Tolman-Oppenheimer-Volkoff Equation

The existence of solutions to Tolman-Openheimer-Volkoff equation with linear equation of state modeling relativistic cloud of interacting particles is proved for mass parameter below certain threshold. For the intermediate values of mass parameters multiplicity result holds. For the small mass parameter the uniqueness is guaranteed. Moreover, there is a threshold value of the mass, which can not be exceeded. It is achieved by considering the related dynamical system in the rescaled mass-density variables which is governed by the global Lyapunov function with sink. Some preliminary extensions to nonlinear equation of state are discussed with numerical density profiles.