Scalaron Gravity near Sagittarius A: Investigation of Spin of the Black Hole and Observing Requirements

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 μ as 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 μ as 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.