Highly relativistic spin-gravity coupling for fermions

TL;DR

This paper investigates the behavior of highly relativistic fermions in gravitational fields, analyzing classical and quantum models, and presents numerical estimates for particles near black holes, highlighting the need for corrected Dirac equations.

Contribution

It introduces a corrected Dirac equation for accurately describing highly relativistic fermions with strong spin-gravity coupling.

Findings

Analysis of Mathisson-Papapetrou equations for spinning particles in black hole backgrounds.

Numerical estimates for electrons, protons, and neutrinos near black holes.

Identification of the need for modified Dirac equations for high-energy fermions.

Abstract

Descriptions of highly relativistic fermions in a gravitational field in the classical (nonquantum) and quantum approaches are discussed. The results following from the Mathisson-Papapetrou equations for a fast spinning particle in Schwarzschild's and Kerr's background are considered. Numerical estimates for electron, proton and neutrino in the gravitational field of black holes are presented.The general relativistic Dirac equation is analyzed from the point of view it is using for the adequate description of highly relativistic fermions in a gravitational field, in the linear and nonlinear spin approximation. It is necessary to have some corrected Dirac equation for a highly relativistic fermion with strong spin-gravity coupling.