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In general relativity, the magnetogravitic tensor is one of the three pieces appearing in the Bel decomposition of the Riemann tensor. General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... 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. ... In differential geometry, the Riemann curvature tensor is the most standard way to express curvature of Riemannian manifolds, or more generally, any manifold with an affine connection, torsionless or with torsion. ...
The magnetogravitic tensor can be interpreted physically as a specifying possible spin-spin forces on spinning bits of matter, such as spinning test particles. In metric theories of gravitation, particularly general relativity, a test particle is an idealized model of a small object whose mass is so small that it does not appreciably disturb the ambient graviational field. ...
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