Confinement of test particles in warped spacetimes

TL;DR

This paper analyzes test particle trajectories in warped spacetimes with a thick brane, revealing conditions for confinement or escape based on the warp factor's behavior, using analytical and numerical dynamical systems methods.

Contribution

It provides a new dynamical systems approach to understanding particle confinement in warped thick brane models with time-dependent extra dimensions.

Findings

Oscillatory motion indicates confinement for growing warp factors.

Runaway trajectories occur with decaying warp factors.

Numerical results confirm analytical dynamical system predictions.

Abstract

We investigate test particle trajectories in warped spacetimes with a thick brane warp factor, a cosmological on--brane line element and a time dependent extra dimension. The geodesic equations are reduced to a first order autonomous dynamical system. Using analytical methods, we arrive at some useful general conclusions regarding possible trajectories. Oscillatory motion, suggesting confinement about the location of the thick brane, arises for a growing warp factor. On the other hand, we find runaway trajectories (exponential-like) for a decaying warp factor. Variations of the extra dimensional scale factor yield certain quantitative differences. Results obtained from explicit numerical evaluations match well with the qualitative conclusions obtained from the dynamical systems analysis.