Brane-localized Gravity

* Foreword by Alan H Guth * Why Higher Dimensions are Interesting * The Randall-Sundrum Set-Up * General Structure of Anti-de Sitter Spacetimes * General Properties of Embeddings * The Israel Junction Conditions * The Newtonian Limit of an Embedded Brane * Embedding of Static Robertson-Walker Branes and Negative Pressure * Embedding of de Sitter and Anti-de Sitter Branes in AdS5 * Embedding of Non-Static Robertson-Walker Branes in AdS5 * Embedding Robertson-Walker Brane Worlds in M(4,2) * Null Geodesics of AdS5 Bulks Containing Robertson-Walker Branes * Generalized Einstein Equations on the Brane * General Structure of Brane-World Gravitational Fluctuations * Transverse-Traceless M4 Fluctuation Modes * Transverse-Traceless dS4/AdS4 Fluctuation Modes * Normalization of Fluctuation Modes and Curved Space Gauss's Law * Fluctuations around an Embedded Positive-Tension Minkowski Brane * Fluctuations around an Embedded Negative-Tension Minkowski Brane * Fluctuations around an Embedded Positive-Tension AdS Brane * Equivalent Schrodinger Equation Treatment of the Fluctuation Equation * Fluctuations around an Embedded Positive-Tension dS Brane * Dynamically Generated Domain Walls and the Brane World * Appendices: * Gauge Invariance of the Fluctuation Equation * Perturbative Weyl Tensor * Transverse and Transverse-Traceless Projection * Fluctuation Energy-Momentum Tensor * Retarded Propagators for Pure AdS and Pure dS Spacetimes * Embedding M(2,1) Branes in AdS4