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 Lluis Bel 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.


Read more about Bel Decomposition:  Decomposition of The Riemann Tensor

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