2003/09/08 by Sanjeev S. Seahra
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.68.104027
published as Phys.Rev. D68 (2003) 104027 · 9 pages, REVTeX4, in press in Phys. Rev. D
arxiv created 2003/09/08 · openalex publication_date 2003/11/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We review the circumstances under which test particles can be localized around a spacetime section \ensuremathΣ0 smoothly contained within a codimension-1 embedding space M. If such a confinement is possible, \ensuremathΣ0 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 \ensuremathΣ0 and M; namely, confined paths are stable against perturbations if the gravitational stress-energy density on M is larger than that on \ensuremathΣ0, as measured by an observed travelling along the unperturbed trajectory. We confirm our general result explicitly in two different cases: the warped-product metric ansatz for (n+1)-dimensional Einstein spaces, and a known solution of the 5-dimensional vacuum field equation embedding certain 4-dimensional 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 5-dimensional scenarios.