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In general relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, the magnetogravitic tensor
is one of the three pieces appearing in the 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 four pieces. It was introduced in 1959 by the physicist Lluis Bel....
of the Riemann tensor.
The magnetogravitic tensor can be interpreted physically as a specifying possible spin-spin forces on spinning bits of matter, such as spinning test particle
In physical theories, a test particle is an idealized model of an object whose physical properties are assumed to be negligible except for the property being studied, which is considered to be insufficient to alter the behavior of the rest of the system...