Topological and Geometrical Properties of Brane-Worlds
arXiv:1102.4468 · doi:10.1142/S0219887811005580
Abstract
We study the geometrical and topological properties of the bulk (environment space) when we modify the geometry or topology of a brane-world. Through the characterization of a spherically symmetric space-time as a local brane-world immersed into six dimensional pseudo-Euclidean spaces, with different signatures of the bulk, we investigate the existence of a topological difference in the immersed brane-world. In particular the Schwarzschild's brane-world and its Kruskal (or Fronsdal) brane-world extension are examined from point of view of the immersion formalism. We prove that there is a change of signature of the bulk when we consider a local isometric immersion and different topologies of a brane-world in that bulk.
arXiv comment9 pages, accepted for publication in Int. J. Geom. Metho. Mod. Phys