English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study the hydrodynamic self-similar mass collapses of general polytropic(GP) spherical clouds to central Schwarzschild black holes and void evolutionwith or without shocks. In order to grossly capture characteristic effects ofgeneral relativity (GR) outside yet close to the event horizon of aSchwarzschild black hole and to avoid mathematical complexity, we adopt theapproximation of the Paczynski-Wiita gravity to replace the simple Newtoniangravity in our model formulation. A new dimensionless parameter s appears withthe physical meaning of the square of the ratio of the sound speed to the speedof light $c$. Various self-similar dynamic solutions are constructed for apolytropic index $\gamma>4/3$. Two (for small enough $s<1$) or no (for largeenough $s<1$) expansion-wave collapse solutions (EWCSs) with central eventhorizons exist when $\gamma>4/3$, representing the collapse of static singularGP spheres towards the central singularity of spacetime. Such GP sphericaldynamic mass collapse is shown to be highly efficient for the rapid formationof supermassive black holes (SMBHs; mass range of $10^6-10^{10}M_{\odot}$) inthe early universe or even hypermassive black holes (HMBHs; mass range of$10^{10}-10^{12}M_{\odot}$) if extremely massive mass reservoirs could besustained for a sufficiently long time, which may evolve into hard X-ray/gammaray sources or quasars according to their surroundings. Self-similar dynamicsolutions of a GP gas are also proposed for the stellar mass black holeformation during the violent supernova explosion of a massive progenitor star,the timescale of which is estimated of $10^{-3}$ seconds. Rebound shockstravelling in supernovae are also discussed based on our self-similar shockexpansion solutions.

Relativistic Self-similar Dynamic Collapses of Black Holes in General Polytropic Spherical Clouds