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In physics, specifically general relativity, the Mathisson–Papapetrou–Dixon equations describe the motion of a spinning massive object, moving in a gravitational field. Other equations with similar names and mathematical forms are the Mathisson-Papapetrou equations and Papapetrou-Dixon equations. All three sets of equations describe the same physics.
They are named for M. Mathisson, W. G. Dixon, and A. Papapetrou.
Throughout, this article uses the natural units c = G = 1, and tensor index notation.
For a particle of mass m, the Mathisson–Papapetrou–Dixon equations are:
where: u is the four velocity (1st order tensor), S the spin tensor (2nd order), R the Riemann curvature tensor (4th order), and the capital "D" indicates the covariant derivative with respect to the particle's proper time s (an affine parameter).
Mathisson–Papapetrou equations
For a particle of mass m, the Mathisson–Papapetrou equations are:
using the same symbols as above.