Alcubierre M. Introduction to 3+1 Numerical Relativity

Oxford University Press, 2008. — 460 p. — (International Series of Monographs on Physics 140). — ISBN: 9780199205677.This book introduces the modern field of 3+1 numerical relativity. The book has been written in a way as to be as self-contained as possible, and only assumes a basic knowledge of special relativity. Starting from a brief introduction to general relativity, it discusses the different concepts and tools necessary for the fully consistent numerical simulation of relativistic astrophysical systems, with strong and dynamical gravitational fields. Among the topics discussed in detail are the following: the initial data problem, hyperbolic reductions of the field equations, gauge conditions, the evolution of black hole space-times, relativistic hydrodynamics, gravitational wave extraction and numerical methods. There is also a final chapter with examples of some simple numerical space-times. The book is aimed at both graduate students and researchers in physics and astrophysics, and at those interested in relativistic astrophysics.Brief Review of General Relativity
The 3+1 Formalism
Initial Data
Gauge Conditions
Hyperbolic Reductions of the Field Equations
Evolving Black Hole Spacetimes
Relativistic Hydrodynamics
Gravitational Wave Extraction
Numerical Methods
Examples of Numerical Spacetimes
Total Mass and Momentum in General Relativity
Spacetime Christoffel Symbols in 3+1 Language
BSSNOK with Natural Conformal Rescaling
Spin-weighted Spherical Harmonics