As it was pointed out recently in Hees et al. (2017), observations of stars near the Galactic Center with current and future facilities provide an unique tool to test general relativity (GR) and alternative theories of gravity in a strong gravitational field regime. In particular, the authors showed that the Yukawa gravity could be constrained with Keck and TMT observations. Some time ago, Dadhich et al. (2001) showed that the Reissner -- Nordstrom metric with a tidal charge is naturally appeared in the framework of Randall -- Sundrum model with an extra dimension ($Q^2$ is called tidal charge and it could be negative in such an approach). Astrophysical consequences of of presence of black holes with a tidal charge are considerered, in particular, geodesics and shadows in Kerr -- Newman braneworld metric are analyzed in (Schee and Stuchlik, 2009a), while profiles of emission lines generated by rings orbiting braneworld Kerr black hole are considered in (Schee and Stuchlik, 2009b). Possible observational signatures of gravitational lensing in a presence of the Reissner -- Nordstrom black hole with a tidal charge at the Galactic Center are discussed in papers by Bin-Nun (2010a, 2010b, 2011). Here we are following such an approach and we obtain analytical expressions for orbital precession for Reissner -- Nordstrom -- de-Sitter solution in post-Newtonian approximation and discuss opportunities to constrain parameters of the metric from observations of bright stars with current and future astrometric observational facilities such as VLT, Keck, GRAVITY, E-ELT and TMT.
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