Introduction to 3+1 Numerical Relativity

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More About This Textbook

Overview


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.
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Product Details

Meet the Author

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

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Table of Contents

1 Brief review of general relativity 1

2 The 3+1 formalism 64

3 Initial data 92

4 Gauge conditions 121

5 Hyperbolic reductions of the field equations 155

6 Evolving black hole spacetimes 198

7 Relativistic hydrodynamics 238

8 Gravitational wave extraction 176

9 Numerical methods 318

10 Examples of numerical spacetimes 357

A Total mass and momentum in general relativity 402

B Spacetime Christoffel symbols in 3+1 language 409

C BSSNOK with natural conformal rescaling 410

D Spin-weighted spherical harmonics 413

References 419

Index 437

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