A simple property of the Weyl tensor for a shear, vorticity and acceleration-free velocity field
Articolo
Data di Pubblicazione:
2018
Citazione:
A simple property of the Weyl tensor for a shear, vorticity and acceleration-free velocity field / L.G. Molinari, C.A. Mantica. - In: GENERAL RELATIVITY AND GRAVITATION. - ISSN 0001-7701. - 50:7(2018 Jul 01), pp. 81.1-81.7. [10.1007/s10714-018-2398-9]
Abstract:
We prove that, in a space-time of dimension n > 3 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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Weyl tensor; Twisted space-time; Generalized Robertson–Walker space-time; Torse-forming vector; Generalized curvature tensor
Elenco autori:
L.G. Molinari, C.A. Mantica
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