This 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is provided for both students and workers in the field, with a significant amount of the material being previously unpublished.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.

Contents:

• 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 Schrödinger 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

“In this book Philip Mannheim has presented a self-contained and fully-detailed description of brane-world physics. It is not just a summary of the literature, but it is truly an elaboration on the literature. All of the derivations are laid out in a consistent formalism and in complete detail. The book should be a valuable resource to anyone who is interested in following the progress of this exciting area of theoretical physics.”