Pulsating models of spherical self-gravitating systems

Since gravitational instabilities in reality arise during the non-stationary stage of the evolution of self-gravitating systems, we present below a method for constructing radially pulsating phase models of such systems. Our models pulsate self-similarly, preserving the property of homogeneous volume density. In this work, we provide the corresponding generalizations of two well-known homogeneous equilibrium models: the Einstein model and the Camm sphere. We also indicate the differences in stellar orbits in the pulsating state.