Solutions of Mathisson-Papapetrou equations for highly relativistic spinning particles

TL;DR

This paper investigates the nongeodesic motions of highly relativistic spinning particles in black hole spacetimes using Mathisson-Papapetrou equations, highlighting the significant effects of spin-gravity coupling and its potential astrophysical implications.

Contribution

It provides new insights into the behavior of relativistic spinning particles in curved spacetime and emphasizes the importance of the Mathisson-Pirani condition for such motions.

Findings

Spin-gravity coupling can be repulsive or attractive depending on spin and velocity signs.

Numerical estimates for particles like electrons and neutrinos near black holes are presented.

The study discusses the relation between Dirac equation and MP equations in this context.

Abstract

Different types of essentially nongeodesic motions of highly relativistic spinning particles in Schwarzschild's and Kerr's background which follows from the Mathisson-Papapetrou (MP) equations are considered. It is shown that dependently on the correlation of signs of the spin and the particle's orbital velocity the spin-gravity coupling acts as a significant repulsive or attractive force. Numerical estimates for electrons, protons, and neutrinos in the gravitational field of black holes are presented. The correspondence between the general relativistic Dirac equation and MP equations is discussed. It is stressed that for the highly relativistic motions the adequate supplementary condition for the MP equations is the Mathisson-Pirani condition. In the following it is important to study the possible role of the highly relativistic spin-gravity coupling in astrophysics, cosmology, and high energy physics.