Approaches to Numerical Relativity
1992This volume includes contributions by leading workers in the field given at the workshop on Numerical Relativity held in Southampton in December 1991. Numerical Relativity, or the numerical solution of astrophysical problems using powerful computers to solve Einstein's equations, has grown rapidly over the last 15 years. It is now an important route to
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