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… 

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

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

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