Mathematical Support to Braneworld Theory

Details Mathematical Support to Braneworld Theory Mathematical Support to Braneworld Theory

2008-03-07

arxiv.org/abs/0803.1004v1

Int.J.Geom.Meth.Mod.Phys.04:1259-1267,2008

Mathematics

Differential Geometry

10 pages

Scientific paper

10.1142/S0219887807002557

The braneworld theory appear with the purpose of solving the problem of the hierarchy of the fundamental interactions. The perspectives of the theory emerge as a new physics, for example, deviation of the law of Newton's gravity. One of the principles of the theory is to suppose that the braneworld is local submanifold in a space of high dimension, the bulk, solution of Einstein's equations in high dimension. In this paper we approach the mathematical consistency of this theory with a new proof of the fundamental theorem of submanifolds for case of semi-Riemannian manifolds. This theorem consist an essential mathematical support for this new theory. We find the integrability conditions for the existence of space-time submanifolds in a pseudo-Euclidean space. Keywords: Submanifolds, Braneworld, Pseudo-Riemannian geometry

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