Mathematical model for Sagittarius A* and related Tolman–Oppenheimer–Volkoff equations

Abstract

We analyze the model describing the interaction of relativistic gravitationally attracting diffusive fermionic particles evaporating at high energy motivated by the recent observations of star trajectories under the influence of the dark matter. We extend to the relativistic case the results for the Michie–King distribution obtained in our previous paper. We consider more general equation of state for the Tolman–Oppenheimer–Volkoff equation. By fixed point arguments, we prove the existence of solutions. Next, by pressure‐density estimates, we show some restrictions on the data of the system. Finally, by numerical simulations, we depict the density profile governed by the specific equation of state adapted to the Sagittarius A* located in the centre of the Milky Way.