# A simple property of the Weyl tensor for a shear, vorticity and acceleration-free velocity field

@article{Molinari2018ASP, title={A simple property of the Weyl tensor for a shear, vorticity and acceleration-free velocity field}, author={Luca Guido Molinari and Carlo Alberto Mantica}, journal={General Relativity and Gravitation}, year={2018}, volume={50}, pages={1-7} }

We prove that, in a space-time of dimension $$n>3$$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…

## 4 Citations

### Correction to: A simple property of the Weyl tensor for a shear, vorticity and acceleration-free velocity field

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In our paper “A simple property of the Weyl tensor for a shear, vorticity and acceleration-free velocity field”.

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## References

SHOWING 1-10 OF 15 REFERENCES

### Weyl compatible tensors

- Mathematics
- 2014

We introduce the new algebraic property of Weyl compatibility for symmetric tensors and vectors. It is strictly related to Riemann compatibility, which generalizes the Codazzi condition while…

### Uniqueness of Noncompact Spacelike Hypersurfaces of Constant Mean Curvature in Generalized Robertson–Walker Spacetimes

- Mathematics
- 2002

On any spacelike hypersurface of constant mean curvature of a Generalized Robertson–Walker spacetime, the hyperbolic angle θ between the future-pointing unit normal vector field and the universal…

### Twisted Lorentzian manifolds: a characterization with torse-forming time-like unit vectors

- Mathematics
- 2016

Robertson–Walker and generalized Robertson–Walker spacetimes may be characterized by the existence of a time-like unit torse-forming vector field, with other constrains. We show that Twisted…

### Minimal tensors and purely electric or magnetic spacetimes of arbitrary dimension

- Mathematics
- 2012

We consider time reversal transformations to obtain twofold orthogonal splittings of any tensor on a Lorentzian space of arbitrary dimension n. Applied to the Weyl tensor of a spacetime, this leads…

### Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes

- Mathematics
- 1995

A new technique is introduced in order to solve the following question:When is a complete spacelike hypersurface of constant mean curvature in a generalized Robertson-Walker spacetime totally…

### A simple characterization of generalized Robertson–Walker spacetimes

- Mathematics
- 2014

A generalized Robertson–Walker spacetime is the warped product with base an open interval of the real line endowed with the opposite of its metric and base any Riemannian manifold. The family of…

### Tensors, differential forms, and variational principles

- Mathematics
- 1975

A self-contained, reasonably modern account of tensor analysis and the calculus of exterior differential forms, adapted to the needs of physicists, engineers and applied mathematicians is presented.

### Rectifying submanifolds of Riemannian manifolds and torqued vector fields

- Mathematics
- 2017

Recently, the author defined and classified rectifying submanifolds in Euclidean spaces in [12]; extending his earlier work on rectifying curves in Euclidean 3-space done in [6]. In this article,…

### Generalized Robertson-Walker spacetimes — A survey

- Economics
- 2017

Generalized Robertson–Walker spacetimes extend the notion of Robertson–Walker spacetimes, by allowing for spatial non-homogeneity. A survey is presented, with main focus on Chen's characterization ...