not centered on the black hole, but arise from a bright spot in the region around the black hole, close to the event horizon, possibly in the accretion disc, or a relativistic jet of material ejected from the disc. If the apparent position of Sagittarius A* were exactly centered on the black hole, it would be possible to see it magnified beyond its size, because of gravitational lensing of the black hole. According to general relativity, this would result in a ring-like structure, which has a diameter about 5.2 times the black hole's Schwarzschild radius (10 μas). For a black hole of around 4 million solar masses, this corresponds to a size of approximately 52 μas, which is consistent with the observed overall size of about 50 μas, the size (apparent diameter) of the black hole Sgr A* itself being 20 μas. Recent lower resolution observations revealed that the radio source of Sagittarius A* is symmetrical. Simulations of alternative theories of gravity depict results that may be difficult to distinguish from GR. However, a 2018 paper predicts an image of Sagittarius A* that is in agreement with recent observations; in particular, it explains the small angular size and the symmetrical morphology of the source. The mass of Sagittarius A* has been estimated in two different ways: Two groups—in Germany and the U.S.—monitored the orbits of individual stars very near to the black hole and used Kepler's laws to infer the enclosed mass. The German group found a mass of solar masses, whereas the American group found solar masses. Given that this mass is confined inside a 44-million-kilometre-diameter sphere, this yields a density ten times higher than previous estimates. More recently, measurement of the proper motions of a sample of several thousand stars within approximately one parsec from the black hole, combined with a statistical technique, has yielded both an estimate of the black hole's mass at , plus a distributed mass in the central parsec amounting to . The latter is thought to be composed of stars and stellar remnants. The comparatively small mass of this supermassive black hole, along with the low luminosity of the radio and infrared emission lines, imply that the Milky Way is not a Seyfert galaxy. Ultimately, what is seen is not the black hole itself, but observations that are consistent only if there is a black hole present near Sgr A*. In the case