MG15 - Talk detail

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The black hole term has been introduced by J. A. Wheeler in 1967. We illustrate an efficiency of the idea for theoretical and observational studies of our Galactic Center. Now there are two basic observational techniques to investigate a gravitational potential at the Galactic Center to prove a presence of a supermassive black hole, namely, (a) monitoring the orbits of bright stars near the Galactic Center with the largest telescopes; (b) measuring the size and shape of shadows around black hole giving an alternative possibility to evaluate black hole parameters with the Event Horizon Telescope. Recently, the joint LIGO -- Virgo team not only discovered gravitational waves and binary black holes but also found an upper limit on graviton mass $m_g < 1.2 \times 10^{-22}$~eV (Abbott et al. 2016). We show that an analysis of bright star trajectories could constrain graviton mass with a comparable accuracy. We discuss opportunities to improve current estimates of graviton mass significantly with subsequent observations of Keck, VLT, GRAVITY, E-ELT and TMT.

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We consider photon geodesics in the Reissner--Nordstrom -- de-Sitter dyon metric. Critical impact parameters for photon geodesics separate capture and scattering regions and the parameters characterize shadow sizes (radii). In paper (Zakharov, 2014) critical impact parameters for ~\RN~ black hole (including Reissner--Nordstrom -- de-Sitter metric with a tidal charge) have been derived analytically while shadow sizes for Schwarzschild -- de Sitter (Kottler) metric have been found in papers (Stuchlik 1983, Zakharov, 2014). In the paper we obtain analytical expressions for the shadow radii of the Reissner--Nordstrom -- de-Sitter black holes and discuss the critical values of relevant parameters, therefore, we generalize results discussed earlier in papers (Zakharov, 2014; Stuchlik 1983). Assuming that such Reissner--Nordstrom -- de-Sitter dyon black holes are located in the Galactic Center and centers of other galaxies (including M87, for instance) one could use the results to analyze current and future observational data obtained with advanced observational facilities such as the Event Horizon Telescope.

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Some years ago a concept of pseudo-complex General Relativity (pc-GR) has been introduced. In consequent papers possible observational signatures for compact objects have been discussed. Such compact objects have been suggested to substitute conventional black holes. We obtain analytical expressions for shadow size in the case of spherical symmetry of compact object (spin is vanishing in this case $a=0$). This relations are generalize the well-known result for Schwarzschild metric when the shadow area is $27\pi M^2$ ($M$ is a black hole mass).

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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 -- Nordström metric with a tidal charge is naturally appeared in the framework of Randall -- Sundrum model with an extra dimension (Q2 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 -- Nordström 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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Accepted

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Abstract

Recently, the LIGO-Virgo collaboration discovered gravitational waves and in their first publication on the subject the authors also presented a graviton mass constraint as m_g < 1.2 \times 10^{-22} eV (Abbott et al. 2016). In our previous papers we considered constraints on Yukawa gravity parameters (Borka et al. 2013) and on graviton mass from analysis of the trajectory of S2 star near the Galactic Center (Zakharov et al. 2016). In the paper we analyze a potential to reduce upper bounds for graviton mass with future observational data on trajectories of bright stars near the Galactic Center. Since gravitational potentials are different for these two cases, expressions for relativistic advance for general relativity and Yukawa potential are different functions on eccentricity and semimajor axis, it gives an opportunity to improve current estimates of graviton mass with future observational facilities. In our considerations of an improvement potential for a graviton mass estimate we adopt a conservative strategy and assume that trajectories of bright stars and their apocenter advance will be described with general relativity expressions and it gives opportunities to improve graviton mass constraints. In contrast with our previous studies, where we present current constraints on parameters of Yukawa gravity (Borka et al. 2013) and graviton mass (Zakharov et al. 2016) from observations of S2 star, in the paper we express expectations to improve current constraints for graviton mass, assuming the GR predictions about apocenter shifts will be confirmed with future observations. We concluded that if future observations of bright star orbits during around fifty years will confirm GR predictions about apocenter shifts of bright star orbits it give an opportunity to constrain a graviton mass at a level around $5 \times 10^{-23}$~eV or slightly better than current estimates obtained with LIGO observations. Reference A.F. Zakharov et al. JCAP 04 (2018) 050; arXiv:1801.04679.

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