# B Limit on the Schwarzchild radius?

1. Jul 26, 2015

### Shaw

Is there theoretically a smallest possible Schwarzchild radius?

2. Jul 26, 2015

### PAllen

Classically, no.

3. Jul 26, 2015

### rootone

Though if a successful quantum theory of gravity is found, then yes most likely.

4. Jul 26, 2015

### Shaw

Thanks, but your replies lack detail, so they're not helpful.

5. Jul 26, 2015

### PAllen

What do you want? For quantum case, there can be no detail because there is no theory. For classical, it is trivial. The Schwazschild radius is proportional to mass. Since there is no lower limit on mass, there is no lower limit on Schwarzschild radius.

I can turn your critique around. It should really not have been necessary to ask this question at all. The most cursory search would have answered as has been done here. I could have ended this at the beginning with a report for 'didn't try google first'.

6. Jul 27, 2015

### PAllen

I guess a few questions you could have intended but didn't specify are:

1) What is the smallest BH that can form from gravitational collapse? This is not well known, but a guesstimate is around 3 solar masses.

2) What is the smallest primordial BH that could survive to the present era, assuming such BH formed in the first place (e.g. from fluctuations in the early universe)? This is about 1011 kg [assuming current models of Hawking radiation remain correct over the whole scale of BH sizes].

3) Some theorists propose that the result of evaporation isn't nothing but is a Planck mass BH that remains. This is just one speculative theory.

4) Various speculative QG theories predict different answers to these questions.

Last edited: Jul 27, 2015
7. Jul 27, 2015

### Stephanus

Yep, I still remember this.

Yeah, unlike $\sqrt{1-v^2}$, here the limit for V is C.

For natural BH you mean? I heard that CERN is creating tiny BH on daily basis.

8. Jul 27, 2015

### Stephanus

Natural of course. Should have read that a minute longer before posting.

9. Jul 27, 2015

### PAllen

There is currently exactly zero evidence than LHC has formed any BH at all. Most theorists believe it is unlikely that it will, but since some speculative theories include such a possibility, it is very interesting to look for them.

10. Jul 27, 2015

### Stephanus

Perhaps if you calculate the momentum energy of two colliding protons each travels at 99.99%c multiply it by 2G in less then $\frac{2GM_{proton}}{c^2}$ radius, I don't know. I should have calculated it. Perhaps the concentration of the momentum energy in much less tiny radius could be called black hole. And I heard that for such tiny black hole, the hawking radiation will evaporate it in less then 1 second. You know better. Btw, I'm still studying your post about doppler effect in SR. Still trying to make sense out of it.

11. Jul 27, 2015

### PAllen

http://phys.org/news/2010-12-large-hadron-collider-signatures-microscopic.html#nRlv

While this article is old, I have not heard of any change in the status.

[edit: a recent reference that the status has not changed, see the footnote in:

https://books.google.com/books?id=q...e&q=evidence black hole formation LHC&f=false
]

Last edited: Jul 27, 2015
12. Jul 27, 2015

### Stephanus

Ok.

13. Jul 27, 2015

### Staff: Mentor

That's because your question lacked detail. If you have a more detailed question, please start another thread. This one is closed.

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