Gravity on branes

Abstract

We consider the four dimensional discontinuity generated by two identical pieces of a five dimensional space pasted along their edge (that is a "brane" in a "$Z_2$-symmetric" "bulk"). Using a four plus one decomposition of the Riemann tensor we write the equations for gravity on the brane and recover in a simple manner a number of known "brane world" scenarios. We study under which conditions these equations reduce, exactly or approximately, to the four dimensional Einstein equations. We conclude that if the bulk is imposed to be only an Einstein space near the brane, Einstein's equations can be recovered approximately on the brane, but if it is imposed to be strictly anti-de Sitter space then the Einstein equations cannot hold, even approximately, on a quasi-Minkowskian brane, unless matter obeys a very contrived equation of state.

16 pages, plain TeX, no figures

References in corpus (3)

• Large-scale cosmological perturbations on the brane
• Cosmological Perturbations in Brane Worlds: Brane Bending and Anisotropic Stresses
• On linearized gravity in the Randall-Sundrum scenario

Cited by in corpus (17)

• Searching Exact Solutions for Compact Stars in Braneworld: a conjecture
• Radion and Holographic Brane Gravity
• On Brane World Cosmological Perturbations
• Cosmological perturbations in the bulk and on the brane
• Collapsing sphere on the brane radiates
• Non-uniform Braneworld Stars: an Exact Solution
• Brane World Cosmology with Gauss-Bonnet Interaction
• Does The Force From an Extra Dimension Contradict Physics in 4D?
• Stars on branes: the view from the brane
• Mass and Charge in Brane-World and Non-Compact Kaluza-Klein Theories in 5 Dim
• On linearized gravity in the Randall-Sundrum scenario
• Invariant definition of rest mass and dynamics of particles in 4D from bulk geodesics in brane-world and non-compact Kaluza-Klein theories
• On the embedding of branes in five-dimensional spaces
• Low energy effective gravitational equations on a Gauss-Bonnet brane
• Cosmological perturbations of an expanding brane in an anti-de Sitter bulk: a short review
• Embeddings for General Relativity
• Linearized Israel Matching Conditions for Cosmological Perturbations in a Moving Brane Background