# Lensing By Sgr A* as a Probe of Modified Gravity - General Relativity and Quantum Cosmology

Abstract: We show that a possible astrophysical experiment, detection of lensed imagesof stars orbiting close to Sgr A*, can provide insight into the form of themetric around a black hole. We model Sgr A* as a black hole and add in a$\frac{1}{r^2}$ term to the Schwarzschild metric near the black hole. We thenattempt to determine the effect of this extra term on the properties of thesecondary images of the S stars in the Galactic Center. When the $\frac{1}{r2}$term is positive, this represents a Reissner-Nordstrom RN metric, and we showthat the there is little observational difference between a Schwarzschild blackhole and a RN black hole, leading to the conclusion that secondary images maynot be a useful probe of electrical charge in black holes. A negative value forthe $\frac{1}{r^2}$ term can enter through modified gravity scenarios. Althoughphysically unlikely to apply in the case of a large black hole, theRandall-Sundrum II braneworld scenario admits a metric of this form, known astidal Reissner- Nordstrom TRN metric. We use values of tidal charge Q in$\frac{Q}{r^2}$ ranging from $-1.6M^2$ to $0.4 M^2$. A negative value of Qenhances the brightness of images at all times and creates an increase inbrightness of up to 0.4 magnitudes for the secondary image of the star S2 atperiapse. We show that for other stars with brighter secondary images andpositions more aligned with the optic axis, using the Tidal Reissner-Nordstrommetric with negative Q enhances the images as well, but the effect is lesspronounced. With the next generation of instruments and increased knowledge ofradiation from Sgr A*, using properties of secondary images to placeconstraints on the size of the $\frac{1}{r^2}$ term. This knowledge will beuseful in constraining any modified gravity theory that adds a similar terminto the strong field near a black hole.

Author: Amitai Y. Bin-Nun

Source: https://arxiv.org/