Spontaneous CPT breaking and fermion propagation in the Schwarzschild geometry

The Schwarzschild solution is used as a background metric to analyze the effects of a vector field undergoing spontaneous symmetry breaking in a Standard Model Extension Bumblebee Model. The corresponding back-reaction of the background field expectation value on the metric is calculated, yielding a consistent model for describing CPT-violating effects within the context of pseudo-Riemannian geometry. The Bianchi identities of general relativity and the gauge theory are found to be mutually consistent and yield no conflicts with Riemannian geometry. This fact is demonstrated to second-order in the background field. Fermions with a spin-dependent, CPT-violating coupling to this background field experience altered geodesics relative to the conventional black hole orbital solutions. The spin-dependent corrections to the orbital velocity and precession rate are calculated.