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- Title
A simple property of the Weyl tensor for a shear, vorticity and acceleration-free velocity field.
- Authors
Molinari, Luca Guido; Mantica, Carlo Alberto
- Abstract
We prove that, in a space-time of dimension n>3<inline-graphic></inline-graphic> with a velocity field that is shear-free, vorticity-free and acceleration-free, the covariant divergence of the Weyl tensor is zero if and only if the contraction of the Weyl tensor with the velocity is zero. This extends a property found in generalised Robertson-Walker spacetimes, where the velocity is also eigenvector of the Ricci tensor. Despite the simplicity of the statement, the proof is involved. As a product of the same calculation, we introduce a curvature tensor with an interesting recurrence property.
- Subjects
TENSOR algebra; VORTEX motion; FLOW velocity; SPACETIME; EIGENVECTORS
- Publication
General Relativity & Gravitation, 2018, Vol 50, Issue 7, p1
- ISSN
0001-7701
- Publication type
Article
- DOI
10.1007/s10714-018-2398-9