KCC-invariants-based geometrization of a theory of electromagnetic and spinor fields on the background of the Schwarzschild spacetime

Abstract

We apply the KCC-geometrical approach to study the radial equation systems arising in two quantum- mechanical problems, i.e. electromagnetic and spinor fields on the background of the Schwarzschild spacetime. The stability analysis in terms of the second invariant demonstrate the difference in the behavior of geodesics at r → ∞ for these two problems that may be associated with different structure of solution (discrete and continuous spectra). The vanishing of the 3-d, 4-th and 5-th invariants means that, in geometrical terms, there exists a nonlinear connection on the tangent bundle, with zero torsion and curvature.