Can Mathisson-Papapetrou equations give clue to some problems in astrophysics?

TL;DR

This paper examines the Mathisson-Papapetrou equations' role in describing relativistic fermions in gravitational fields and explores their potential implications for astrophysical phenomena, including possible links to OPERA results.

Contribution

It highlights the importance of the Mathisson-Papapetrou equations for accurate classical limits and suggests their solutions may explain certain high-velocity astrophysical effects.

Findings

Spin in general relativity is Fermi-transported, not parallel transported.

Mathisson-Papapetrou equations predict strong antigravity effects at high velocities.

Potential connection to unexplained astrophysical phenomena and OPERA results.

Abstract

First, we stress that for correct description of highly relativistic fermions in a gravitational field it is necessary to have an equation which in the limiting transition to the classical (non-quantum) case corresponds to the exact Mathisson-Papapetrou equations. According to these equations the spin in general relativity is Fermi-transported, and the parallel transport of spin is realized only in some approximation. The traditional general-relativistic Dirac equation (1929) is based on the parallel transported spinors and does not ensure the correspondent transition. Second, because in the range of very high velocity (close to the speed of light) of a spinning particle relative to the Schwarzschild or Kerr sources the Mathisson-Papapetrou equations have the solutions which reveal that the spin-gravity interaction acts as a strong antigravity force, we suppose that this fact can be useful for explanation some astrophysical phenomena. Some association with the OPERA results is possible.