Lensing By Sgr A* as a Probe of Modified Gravity

We show that a possible astrophysical experiment, detection of lensed images of stars orbiting close to Sgr A*, can provide insight into the form of the metric 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 then attempt to determine the effect of this extra term on the properties of the secondary 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 show that the there is little observational difference between a Schwarzschild black hole and a RN black hole, leading to the conclusion that secondary images may not be a useful probe of electrical charge in black holes. A negative value for the $\frac{1}{r^2}$ term can enter through modified gravity scenarios. Although physically unlikely to apply in the case of a large black hole, the Randall-Sundrum II braneworld scenario admits a metric of this form, known as tidal 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 Q enhances the brightness of images at all times and creates an increase in brightness of up to 0.4 magnitudes for the secondary image of the star S2 at periapse. We show that for other stars with brighter secondary images and positions more aligned with the optic axis, using the Tidal Reissner-Nordstrom metric with negative Q enhances the images as well, but the effect is less pronounced. With the next generation of instruments and increased knowledge of radiation from Sgr A*, using properties of secondary images to place constraints on the size of the $\frac{1}{r^2}$ term. This knowledge will be useful in constraining any modified gravity theory that adds a similar term into the strong field near a black hole.