Brane Universe: Global Geometry

The global geometries of bulk vacuum space-times in the brane-universe models are investigated and classified in terms of geometrical invariants. The corresponding Carter-Penrose diagrams and embedding diagrams are constructed. It is shown that for a given energy-momentum induced on the brane there can be different types of global geometries depending on the signs of a bulk cosmological term and surface energy density of the brane (the sign of the latter does not influence the internal cosmological evolution). It is shown that in the Randall-Sundrum scenario it is possible to have an asymmetric hierarchy splitting even with a $Z_2$-symmetric matching of "our" brane to the bulk.

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