Motion in Brane World Models: The Bazanski Approach

Recently, path equations have been obtained for charged, spinning objects in brane world models, using a modified Bazanski Lagrangian. In this study, path deviation equations of extended objects are derived. The significance of moving extended objects in brane world models is examined. Motion in non- symmetric brane world models is also considered.Comment: A paper presented at the Thirteenth International Symposium on Particles, Strings and Cosmology PASCOS-07, held in London, 2-7 July 200

Path and Path Deviation Equations for p-branes

Path and path deviation equations for neutral, charged, spinning and spinning charged test particles, using a modified Bazanski Lagrangian, are derived. We extend this approach to strings and branes. We show how the Bazanski Lagrangian for charged point particles and charged branes arises `a la Kaluza-Klein from the Bazanski Lagrangian in 5-dimensions.Comment: 13 pages, LaTeX fil

Geodesic motion in the neighbourhood of submanifolds embedded in warped product spaces

We study the classical geodesic motions of nonzero rest mass test particles and photons in (3+1+n)- dimensional warped product spaces. An important feature of these spaces is that they allow a natural decoupling between the motions in the (3+1)-dimensional spacetime and those in the extra n dimensions. Using this decoupling and employing phase space analysis we investigate the conditions for confinement of particles and photons to the (3+1)- spacetime submanifold. In addition to providing information regarding the motion of photons, we also show that these motions are not constrained by the value of the extrinsic curvature. We obtain the general conditions for the confinement of geodesics in the case of pseudo-Riemannian manifolds as well as establishing the conditions for the stability of such confinement. These results also generalise a recent result of the authors concerning the embeddings of hypersurfaces with codimension one.Comment: 8 pages, 1 figure. To appear in General Relativity and Gravitation as a contributed paper to Mashhoon Festschrif