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In continuum physics is presupposed that general-relativistic balanceequations are valid which are created from the Lorentz-covariant ones byapplication of the equivalence principle. Consequently, the question arises,how to make these general-covariant balances compatible with Einstein's fieldequations. The compatibility conditions are derived by performing a modifiedBelinfante-Rosenfeld symmetrization for the non-symmetric and notdivergence-free general-relativistic energy-momentum tensor. The procedureresults in the Mathisson-Papapetrou equations.

Mathisson-Papapetrou Equations as Conditions for Compatibility of General Relativity and Continuum Physics