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.
