2018ApJ...855...70K

Upcoming Extremely Large Telescopes (ELTs) are promising probes of gravity in or near the galactic center (GC). Effects of alternative theories of gravity, namely the Brans-Dicke theory (BDT) and f(R) gravity, are studied near the GC black hole by calculating departure from general relativity (GR) in periastron advance of the S stars and light deflection. For these estimations, black hole spin and quadrupole moments are taken in the ranges χ = 0.1-2.0 and J₂=10^–6–2.0, respectively. Periastron advance ({dot}θ_prec) has been calculated for hypothetical S stars with orbital period one-fifth of S0-2 and eccentricity e = 0.8. The difference between BDT and GR (Δ_th{dot}θ_prec) lies in the range 10^–3-2.3 µas yr^–1, even for a large departure from GR. The difference between quadrupoles J₂=10^–6 and J₂ = 2.0 lies in the range Δ_J2_{dot}θ_prec=0.268–0.281µasyr^–1. These ranges are not only outside the astrometric capability of the ELTs, but are also contaminated by stellar perturbations. Parameter degeneracy among χ, J₂, and ω_BD is discussed. For black hole-S-star distances, D_LS = 100 and 50 au, the difference in light deflection between BDT and GR lies in the range d(δφ)_defl=10^–5–10^–1µas, making it difficult to distinguish them. From the relation between scalaron mass, M_ψ in f(R) gravity, and calculated d(δφ)_defl, it is found that M_ψ=10^–18–10^–17eV can form a stable "dark cloud" near the black hole. Scalarons with 10^–21eV are found to bring d(δφ)_defl close to the astrometric range of the ELTs. Prospects for these scalarons in the tests of gravity are discussed.