## Brane-localized GravityThis timely and valuable book provides a detailed pedagogical introduction and treatment of the brane-localized gravity program of Randall and Sundrum, in which gravitational signals are able to localize around our four-dimensional world in the event that it is a brane embedded in an infinitely-sized, higher dimensional anti-de Sitter bulk space. A completely self-contained development of the material needed for brane-world studies is provided for both students and workers in the field, with a significant amount of the material being previously unpublished. Particular attention is given to issues not ordinarily treated in the brane-world literature, such as the completeness of tensor gravitational fluctuation modes, the causality of brane-world propagators, and the status of the massless graviton fluctuation mode in brane worlds in which it is not normalizable. |

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### Contents

I | 1 |

II | 7 |

III | 15 |

IV | 23 |

V | 27 |

VI | 33 |

VII | 39 |

VIII | 45 |

XIII | 81 |

XIV | 89 |

XV | 99 |

XVI | 109 |

XVII | 133 |

XVIII | 167 |

XIX | 189 |

XX | 229 |

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### Common terms and phrases

4-dimensional AdS5 AdSf analog asymptotic axial gauge background based propagator basis modes behave Bessel functions brane world bulk causal propagator Chapter components contribution coordinate cosmological constant covariant delta function derivative discrete domain wall Einstein equations Einstein tensor embedded energy energy-momentum tensor evaluate exact solution finite fluctuation equations gauge invariant gauge transformation geometry given in Eq gravity harmonic gauge integration iY2 based junction condition KK continuum lightcone massless graviton metric of Eq mode basis negative non-normalizable normalizable null geodesies obey obtain parameter perturbative plane potential propagator of Eq quantity Randall-Sundrum region Riemann tensor RW brane scalar field second order sector singular small H limit solutions to Eq source-free spacetime Specifically square step static surface term symmetry take support take the form term in Eq theory transverse TT mode TT TT warp factor wave equation wave function Weyl tensor yield zero