Geodesics, the Equivalence Principle and Singularities in Higher-dimensional General Relativity and Braneworlds

Abstract

The geodesics of a spacetime seldom coincide with those of an embedded submanifold of codimension one. We investigate this issue for higher-dimensional general relativity-like models, firstly in the simpler case without branes to isolate which features are already present, and then in the more complicated case with branes. The framework in which we consider branes is general enough to include asymmetric braneworlds but not thick branes. We apply our results on geodesics to study both the equivalence principle and cosmological singularities. Among the models we study these considerations favour $Z_2$ symmetric braneworlds with a negative bulk cosmological constant.

20 pages, 2 figures. Accepted by JCAP. Minor proofreading corrections; several references added

References in corpus (5)

• Can codimension-two branes solve the cosmological constant problem?
• Asymmetric brane-worlds with induced gravity
• Bulk phantom fields, increasing warp factors and fermion localisation
• Asymmetric radiating brane-world
• Generalised cosmology of codimension-two braneworlds

Cited by in corpus (8)

• Black string corrections in variable tension braneworld scenarios
• Warped product spaces and geodesic motion in the neighbourhood of hypersurfaces
• Confinement and stability of the motion of test particles in thick branes
• Regular Bulk Solutions and Black Strings from Dynamical Braneworlds with Variable Tension
• Construction of topological defect networks with complex scalar fields
• Geodesic motion in the neighbourhood of submanifolds embedded in warped product spaces
• Quantum Cosmological Relational Model of Shape and Scale in 1-d
• Evolution of thin shells in D-dimensional General Relativity