On the embedding of spacetime in five-dimensional Weyl spaces
arXiv:0711.2754 · doi:10.1063/1.3000049
Abstract
We revisit Weyl geometry in the context of recent higher-dimensional theories of spacetime. After introducing the Weyl theory in a modern geometrical language we present some results that represent extensions of Riemannian theorems. We consider the theory of local embeddings and submanifolds in the context of Weyl geometries and show how a Riemannian spacetime may be locally and isometrically embedded in a Weyl bulk. We discuss the problem of classical confinement and the stability of motion of particles and photons in the neighbourhood of branes for the case when the Weyl bulk has the geometry of a warped product space. We show how the confinement and stability properties of geodesics near the brane may be affected by the Weyl field. We construct a classical analogue of quantum confinement inspired in theoretical-field models by considering a Weyl scalar field which depends only on the extra coordinate.
16 pages, new title and references added
References in corpus (20)
- A Large Mass Hierarchy from a Small Extra Dimension
- An Alternative to Compactification
- Kaluza-Klein Gravity
- Brane-world gravity
- Large and infinite extra dimensions
- Four-dimensional gravity on a thick domain wall
- Thick Brane Worlds Arising From Pure Geometry
- Localization of 4D gravity on pure geometrical Thick branes
- Classical confinement of test particles in higher-dimensional models: stability criteria and a new energy condition
- Gauge-Dependent Cosmological "Constant"
- The embedding of the spacetime in five dimensions: an extension of Campbell-Magaard theorem
- Embeddings in Non-Vacuum Spacetimes
- The embedding of the spacetime in five-dimensional spaces with arbitrary non-degenerate Ricci tensor
- Dynamically generated embeddings of spacetime
- Embeddings in Spacetimes Sourced by Scalar Fields
- Warped product spaces and geodesic motion in the neighbourhood of hypersurfaces
- On the embedding of branes in five-dimensional spaces
- Wesson's IMT with a Weylian bulk
- Confinement and stability of the motion of test particles in thick branes
- Einstein spaces in warped geometries in five dimensions
Cited by in corpus (13)
- General Relativity and Weyl Geometry
- From Brans-Dicke gravity to a geometrical scalar-tensor theory
- Inducing the cosmological constant from five-dimensional Weyl space
- Space-time singularities in Weyl manifolds
- Cosmological models in Weyl geometrical scalar-tensor theory
- Acceleration in Weyl integrable spacetime
- Brane Cosmology and Motion of Test Particles in Five-Dimensional Warped Product Spacetimes
- An Invariant Approach to Weyl's unified field theory
- A scalar field inducing a non-metrical contribution to gravitational acceleration and a compatible add-on to light deflection
- Pure Geometric Branes and Mass Hierarchy
- On the embedding of Weyl manifolds
- Fermion confinement induced by geometry
- Weyl frames and canonical transformations in geometrical scalar-tensor theories of gravity