# Introduction to 3+1 Numerical Relativity

## Miguel Alcubierre

### Abstract

This book introduces the modern field of 3+1 numerical relativity. It has been written in a way as to be as self-contained as possible, and 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 b ... More

This book introduces the modern field of 3+1 numerical relativity. It has been written in a way as to be as self-contained as possible, and 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.

*Keywords: *
relativistic astrophysical systems,
dynamical gravitational fields,
initial data problem,
hyperbolic reductions,
gauge conditions,
black hole space-times,
relativistic hydrodynamics,
gravitational wave extraction

### Bibliographic Information

Print publication date: 2008 |
Print ISBN-13: 9780199205677 |

Published to Oxford Scholarship Online: September 2008 |
DOI:10.1093/acprof:oso/9780199205677.001.0001 |

### Authors

#### Affiliations are at time of print publication.

Miguel Alcubierre, *author*

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

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