Tensors in general relativity | Lorentzian manifolds

Bel decomposition

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 lower order tensors with properties similar to the electric field and magnetic field. Such a decomposition was partially described by Alphonse Matte in 1953 and by in 1958. This decomposition is particularly important in general relativity. This is the case of four-dimensional Lorentzian manifolds, for which there are only three pieces with simple properties and individual physical interpretations. (Wikipedia).

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Related pages

Bel–Robinson tensor | Tidal tensor | Ricci decomposition | Curvature invariant | Pseudo-Riemannian manifold | Electrovacuum solution