Decomposition of geometric perturbations

Details Decomposition of geometric perturbations Decomposition of geometric perturbations

2008-11-12

arxiv.org/abs/0811.1781v1

Phys.Lett.B674:313-315,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages

Scientific paper

10.1016/j.physletb.2009.03.043

For an infinitesimal deformation of a Riemannian manifold, we prove that the scalar, vector, and tensor modes in decompositions of perturbations of the metric tensor, the scalar curvature, the Ricci tensor, and the Einstein tensor decouple if and only if the manifold is Einstein. Four-dimensional space-time satisfying the condition of the theorem is homogeneous and isotropic. Cosmological applications are discussed.

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