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

TL;DR

This paper derives compatibility conditions between general relativity and continuum physics, showing that the Mathisson-Papapetrou equations emerge from a modified symmetrization process of the energy-momentum tensor.

Contribution

It introduces a novel approach to derive the Mathisson-Papapetrou equations as compatibility conditions for Einstein's field equations and continuum physics.

Findings

Mathisson-Papapetrou equations are compatibility conditions.

Modified Belinfante-Rosenfeld symmetrization yields these equations.

Provides a link between continuum physics and general relativity.

Abstract

In continuum physics is presupposed that general-relativistic balance equations are valid which are created from the Lorentz-covariant ones by application of the equivalence principle. Consequently, the question arises, how to make these general-covariant balances compatible with Einstein's field equations. The compatibility conditions are derived by performing a modified Belinfante-Rosenfeld symmetrization for the non-symmetric and not divergence-free general-relativistic energy-momentum tensor. The procedure results in the Mathisson-Papapetrou equations.