https://doi.org/10.1140/epjc/s10052-018-6166-5
Regular Article - Theoretical Physics
Constraints on tidal charge of the supermassive black hole at the Galactic Center with trajectories of bright stars
1
National Astronomical Observatories of Chinese Academy of Sciences, 20A Datun Road, Beijing, 100012, China
2
Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya, 25, Moscow, 117218, Russia
3
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe highway 31, Moscow, 115409, Russia
4
Joint Institute for Nuclear Research, Dubna, Russia
5
North Carolina Central University, Durham, NC, 27707, USA
* e-mail: zakharov@itep.ru
Received:
26
June
2018
Accepted:
20
August
2018
Published online:
29
August
2018
As it was pointed out recently in Hees et al. (Phys Rev Lett 118:211101, 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. (Phys Lett B 487:1, 2001) showed that the Reissner–Nordström metric with a tidal charge is naturally appeared in the framework of Randall–Sundrum model with an extra dimension (
is called tidal charge and it could be negative in such an approach). Astrophysical consequences 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 Stuchlík (Intern J Mod Phys D 18:983, 2009), while profiles of emission lines generated by rings orbiting braneworld Kerr black hole are considered in Schee and Stuchlík (Gen Relat Grav 52:1795, 2009). Possible observational signatures of gravitational lensing in a presence of the Reissner–Nordström black hole with a tidal charge at the Galactic Center are discussed in papers (Bin-Nun in Phys Rev D 81:123011, 2010; Bin-Nun in Phys Rev D 82:064009, 2010; Bin-Nun in Class Quant Grav 28:114003, 2011). Here we are following such an approach and we obtain analytical expressions for orbital precession for Reissner–Nordström–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.
© The Author(s), 2018
