On the classical confinement of test particles to a thin 3-brane in the absence of non-gravitational forces

Abstract

The classical confinement condition of test particles to a brane universe in the absence of non-gravitational forces is transformed using the Hamilton-Jacobi formalism. The transformed condition provides a direct criterion for selecting in a cosmological scenario 5D bulk manifolds wherein it is possible to obtain confinement of trajectories to 4D hypersurfaces purely due to classical gravitational effects.

12 pages, version to appear in MPLA

References in corpus (3)

• Extra force in $f(R)$ modified theories of gravity
• Warped product spaces and geodesic motion in the neighbourhood of hypersurfaces
• Geodesic motion in the neighbourhood of submanifolds embedded in warped product spaces