We consider a metric-affine extension to the gravitational sector of the
Standard-Model Extension for the Lorentz-violating coefficients u and
sμν. The general results, which are applied to a specific model called
metric-affine bumblebee gravity, are obtained. A Schwarzschild-like solution,
incorporating effects of the Lorentz symmetry breaking through coefficient
X=ξb2, is found. Furthermore, a complete study of the geodesics
trajectories of particles has been accomplished in this background, emphasizing
the departure from general relativity. We also compute the deflection of light
within the context of the weak field approximation and verify that there exist
two new contributions ascribed to the Lorentz symmetry breaking. As a
phenomenological application, we compare our theoretical results with
observational data in order to estimate the coefficient X.Comment: 22 pages, 5 figure