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As it was pointed out recently in Hees et al. (2017), observations of starsnear the Galactic Center with current and future facilities provide an uniquetool to test general relativity (GR) and alternative theories of gravity in astrong gravitational field regime. In particular, the authors showed that theYukawa gravity could be constrained with Keck and TMT observations. Some timeago, Dadhich et al. (2001) showed that the Reissner -- Nordstr\"om metric witha tidal charge is naturally appeared in the framework of Randall -- Sundrummodel with an extra dimension ($Q^2$ is called tidal charge and it could benegative in such an approach). Astrophysical consequences of of presence ofblack holes with a tidal charge are considerered, in particular, geodesics andshadows in Kerr -- Newman braneworld metric are analyzed in (Schee andStuchlik, 2009a), while profiles of emission lines generated by rings orbitingbraneworld Kerr black hole are considered in (Schee and Stuchlik, 2009b).Possible observational signatures of gravitational lensing in a presence of theReissner -- Nordstr\"om black hole with a tidal charge at the Galactic Centerare discussed in papers by Bin-Nun (2010a, 2010b, 2011). Here we are followingsuch an approach and we obtain analytical expressions for orbital precessionfor Reissner -- Nordstrom -- de-Sitter solution in post-Newtonian approximationand discuss opportunities to constrain parameters of the metric fromobservations of bright stars with current and future astrometric observationalfacilities such as VLT, Keck, GRAVITY, E-ELT and TMT.

Constraints on tidal charge of the supermassive black hole at the Galactic Center with trajectories of bright stars