Gravitational collapse and self-oscillations of two-phase celestial bodies

The phenomenon of gravitational collapse (GC) is well-known in theoretical astro- and planetary physics. It occurs when the incompressibility of substances is unable to withstand the pressure due to gravitational forces in celestial bodies of sufficiently large mass. The GC is the key mechanism of fragmentation and origin of stars from interstellar clouds. Typically, the GC does not occur in incompressible models of substance. In fact, the wavelength of fragmentation is proportional to the sound velocity and it approaches infinity when approaches infinity. The situation changes dramatically when the substance undergoes phase transformation (even when the phases can be described by the model of incompressible substance). The possibility of destabilization in such system becomes realistic, as it was first discovered in the Ramsey’s static analysis of 1950. In our opinion, the Ramsey instability is a variant of the GC phenomena for which the “effective” compressibility appears due to densification caused by phase transformation. We will present our generalization of the Ramsey’s results using dynamic approach and establish relationships for the case of finite kinetics of transformation.