2024/12/30 by Robert Stańczy, Stańczy, Robert, Dorota Bors +1
Physics and Astronomy · Engineering · #Cosmology and Gravitation Theories #Relativity and Gravitational Theory #Material Science and Thermodynamics
paper · pdf · doi:10.48550/arxiv.2412.20791
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.