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Topological and Geometrical Properties of Brane-Worlds

By Edmundo M. Monte

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.Comment: 9 pages, accepted for publication in Int. J. Geom. Metho. Mod. Phy

Topics: General Relativity and Quantum Cosmology, Mathematical Physics
Year: 2011
DOI identifier: 10.1142/S0219887811005580
OAI identifier: oai:arXiv.org:1102.4468
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