Ideally embedded space-times

Details Ideally embedded space-times Ideally embedded space-times

2003-08-21

arxiv.org/abs/gr-qc/0308066v2

J.Math.Phys. 45 (2004) 1497-1510

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

layout changed and typos corrected; uses revtex4

Scientific paper

10.1063/1.1668333

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.

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