TY - GEN AU - Shibata,Masaru AU - Ashtekar,Abhay TI - Numerical relativity/ T2 - 100 years of General Relativity SN - 9789814699723 (paper back) U1 - 530.11 23 PY - 2016/// CY - New Jersey PB - World Scientific KW - Mathematical General Relativity KW - Cosmology KW - Relativistic Astrophysics KW - Gravitational Waves KW - Einstein's Evolution Equations KW - Relativistic Hydrodynamics KW - Black Hole N1 - 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 N2 - 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 ER -