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• Weyl_tensor abstract "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. It is a tensor that has the same symmetries as the Riemann tensor with the extra condition that it be trace-free: metric contraction on any pair of indices yields zero.In general relativity, the Weyl curvature is the only part of the curvature that exists in free space—a solution of the vacuum Einstein equation—and it governs the propagation of gravitational radiation through regions of space devoid of matter. More generally, the Weyl curvature is the only component of curvature for Ricci-flat manifolds and always governs the characteristics of the field equations of an Einstein manifold.In dimensions 2 and 3 the Weyl curvature tensor vanishes identically. In dimensions ≥ 4, the Weyl curvature is generally nonzero. If the Weyl tensor vanishes in dimension ≥ 4, then the metric is locally conformally flat: there exists a local coordinate system in which the metric tensor is proportional to a constant tensor. This fact was a key component of Nordström's theory of gravitation, which was a precursor of general relativity.".
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• Weyl_tensor wikiPageLength "8502".
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• Weyl_tensor wikiPageRevisionID "639308797".
• Weyl_tensor wikiPageWikiLink Antisymmetric_tensor.
• Weyl_tensor wikiPageWikiLink Atlas_(topology).
• Weyl_tensor wikiPageWikiLink Category:Riemannian_geometry.
• Weyl_tensor wikiPageWikiLink Category:Tensors_in_general_relativity.
• Weyl_tensor wikiPageWikiLink Christoffel_symbols.
• Weyl_tensor wikiPageWikiLink Conformal_map.
• Weyl_tensor wikiPageWikiLink Conformally_flat.
• Weyl_tensor wikiPageWikiLink Conformally_flat_manifold.
• Weyl_tensor wikiPageWikiLink Cotton_tensor.
• Weyl_tensor wikiPageWikiLink Curvature.
• Weyl_tensor wikiPageWikiLink Curvature_of_Riemannian_manifolds.
• Weyl_tensor wikiPageWikiLink Differential_geometry.
• Weyl_tensor wikiPageWikiLink Direct_sum_of_vector_bundles.
• Weyl_tensor wikiPageWikiLink Einstein_field_equation.
• Weyl_tensor wikiPageWikiLink Einstein_field_equations.
• Weyl_tensor wikiPageWikiLink Einstein_manifold.
• Weyl_tensor wikiPageWikiLink General_relativity.
• Weyl_tensor wikiPageWikiLink Geodesic.
• Weyl_tensor wikiPageWikiLink Gravitational_radiation.
• Weyl_tensor wikiPageWikiLink Gravitational_wave.
• Weyl_tensor wikiPageWikiLink Hermann_Weyl.
• Weyl_tensor wikiPageWikiLink Integrability_condition.
• Weyl_tensor wikiPageWikiLink Integrability_conditions_for_differential_systems.
• Weyl_tensor wikiPageWikiLink Irreducible_representation.
• Weyl_tensor wikiPageWikiLink Isothermal_coordinates.
• Weyl_tensor wikiPageWikiLink Kulkarni–Nomizu_product.
• Weyl_tensor wikiPageWikiLink Lanczos_tensor.
• Weyl_tensor wikiPageWikiLink Local_coordinate_system.
• Weyl_tensor wikiPageWikiLink Method_of_characteristics.
• Weyl_tensor wikiPageWikiLink Metric_tensor.
• Weyl_tensor wikiPageWikiLink Necessary_condition.
• Weyl_tensor wikiPageWikiLink Necessity_and_sufficiency.
• Weyl_tensor wikiPageWikiLink Nordstrxc3xb6ms_theory_of_gravitation.
• Weyl_tensor wikiPageWikiLink Orthogonal.
• Weyl_tensor wikiPageWikiLink Orthogonal_group.
• Weyl_tensor wikiPageWikiLink Orthogonality.
• Weyl_tensor wikiPageWikiLink Peeling_theorem.
