## Numerical Relativity: Solving Einstein's Equations on the ComputerAimed at students and researchers entering the field, this pedagogical introduction to numerical relativity will also interest scientists seeking a broad survey of its challenges and achievements. Assuming only a basic knowledge of classical general relativity, the book develops the mathematical formalism from first principles, and then highlights some of the pioneering simulations involving black holes and neutron stars, gravitational collapse and gravitational waves. The book contains 300 exercises to help readers master new material as it is presented. Numerous illustrations, many in color, assist in visualizing new geometric concepts and highlighting the results of computer simulations. Summary boxes encapsulate some of the most important results for quick reference. Applications covered include calculations of coalescing binary black holes and binary neutron stars, rotating stars, colliding star clusters, gravitational and magnetorotational collapse, critical phenomena, the generation of gravitational waves, and other topics of current physical and astrophysical significance. |

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### Contents

The3+1 decompostion of Einsteins equations | 23 |

Constructing initial data | 54 |

the lapse and shift | 98 |

Matter sources | 123 |

Numerical methods | 183 |

Locating black hole horizons | 229 |

Spherically symmetric spacetimes | 253 |

Gravitational waves | 311 |

Rotating stars | 459 |

Binary neutron star initial data | 506 |

Binary neutron star evolution | 533 |

initial data and evolution | 562 |

Epilogue | 596 |

B Solving the vector Laplacian | 608 |

E PostNewtonian results | 616 |

basic equations | 629 |

Collapse of collisionless clusters in axisymmetry | 352 |

Recasting the evolution equations | 375 |

Binary black hole initial data | 394 |

Binary black hole evolution | 429 |

analytical results | 637 |

647 | |

684 | |

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### Common terms and phrases

3-dimensional ADM mass angular momentum apparent horizon approximation binary black hole binary neutron stars boundary conditions Chapter coefﬁcients collapse collisionless components computational conﬁguration conformal ﬂatness constant constraint equations construct corotational deﬁned deﬁnition density discussion disk dynamical Einstein’s equations energy equilibrium event horizon evolution equations evolve Exercise extrinsic curvature ﬁeld ﬁeld equations Figure ﬁnal ﬁnd ﬁnite difference ﬁrst ﬂuid function geodesic gravitational ﬁeld gravitational radiation gravitational wave grid points Hamiltonian constraint hydrodynamics hypermassive hypersurface inﬁnity initial data integral irrotational ISCO Killing vector lapse Lie derivative linear magnetic ﬁeld maximal slicing merger neutron star Newtonian numerical relativity parameter particles perturbation polar polytropic quasiequilibrium relativistic rest mass rotating satisﬁes scalar ﬁeld scheme Schwarzschild Section Shapiro and Teukolsky Shibata shift Show simulations singularity solution solve source terms spacetime spatial metric speciﬁc spherical symmetry spin stellar stress-energy tensor sufﬁciently supermassive black hole surface tensor variables velocity