2021MNRAS.506.6125L

We study the self-similar spherical hydrodynamics of γ = 4/3, with or without shocks, of general polytropic (GP) relativistically degenerate or hot matter in global mass reservoirs under the Paczynski-Wiita (PW) gravity that retains essential general relativistic (GR) effects for dynamic accretions on to growing Schwarzschild black holes (BHs). Various self-similar dynamic solutions are derived and constructed. Among others, one important solution type is the expansion-wave collapse solution (EWCS) with a central mass-growing BH event horizon in expansion. Such GP dynamic collapses are highly efficient for the rapid dynamic growth of supermassive and hypermassive BHs (SMBHs and HMBHs) in the Universe including the early Universe, in contrast to much slower disc mass accretion and BH merger processes. Particularly, the extra degree of freedom for the effective pressure of those relativistically degenerate or hot mass reservoirs makes it possible to construct EWCSs with even higher efficiency for BH growths. Pertinent astrophysical applications of our model also include dynamic core collapses of massive or very massive stars or supermassive stars and compact objects as well as supernova explosions. Under joint actions of effective pressure and the PW gravity, self-similar dynamic solutions with central expanding spherical voids or cavities with either sharp or smooth density transitions across their rims can emerge. Dynamic expansion shocks are also constructed and examined.