Gravitational Theories near the Galactic Center

Abstract

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.

Effect of Dark Matter Distribution on Scalaron Gravity near the Galactic Center Black Hole and Its Prospects

“…The GC black hole is not isolated. It hosts a rich environment of nuclear star cluster, intermediate mass black holes, pulsars, and extended distribution of dark mass (Genzel et al 2010;Johannsen 2016;Do et al 2019), which affects tests of gravitational physics (Gravity Collaboration et al 2020;Kalita 2018;Lalremruati & Kalita 2021) performed through pericenter shift of stellar orbits. The Gravity Collaboration et al (2022) has been able to constrain unknown mass distribution extending up to 3″ of the GC.…”

“…One of the cosmologically inspired gravitational theories is the f(R) scalaron gravity (Starobinsky 1980(Starobinsky , 2007, which accounts for primordial cosmic inflation and late-time cosmic acceleration (Capozziello & Fang 2002;Capozziello et al 2003;Nojiri & Odintsov 2004) without introducing exotic dark energy and provides gravitational alternatives to dark matter (Capozziello et al 2007(Capozziello et al , 2014. These theories naturally predict a scalaron fifth force (a scalar mode of gravity given by the field, ψ = df(R)/dR), which modifies the weak-field limit of the theories (Kalita 2018). The situation of introducing modified gravity as an alternative to dark matter and dark energy is similar to the "Vulcan or new theory of gravity" that arose while explaining the perihelion anomaly of Mercury.…”

“…The only way to evade this problem is to invoke a screening mechanism where the mass of the scalaron becomes an environmental quantity. It is to be noted that the potential of the scalaron gravity behaves as a Yukawa field (Kalita 2018(Kalita , 2020…”

“…where 1 3 0 y is the scalaron coupling strength (usually denoted by α) and M is the central mass (in this case, the GC black hole). It is to be noted that the scalaron potential arises from a weak-field limit of f(R) gravity vacuum field equations (see Kalita 2018). The scalaron induced weak-field metric derived in Kalita (2018) from which the above potential is taken, is independent of the specific form of the f(R) function (model independent).…”

“…It is to be noted that the scalaron potential arises from a weak-field limit of f(R) gravity vacuum field equations (see Kalita 2018). The scalaron induced weak-field metric derived in Kalita (2018) from which the above potential is taken, is independent of the specific form of the f(R) function (model independent). The total scalaron potential is given by…”