Bel decomposition

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In semi-Riemannian geometry, the Bel decomposition, taken with respect to a specific timelike congruence, is a way of breaking up the Riemann tensor of a pseudo-Riemannian manifold into four pieces. It was introduced in 1959 by the physicist Lluis Bel.

This decomposition is particularly important in general relativity. This is the four dimensional case of Lorentzian manifolds, for which there are only three pieces with particularly simple properties, which have individual physical interpretations.

[edit] See also

• electrogravitic tensor
• magnetogravitic tensor
• topogravitic tensor
• Ricci decomposition