Dynamic Collapses Of Central Black Holes In Relativistically Degenerate Or Hot Mass Reservoirs

We investigate the self-similar dynamics,with or without shocks,of a general polytropic(GP)relativistically degenerate or hot gas under the Paczynski-Wiita gravity which captures essential general relativistic effects of a dynamically accreting Schwarzschild black hole(BH).The model system is taken to be spherically symmetric and the formal conservation of specific entropy along streamlines is adopted for a relativistically degenerate or hot medium that can be well approximated by an equation of state with a polytropic index of ?=4/3.Various self-similar dynamic solutions are constructed under this setting.One important solution among others is the expansion-wave collapse solution(EWCS)with central event horizons in expansion.One or no EWCS for a polytropic index ?=4/3 exists,representing the dynamic collapse of static singular GP spheres towards the central singularity.Such GP dynamic collapse is shown to be highly efficient for the rapid formation of supermassive black holes(SMBHs)or even hypermassive black holes(HMBHs)in the Universe including the early Universe,comparing to rotating disc accretion.Furthermore,the extra degree of freedom in pressure of those relativistically degenerate or hot media makes it possible for us to look for EWCSs with even higher efficiency for Schwarzschild black hole formation.Other astrophysical applications of our model formulation may include dynamic core collapses of massive or very massive stars and compact objects as well as supernova explosions.Under the joint action of effective pressure and Paczynski-Wiita gravity,those interesting self-similar dynamic solutions with central expanding spherical voids suffering sharp(or none)density variations along their edges can emerge.Dynamic shocks are also examined within our model framework.