Periapsis shift and deflection of light by hairy black holes
  We investigate the orbit equations and the eikonal equation for light
respectively, under influence of the hairy black holes (asymptotically flat) in
four dimensions. We consider two hairy black hole solutions with non-trivial
potentials, and one of these solutions has Schwarzschild case as a smooth
limit. Following to Landau and Lifshitz, we use the Hamilton-Jacobi method, and
we show hairy corrections for periapsis shift, where the effect of the hair is
to increase it. In the same way, using the eikonal equation we show the
deflection of the light and the relevant scalar hair corrections. Interestingly
we find that the hair screening the gravitational field, decreasing the angle
of deflection as the hair increases.
