## Theory of Gravitational InteractionsThis is the second edition of a well-received book that is a modern, self-contained introduction to the theory of gravitational interactions. The new edition includes more details on gravitational waves of cosmological origin, the so-called brane world scenario, and gravitational time-delay effects.The first part of the book follows the traditional presentation of general relativity as a geometric theory of the macroscopic gravitational field, while the second, more advanced part discusses the deep analogies (and differences) between a geometric theory of gravity and the gauge theories of the other fundamental interactions. This fills a gap within the traditional approach to general relativity which usually leaves students puzzled about the role of gravity. The required notions of differential geometry are reduced to the minimum, allowing room for aspects of gravitational physics of current phenomenological and theoretical interest, such as the properties of gravitational waves, the gravitational interactions of spinors, and the supersymmetric and higher-dimensional generalization of the Einstein equations. This textbook is primarily intended for students pursuing a theoretical or astroparticle curriculum but is also relevant for PhD students and young researchers. |

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### Contents

1 | |

3 Tensor Calculus in a Riemann Manifold | 41 |

5 Test Bodies and Signals in a Riemann SpaceTime | 80 |

6 Geodesic Deviation and Curvature Tensor | 95 |

7 The Einstein Equations for the Gravitational Field | 115 |

8 The WeakField Approximation | 141 |

9 Gravitational Waves | 159 |

10 The Schwarzschild Solution | 202 |

11 The Kasner Solution | 231 |

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### Common terms and phrases

action antisymmetric tensor applying brane characterized chart components compute condition consider constant context contravariant contribution coordinate transformation corresponding cosmological covariant derivative curvature curved defined definition density described differential dimensions Dirac effective Einstein equations electromagnetic energy-momentum tensor equations of motion explicit explicitly exterior exterior covariant derivative four-dimensional Gauss theorem geodesic geometry given global gravitational field gravitational interaction gravitational waves gravitino higher-dimensional hypersurface infinitesimal integration invariance isometry Killing vectors Lagrangian line-element linear Lorentz connection metric tensor Minkowski metric Minkowski space–time momentum obtain parameter particle particular physical polarization propagation properties radiation recall respect result Riemann geometry Riemann tensor satisfied scalar scalar curvature Schwarzschild Sect so-called solution sources space–time manifold spatial spinor static supergravity supersymmetry symmetric test body theory torsion trajectory vanishing variation vierbeins ξμ