• Weyl_tensor wikiPageWikiLink Petrov_classification.
• Weyl_tensor wikiPageWikiLink Plebanski_tensor.
• Weyl_tensor wikiPageWikiLink Pseudo-Riemannian_manifold.
• Weyl_tensor wikiPageWikiLink Ricci-flat_manifold.
• Weyl_tensor wikiPageWikiLink Ricci_curvature.
• Weyl_tensor wikiPageWikiLink Ricci_decomposition.
• Weyl_tensor wikiPageWikiLink Ricci_tensor.
• Weyl_tensor wikiPageWikiLink Riemann_curvature_tensor.
• Weyl_tensor wikiPageWikiLink Scalar_curvature.
• Weyl_tensor wikiPageWikiLink Schouten_tensor.
• Weyl_tensor wikiPageWikiLink Spacetime.
• Weyl_tensor wikiPageWikiLink Special_orthogonal_group.
• Weyl_tensor wikiPageWikiLink Springer-Verlag.
• Weyl_tensor wikiPageWikiLink Springer_Science+Business_Media.
• Weyl_tensor wikiPageWikiLink Sufficient_condition.
• Weyl_tensor wikiPageWikiLink Tensor.
• Weyl_tensor wikiPageWikiLink Tensor_contraction.
• Weyl_tensor wikiPageWikiLink The_Large_Scale_Structure_of_Space-Time.
• Weyl_tensor wikiPageWikiLink Tidal_force.
• Weyl_tensor wikiPageWikiLink Trace_(linear_algebra).
• Weyl_tensor wikiPageWikiLink Traceless.
• Weyl_tensor wikiPageWikiLink Vector_bundle.
• Weyl_tensor wikiPageWikiLink Weyl_curvature_hypothesis.
• Weyl_tensor wikiPageWikiLink Weyl_scalar.
• Weyl_tensor wikiPageWikiLinkText "Weyl Tensor".
• Weyl_tensor wikiPageWikiLinkText "Weyl curvature tensor".
• Weyl_tensor wikiPageWikiLinkText "Weyl tensor".
• Weyl_tensor wikiPageWikiLinkText "Weyl".
• Weyl_tensor wikiPageWikiLinkText "Weyl's tensor".
• Weyl_tensor hasPhotoCollection Weyl_tensor.
• Weyl_tensor id "Weyl_tensor".
• Weyl_tensor title "Weyl tensor".
• Weyl_tensor wikiPageUsesTemplate Template:Citation.
• Weyl_tensor wikiPageUsesTemplate Template:EquationNote.
• Weyl_tensor wikiPageUsesTemplate Template:Harv.
• Weyl_tensor wikiPageUsesTemplate Template:NumBlk.
• Weyl_tensor wikiPageUsesTemplate Template:Reflist.
• Weyl_tensor wikiPageUsesTemplate Template:Springer.
• Weyl_tensor wikiPageUsesTemplate Template:Tensors.
• Weyl_tensor subject Category:Riemannian_geometry.
• Weyl_tensor subject Category:Tensors_in_general_relativity.
• Weyl_tensor hypernym Measure.
• Weyl_tensor type Article.
• Weyl_tensor type Work.
• Weyl_tensor type Article.
• Weyl_tensor type Method.
• Weyl_tensor type Tensor.
• Weyl_tensor comment "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.".
• Weyl_tensor label "Weyl tensor".
• Weyl_tensor sameAs Tenseur_de_Weyl.
• Weyl_tensor sameAs Tensore_di_Weyl.
• Weyl_tensor sameAs 바일_곡률_텐서.
• Weyl_tensor sameAs Tensor_de_Weyl.
• Weyl_tensor sameAs m.03_gcm.
• Weyl_tensor sameAs Тензор_Вейля.
• Weyl_tensor sameAs Q869108.
• Weyl_tensor sameAs Q869108.
• Weyl_tensor wasDerivedFrom Weyl_tensor?oldid=639308797.

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