Periastron shift in Weyl class spacetimes

The periastron position advance for geodesic motion in axially
symmetric solutions of the Einstein field equations belonging to
the Weyl class of vacuum solutions is investigated. Explicit
examples corresponding to either static solutions (single
Chazy-Curzon, Schwarzschild and a pair of them), or stationary
solution (single rotating Chazy-Curzon and Kerr black hole) are
discussed. The results are then applied to the case of S2-SgrA$^*$
binary system of which the periastron position advance will be
soon measured with a great accuracy.