Testing the nature of the supermassive black hole candidate in SgrA*   with light curves and images of hot spots
  General relativity makes clear predictions about the spacetime geometry around black holes. In the near future, new facilities will have the capability to explore the metric around SgrA$^*$, the supermassive black hole candidate at the Center of our Galaxy, and open a new window to test the Kerr black hole hypothesis. In this paper, we compute light curves and images associated with compact emission regions (hot spots) orbiting around Kerr and non-Kerr black holes. We study how the analysis of the properties of the radiation emitted by a hot spot can be used to test the Kerr nature of SgrA$^*$. We find that the sole observation of the hot spot light curve can at most constrain a combination of the black hole spin and of possible deviations from the Kerr solution. This happens because the same orbital frequency around a Kerr black hole can be found for a non-Kerr object with a different spin parameter. Second order corrections in the light curve due to the background geometry are typically too small to be identified. While the observation of the hot spot centroid track can potentially bound possible deviations from the Kerr solution, that is out of reach for the near future VLTI instrument GRAVITY. The Kerr black hole hypothesis could really be tested in the case of the discovery of a radio pulsar in a compact orbit around SgrA$^*$. Radio observations of such a pulsar would provide precise estimates of the mass and the spin of SgrA$^*$, and the combination of these measurements (probing the weak field) with the hot spot light curve information (probing the strong field) may constrain/find possible deviations from the Kerr solution with quite good precision. 
Zilong Li, Lingyao Kong, Cosimo Bambi
gr-qc astro-ph.HE