Living Reviews in Relativity

"Brane-World Gravity"
by
Roy Maartens  

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Abstract
1 Introduction
1.1 Heuristics of higher-dimensional gravity
1.2 Brane-worlds and M theory
1.3 Heuristics of KK modes
2 Randall–Sundrum Brane-Worlds
3 Covariant Approach to Brane-World Geometry and Dynamics
3.1 Field equations on the brane
3.2 5-dimensional equations and the initial-value problem
3.3 The brane viewpoint: A 1+3-covariant analysis
3.4 Conservation equations
3.5 Propagation and constraint equations on the brane
4 Gravitational Collapse and Black Holes on the Brane
4.1 The black string
4.2 Taylor expansion into the bulk
4.3 The “tidal charge” black hole
4.4 Realistic black holes
4.5 Oppenheimer–Snyder collapse gives a non-static black hole
4.6 AdS/CFT and black holes on 1-brane RS-type models
5 Brane-World Cosmology: Dynamics
5.1 Brane-world inflation
5.2 Brane-world instanton
5.3 Models with non-empty bulk
6 Brane-World Cosmology: Perturbations
6.1 1 + 3-covariant perturbation equations on the brane
6.2 Metric-based perturbations
6.3 Density perturbations on large scales
6.4 Curvature perturbations and the Sachs–Wolfe effect
6.5 Vector perturbations
6.6 Tensor perturbations
7 Gravitational Wave Perturbations in Brane-World Cosmology
8 CMB Anisotropies in Brane-World Cosmology
8.1 The low-energy approximation
8.2 The simplest model
9 Conclusion
10 Acknowledgments
Open References References
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