Classical confinement of test particles in higherdimensional models: Stability criteria and a new energy condition
Abstract
We review the circumstances under which test particles can be localized around a spacetime section Σ_{0} smoothly contained within a codimension1 embedding space M. If such a confinement is possible, Σ_{0} is said to be totally geodesic. Using three different methods, we derive a stability condition for trapped test particles in terms of intrinsic geometrical quantities on Σ_{0} and M; namely, confined paths are stable against perturbations if the gravitational stressenergy density on M is larger than that on Σ_{0}, as measured by an observed travelling along the unperturbed trajectory. We confirm our general result explicitly in two different cases: the warpedproduct metric ansatz for (n+1)dimensional Einstein spaces, and a known solution of the 5dimensional vacuum field equation embedding certain 4dimensional cosmologies. We conclude by defining a confinement energy condition that can be used to classify geometries incorporating totally geodesic submanifolds, such as those found in thick braneworld and other 5dimensional scenarios.
 Publication:

Physical Review D
 Pub Date:
 November 2003
 DOI:
 10.1103/PhysRevD.68.104027
 arXiv:
 arXiv:hepth/0309081
 Bibcode:
 2003PhRvD..68j4027S
 Keywords:

 04.20.Jb;
 11.10.Kk;
 Exact solutions;
 Field theories in dimensions other than four;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 9 pages, REVTeX4, in press in Phys. Rev. D