Is there? I have read about lower critical size limits required for a black hole to form, but are there upper critical theoretical size limits as to how large a black hole can be?
No, there isn’t, except the mass of the universe
Some scientists suggest (I think Steven Hawking) that at a certain point a black hole can re-incorporate with the rest of the universe. The basic theory is that matter and antimatter can spontaneously occur in the universe at any point, but they annihilate one another instantaneously. Occasionally this matter/antimatter pair can form on the event horizon of a black hole, and the antimatter will react inside with matter, while the matter remains outside the black hole’s grasp. The chances of this happening increases as the size of a black hole increases. I’ve also read radiation can play a factor, but am unsure of the specifics.
If you’re talking about Hawking radiation, the amount of radiation decreases as the mass increases. Also, the chance that the matter particle will escape is the same as the chance that the anti-matter particle will escape.
I don’t think there is an upper limit to the mass of a black hole.
The tidal forces(using common language) of black holes have steeper gradients as the get smaller. It is these tidal forces that allow for the particle/anti-particle to separate. So the smaller the black hole, the more likely to separate the particle, and so the chance decrease as the size of the black hole increases.
I don’t know about the upper limits…I’m not even sure they exist. You believe everything you read???
Is there any point where a black hole becomes so large it prevents ANY Hawking radiation from escaping? To my imagination, I would say no… the flow would just keep getting infinitesimally smaller… but hey, maybe the maths says something else?
The upper size limit of a black hole is not at all a question that can be analyzed given the current understaning of the universe.
As we now believe, a black hole, or ‘singularity’ has no size in the space-time continuum, instead, it is a one dimensional point.
The gravitational attraction of the sigularity causes space to be warped around it in such a way as to cause objects coming within a certain distance of it (depending on the mass of the singularity) to become permanently trapped within what is called the ‘event horizon.’
Anything travelling inside the event horizon will never escape and so no reporting of the size of the singularity can be gathered.
Here, I think that you are asking more about the event horizon rather than the singularity.
Now, there are some who believe that the universe will eventually collapse due to the gravitational attraction of its mass. That would mean that the size of the universe itself is the upper limit to the size an event horizon.
Otherwise, I know of no other theoretical limit to the size of an event horizon.
-Anga
Actually, I think he meant mass, not technically size.
Because Schwarzschild black holes (SBH’s) can be parameterized in terms of a single value, the mass-energy M, we tend to treat this as the “size” of the black hole. A 10-M[sub]SUN[/sub] SBH is completely described. In general, black hole theory as most people hear it is a black hole of this type. It’s likely that any analysis of Hawking radiation, for instance, that you read assumes a SBH.
However, the Schwarzschild analysis assumes space outside the black hole is asymptotically flat. When the black hole gets big enough that cosmological curvature is important, this assumption falls apart. I don’t know if a black hole the size of the Universe would emit Hawking radiation, but you can’t just apply the idea that “all black holes emit Hawking radiation” because the assumptions for SBH are no longer met.
The surface temperature of a Schwarzchild black hole is given by:
T[sub]BH[/sub] = ħc[sup]3[/sup]/8πGkm[sub]BH[/sub]
As you can see the only variable is the mass of the black hole (m[sub]BH[/sub]) so therefore:
T[sub]BH[/sub] ∠m[sub]BH[/sub][sup]-1[/sup]
So the larger the black hole the smaller it’s surface temperature.
The size of a black hole generally means it’s mass/radius of the event horizion (the two are proportional), for example the surface area of a black hole means the surface area of it’s event horizion (which is directly proportional to it’s entropy).