The Galactic Center black hole (Sgr A*) provides an ideal laboratory for astronomical tests of new gravitational physics. This work reports that curvature correction (f(R)) to quantum vacuum fluctuations naturally yields a Yukawa-type scalar fifth force with potential , where M ψ is the mass of the f(R) scalarons. Estimating the UV and IR cutoff scales of vacuum fluctuations, the Yukawa coupling strength is connected to the scalaron field amplitude. Whereas recently constrained Yukawa coupling and range correspond to light scalarons with M ψ = (1.37 × 10−21–5.49 × 10−20) eV, vacuum fluctuations yield a massive scalaron with M ψ = 10−16 eV. Scalaron-induced periastron shift of stellar orbits near Sgr A* has been studied with respect to the semimajor axis in the range a = 10–1000 au. It is found that the scalarons resulting from quantum fluctuations affect the precession of orbits with a = 128–256 R s . The possibility of future constraints on massive scalarons in observations near Sgr A* is discussed. This is a new and independent effort to express a prototype quantum gravity effect in terms of astronomically accessible quantities.
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 , respectively. Periastron advance ( ) 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 ( ) lies in the range 10−3–2.3 μas yr−1, even for a large departure from GR. The difference between quadrupoles and J 2 = 2.0 lies in the range . These ranges are not only outside the astrometric capability of the ELTs, but are also contaminated by stellar perturbations. Parameter degeneracy among χ, J 2, and 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 , making it difficult to distinguish them. From the relation between scalaron mass, in f(R) gravity, and calculated , it is found that can form a stable “dark cloud” near the black hole. Scalarons with are found to bring close to the astrometric range of the ELTs. Prospects for these scalarons in the tests of gravity are discussed.
The Galactic Centre (Sgr A*), hosting a supermassive black hole carries sufficient potential for testing gravitational theories. Existing astrometric facilities on Very Large Telescope (VLT) and the Keck Telescope have enabled astronomers to study stellar orbits near Sgr A* and perform new astronomical tests of gravitational theories. These observations have provided strong field tests of gravity (φ/c2 ∼ 10−3 , which is much greater than φ/c2 for the solar system ). In this work, we have estimated magnitudes of various contributions to the periastron shift of compact stellar orbits near Sgr A* for pericentre distance in the range rp= (0.3 - 50)au at a fixed orbital inclination, i = 90°. We take the spin of the black hole as χ = 0.1, 0.44 and 0.9 and eccentricities of the orbit as e = 0.9. The relativistic effects including orders beyond 1PN and spin induced effects are incorporated in the contributions. Effect of tidal distortion on periastron shift has also been added into the estimation by considering gravitational Love numbers for polytropic models of the stars. For the tidal effect, we have considered updated mass-radii relations for Low Mass Stars (LMS) and High Mass Stars (HMS) . It has been found that the tidal effect on periastron shift arising from stars represented by polytropes of indices n = 1 and n = 3 terminate above rp ∼ 2 au and rp ∼ 1 au respectively. The periastron shift angle for the stars has been compared with the astrometric capabilities of existing large telescopes and upcoming Extremely Large Telescopes (ELTs). Challenges and prospects associated with the estimations are highlighted.
In this paper the author applies the scalaron gravity field and corresponding Yukawa coupling (derived by Kalita from the consideration of quantum vacuum fluctuations with UV and IR scales) to examine the scales of stellar orbits near the Galactic Center black hole, which can be probed by upcoming astrometric facilities for constraining modified gravity. Through the assumption that the pericenter shift of stellar orbits becomes of the order of spin and quadrupole moment effects of the black hole, it is found that for semimajor axes bounded below by time scales of gravitational wave emission and stellar age and above by S-2 like orbits (a = 990 au) the black hole spin with 0.1 ≤ χ ≤ 0.980 is eligible to probe scalaron masses within (10−22–10−18) eV and also the scalaron coupling, α = 2.73 × 10−4 derived earlier from quantum vacuum fluctuations. The orbital eccentricities are considered as e = 0.1, 0.5, and 0.9. Astrometric categories with σ = 10, 50, and 100 μas are used to probe the time scales and number of observing campaigns required for simultaneously constraining scalaron mass and black hole spin. It is found that extraction of black hole spin is possible within a = (74–433) au through 10 μas facilities. The present analysis is realized to be an independent opportunity to simultaneously constrain scalaron coupling, black hole spin, and tidal charge and hence to reveal the true nature of the spacetime structure of our nearest supermassive black hole.
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