On the Yang - Mills Gravity

Abstract

The parallel between Yang-Mills theory and General Relativity is
an attractive topic that motivated a lot of interesting
researches. Various versions of the gauge theory of gravity were
proposed which provided a deep understanding of such basis
concepts as the geometry of space-time, the connection between
symmetry and dynamics. In this work we consider the problem of
interaction between intrinsic degrees of freedom of particles with
the Lorentz gauge field solution that has the same singular
feature as for the Schwarzschild solution of General Relativity.
The effective potential for a particle in the Schwarzschild-like
Lorentz gauge field was investigated in comparison with Einstein
and Newtonian theories of gravity. The equations of motion for
particles allows planar motions that can be solved numerically. We
have shown that there exit the Kepler-like orbits which correspond
to certain sets of parameters and initial conditions. The obtained
results can be regarded as an experimental evidence for the
existence of the "internal Lorentz symmetry" of point particles
that is analogue to internal unitary symmetries.