Dynamical system describing cloud of particles in relativistic and non-relativistic framework
Robert Sta’nczy, Dorota Bors
arXiv:2412.20791v1 Announce Type: cross
Abstract: We consider fairly general class of dynamical systems under the assumptions guaranteeing the existence of Lyapunov function around some nontrivial stationary point. Moreover, the existence of heteroclinic trajectory is proved motivated by integrated densities approach to some astrophysical models of self-gravitating particles both in relativistic and non–relativistic frameworks. Finally, with the aid of geometric and topological reasoning we find the upper bounds for this trajectory yielding the critical mass–radius theorem for the astrophysical model.arXiv:2412.20791v1 Announce Type: cross
Abstract: We consider fairly general class of dynamical systems under the assumptions guaranteeing the existence of Lyapunov function around some nontrivial stationary point. Moreover, the existence of heteroclinic trajectory is proved motivated by integrated densities approach to some astrophysical models of self-gravitating particles both in relativistic and non–relativistic frameworks. Finally, with the aid of geometric and topological reasoning we find the upper bounds for this trajectory yielding the critical mass–radius theorem for the astrophysical model.