Loterre: Mathematics: Weyl curvature tensor

geometry > differential geometry > Riemannian geometry > Weyl curvature tensor

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Weyl curvature tensor

In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo-Riemannian manifold. Like the Riemann curvature tensor, the Weyl tensor expresses the tidal force that a body feels when moving along a geodesic. The Weyl tensor differs from the Riemann curvature tensor in that it does not convey information on how the volume of the body changes, but rather only how the shape of the body is distorted by the tidal force. The Ricci curvature, or trace component of the Riemann tensor contains precisely the information about how volumes change in the presence of tidal forces, so the Weyl tensor is the traceless component of the Riemann tensor. This tensor has the same symmetries as the Riemann tensor, but satisfies the extra condition that it is trace-free: metric contraction on any pair of indices yields zero. It is obtained from the Riemann tensor by subtracting a tensor that is a linear expression in the Ricci tensor.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Weyl_tensor)

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