## Gravity: Newtonian, Post-Newtonian, RelativisticThis textbook explores approximate solutions to general relativity and their consequences. It offers a unique presentation of Einstein's theory by developing powerful methods that can be applied to astrophysical systems. Beginning with a uniquely thorough treatment of Newtonian gravity, the book develops post-Newtonian and post-Minkowskian approximation methods to obtain weak-field solutions to the Einstein field equations. The book explores the motion of self-gravitating bodies, the physics of gravitational waves, and the impact of radiative losses on gravitating systems. It concludes with a brief overview of alternative theories of gravity. Ideal for graduate courses on general relativity and relativistic astrophysics, the book examines real-life applications, such as planetary motion around the Sun, the timing of binary pulsars, and gravitational waves emitted by binary black holes. Text boxes explore related topics and provide historical context, and over 100 exercises present challenging tests of the material covered in the main text. |

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### Contents

Foundations of Newtonian gravity | 1 |

Structure of selfgravitating bodies | 63 |

Newtonianorbitaldynamics | 138 |

Minkowskispacetime | 189 |

Curvedspacetime | 217 |

Formulation | 290 |

Implementation | 328 |

Fundamentals | 371 |

System of isolated bodies | 414 |

PostNewtonian celestial mechanics astrometry and navigation | 480 |

Gravitationalwaves | 539 |

Radiative losses and radiation reaction | 624 |

Alternative theories of gravity | 699 |

760 | |

771 | |

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acceleration angular momentum approximation back in Sec binary body body’s calculate center-of-mass Christoffel symbols components computation conservation constant contribution deﬁned derivative described differential displayed in Eq dynamics Earth Einstein Einstein field equations energy energy-momentum tensor equations of motion evaluated expansion expression ﬁeld field equations ﬁnal ﬁnd ﬁrst fluid element frame function gauge geodesic gravitational field gravitational potentials gravitational waves gravitational-wave harmonic implies inertial insert involving Keplerian mass density measured metric multipole moments neutron stars Newtonian potential observer obtain ofthe orbital elements parameter particle pericenter perturbation photon plane post-Minkowskian post-Newtonian post-Newtonian expansion precession pseudotensor quadrupole radiation radiation-reaction radiative radius relativistic relativity Riemann tensor rotating scalar solution spatial spherical spin surface integral symmetric theory tidal transformation vanishes variables vector virial theorem wave equation wave zone world line αβ