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Numerical relativity/ Masaru Shibata

By: Contributor(s): Series: 100 years of General Relativity ; Vol 1Publication details: New Jersey: World Scientific, 2016Description: xxii, 821 pages; illustrations; 24.5 cmISBN:
  • 9789814699723 (paper back)
Subject(s): DDC classification:
  • 23 530.11 Sh555
Contents:
Preliminaries for Numerical Relativity Methodology: Formulation for Initial-Value Problems of General Relativity Numerical Methods for a Solution of Einstein's Evolution Equation Matter Equations in General Relativity Formulations for Initial Data, Equilibrium, and Quasi-Equilibrium Extracting Gravitational Waves Finding Black Holes Applications: Coalescence of Binary Compact Objects Gravitational Collapse to a Black Hole Non-Radial Instability and Magnetohydrodynamics Instability Higher-Dimensional Simulations Conclusion Appendices: Killing Vector and Frobenius' Theorem Numerical Relativity in Spherical Symmetry Decomposition by Spherical Harmonics Lagrangian and Hamiltonian Formulations of General Relativity Solutions of Riemann Problems in Special Relativistic Hydrodynamics Landau–Lifshitz Pseudo Tensor Laws of Black Hole and Apparent Horizon Post–Newtonian Results for Coalescing Compact Binaries
Summary: This book is composed of two parts: First part describes basics in numerical relativity, that is, the formulations and methods for a solution of Einstein's equation and general relativistic matter field equations. This part will be helpful for beginners of numerical relativity who would like to understand the content of numerical relativity and its background. The second part focuses on the application of numerical relativity. A wide variety of scientific numerical results are introduced focusing in particular on the merger of binary neutron stars and black holes.
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Preliminaries for Numerical Relativity
Methodology:
Formulation for Initial-Value Problems of General Relativity
Numerical Methods for a Solution of Einstein's Evolution Equation
Matter Equations in General Relativity
Formulations for Initial Data, Equilibrium, and Quasi-Equilibrium
Extracting Gravitational Waves
Finding Black Holes
Applications:
Coalescence of Binary Compact Objects
Gravitational Collapse to a Black Hole
Non-Radial Instability and Magnetohydrodynamics Instability
Higher-Dimensional Simulations
Conclusion
Appendices:
Killing Vector and Frobenius' Theorem
Numerical Relativity in Spherical Symmetry
Decomposition by Spherical Harmonics
Lagrangian and Hamiltonian Formulations of General Relativity
Solutions of Riemann Problems in Special Relativistic Hydrodynamics
Landau–Lifshitz Pseudo Tensor
Laws of Black Hole and Apparent Horizon
Post–Newtonian Results for Coalescing Compact Binaries

This book is composed of two parts: First part describes basics in numerical relativity, that is, the formulations and methods for a solution of Einstein's equation and general relativistic matter field equations. This part will be helpful for beginners of numerical relativity who would like to understand the content of numerical relativity and its background. The second part focuses on the application of numerical relativity. A wide variety of scientific numerical results are introduced focusing in particular on the merger of binary neutron stars and black holes.

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