TL;DR
This paper classifies the global geometries of bulk vacuum space-times in brane-universe models, analyzing how different parameters affect the overall structure and hierarchy, with implications for Randall-Sundrum scenarios.
Contribution
It provides a comprehensive classification of bulk geometries in brane models using invariants and constructs diagrams to illustrate their structures.
Findings
Multiple global geometries exist for a given brane energy-momentum.
Different signs of bulk cosmological constant and brane surface energy lead to distinct geometries.
Asymmetric hierarchy splitting can occur even with symmetric brane-bulk matching.
Abstract
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 -symmetric matching of "our" brane to the bulk.
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