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${}^{\ast }$ binary system of which the periastron position advance will be soon measured with a great accuracy.