Numerical Relativity

Preliminaries for Numerical Relativity; 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; 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;