Homologously collapsing stellar cores
The paper investigates the collapse of nonrotating gas spheres with a polytropic equation of state for n = 3, corresponding to gamma = 4/3. Such polytropes provide a reasonable approximation to collapsing stellar cores during the early phase before nuclear density is reached. A family of exact homologously collapsing configurations is found. Homologous collapse of the entire core is possible if the pressure at a given density is reduced by up to 3% from the value for a marginally stable static core. For a greater pressure reduction, an inner core can collapse homologously, the mass of which varies as the 3/2 power of the reduced pressure at the onset of the collapse.