TOPOLOGICAL AND GEOMETRICAL PROPRIETIES OF BRANE-WORLDS

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 Frønsdal) 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.