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I would like to know, what happen with accretion (cloud) when drop toward a black hole. In Bondi case and terminology. If I understand:

1) We describe the cloud falling to star (black hole) by EoS [itex]P(\rho)=K\rho^\Gamma [/itex].

2) This accretion is steady it means [itex]\dot{M}=4\pi r^2u\rho=const. [/itex].

3) Accretion to black hole is possible just for supersonic speed => solution of Bondi equation has to come through critical sound speed point.

4) For [itex]\Gamma>\frac{5}{3} [/itex] doesnt exist critical point and accretion is not supersonic => no steady accretion on black hole for cloud with [itex]\Gamma>\frac{5}{3} [/itex].

Are these 4 claims right?

Bondi solution is dealing just with [itex]\Gamma<\frac{5}{3} [/itex]. It is quit hard constrain.

My question are:

a) What is the matter with cloud with [itex]\Gamma>\frac{5}{3} [/itex] during falling to black hole? Reaches the event horizon?

b) How do we must change in assumptions for dealing with cloud with [itex]\Gamma>\frac{5}{3} [/itex]?

I was checking in literature for this part of problem, but I didn't find anything important. Please let me know, comments or links.

Thank you.

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# An accretion of steady flow for Gamma > 5/3?

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