Testing GR with Galactic-centre Stars
  The Galactic Centre S-stars orbiting the central supermassive black hole
reach velocities of a few percent of the speed of light. The GR-induced
perturbations to the redshift enter the dynamics via two distinct channels. The
post-Newtonian regime perturbs the orbit from the Keplerian (Zucker et al.,
2006, Kannan & Saha 2009), and the photons from the Minkowski (Angelil & Saha
2010). The inclusion of gravitational time dilation at order v^2 marks the
first departure of the redshift from the line-of-sight velocities. The
leading-order Schwarzschild terms curve space, and enter at order v^3. The
classical Keplerian phenomenology dominates the total redshift. Spectral
measurements of sufficient resolution will allow for the detection of these
post-Newtonian effects. We estimate the spectral resolution required to detect
each of these effects by fitting the redshift curve via the five keplerian
elements plus black hole mass to mock data. We play with an exaggerated S2
orbit - one with a semi-major axis a fraction of that of the real S2. This
amplifies the relativistic effects, and allows clear visual distinctions
between the relativistic terms. We argue that spectral data of S2 with a
dispersion of about 10km/s would allow for a clear detection of gravitational
redshift, and about 1 km/s would suffice for leading-order space curvature
detection.
