Abstract Upon specifying an equation of state, spherically symmetric steady states the Einstein-Euler system are embedded in 1-parameter families solutions, characterized by value their central redshift. In 1960’s Zel’dovich (Voprosy Kosmogonii 9:157–170, 1963) and Harrison et al. (Gravitation Theory Gravitational Collapse. The University Chicago press, Chicago, 1965) formulated a turning point...