Constraints on tidal charge of the supermassive black hole at the
  Galactic Center with trajectories of bright stars
  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 -- Nordstr\"om 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 -- Nordstr\"om 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.
