Introduction to 3+1 Numerical Relativity International Series of Monographs on Physics Series, Vol. 140

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.

1. Brief Review of General Relativity. 2. The 3+1 Formalism. 3. Initial Data. 4. Gauge Conditions. 5. Hyperbolic Reductions of the Field Equations. 6. Evolving Black Hole Spacetimes. 7. Relativistic Hydrodynamics. 8. Gravitational Wave Extraction. 9. Numerical Methods. 10. Examples of Numerical Spacetimes. A. Total Mass and Momentum in General Relativity. B. Spacetime Christoffel Symbols in 3+1 Language. C. BSSNOK with Natural Conformal Rescaling. D. Spin-weighted Spherical Harmonics. References. Index.

Miguel Alcubierre, Department of Gravitation and Mathematical Physics, Institute of Nuclear Science, Universidad Nacional Autonoma de Mexico

An excellent book, and a good starting point for those making an effort to enter the field.