Аннотация
We consider a toy model for the relativistic collapse of a homogeneous perfect fluid that takes into account an equation of state for high density matter, in the form of a Hagedorn phase, and semiclassical corrections in the strong field. We show that collapse reaches a critical minimum size and then bounces. We discuss the conditions needed for the collapse to halt and form a compact object. We argue that implications of models such as the one presented here are of great importance for astrophysics as they show that black holes may not be the only final outcome of collapse of very massive stars.