The Embedding of Schwarzschild in Braneworld

Abstract

The braneworlds models were inspired partly by Kaluza-Klein's theory, where both the gravitational and the gauge fields are obtained from the geometry of a higher dimensional space. The positive aspects of these models consist in perspectives of modifications it could bring in to particle physics, such as: unification in a TeV scale, quantum gravity in this scale and deviation of Newton's law for small distances. One of the principles of these models is to suppose that all space-times can be embedded in a bulk of higher dimension. The main result in these notes is a theorem showing a mathematical inconsistency of the Randall-Sundrum braneworld model, namely that the Schwarzschild space-time cannot be embedded locally and isometrically in a five dimensional bulk with constant curvature,(for example AdS-5). From the point of view of semi-Riemannian geometry this last result represents a serious restriction to the Randall-Sundrum's braneworld model.

Published in the Int. J. Theor. Phys, 2008

References in corpus (11)

• A Large Mass Hierarchy from a Small Extra Dimension
• The Hierarchy Problem and New Dimensions at a Millimeter
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• Large and infinite extra dimensions
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Cited by in corpus (4)

• Null fluid collapse in brane world models
• On the thermal stability of a static spherically symmetric black holes in Nash embedding framework
• On Quasinormal Modes for Scalar Perturbations of Static Spherically Symmetric Black Holes in Nash Embedding Framework
• Topological and Geometrical Properties of Brane-Worlds