Abstract
We investigate the motion of stars at the central region of the Milky Way Galaxy. We consider two possible scenarios: 1) there is a supermassive black hole without dark matter distribution and 2) there is a dark matter core without any black hole in the galactic center. We remark that, with current observations, one cannot distinguish the two separate cases from each other at distances larger than 100 astronomical units. Here, we present improved analyses regarding the motion of stars and show that differences between these two cases appear at distances smaller than 30 astronomical units. We adopt here the so-called exponential density profile for dark matter distribution which is usually used to explain the rotation curve data points in the bulge of galaxies. We underline our outcomes are model-dependent, i.e. they depend on the choice of the particular dark matter model employed for the analysis.