Ideally embedded space-times

Abstract

Due to the growing interest in embeddings of space-time in higher-dimensional spaces we consider a specific type of embedding. After proving an inequality between intrinsically defined curvature invariants and the squared mean curvature, we extend the notion of ideal embeddings from Riemannian geometry to the indefinite case. Ideal embeddings are such that the embedded manifold receives the least amount of tension from the surrounding space. Then it is shown that the de Sitter spaces, a Robertson-Walker space-time and some anisotropic perfect fluid metrics can be ideally embedded in a five-dimensional pseudo-Euclidean space.

layout changed and typos corrected; uses revtex4

References in corpus (9)

• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• Kaluza-Klein Gravity
• Application of the Campbell-Magaard theorem to higher-dimensional physics
• On Applications of Campbell's Embedding Theorem
• The embedding of the spacetime in five dimensions: an extension of Campbell-Magaard theorem
• The Structure of the Big Bang from Higher-Dimensional Embeddings
• Embeddings in Non-Vacuum Spacetimes
• The embedding of the spacetime in five-dimensional spaces with arbitrary non-degenerate Ricci tensor

Cited by in corpus (2)

• Modified Brans-Dicke theory of gravity from five-dimensional vacuum
• Classification of ideal submanifolds of real space forms with type number $\le 2$