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

TL;DR

This paper reformulates the classical confinement condition of test particles to a brane universe using Hamilton-Jacobi formalism, providing a criterion for confinement via gravitational effects in 5D bulk scenarios.

Contribution

It introduces a Hamilton-Jacobi-based criterion to identify 5D bulk manifolds that allow gravitational confinement of particles to a 4D brane.

Findings

Provides a direct confinement criterion in 5D cosmological models

Shows confinement can occur purely through gravitational effects

Offers a new perspective on brane-world particle dynamics

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.