28 Jan 2009 0:43:44 UTC

Topic 194162

(moderation:

Great Scott Batman!! Fox News web site has a story on the LHC collider having a slightly higher chance of creating black holes that last perhaps as long as 1 second or so. Interesting stuff, but me thinks our doom it spelleth not.

Burning question after reading the aforementioned: Why do microscopic black holes decay into nothing so quickly? Would not they just feast faster with all of the matter surrounding them?

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## LHC and Micro Black Holes

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Hawking radiation. The smaller the black hole the higher the gravitational field strength at the event horizon. This increases the chances of particle/anti-particle creation nearby so that one of the pair falls in the hole and the other escapes into the distance - with the nett effect of loss of energy ( = mass ) from the hole. This is termed evaporation. A black hole ( the event horizon actually ) can be deemed to have a temperature because of this business. It acts as a source/sink of heat and thus interacts with the surrounding material/space. A stellar size black hole has a temperature ( as defined by this mechanism ) barely above absolute zero, and hence is lower than the temperature of the cosmic microwave background. A mountain size black hole will be like a terrestrial open fireplace. An elementary particle size black hole ( ie. LHC ) has a temperature in the millions, will flick out gamma rays and burn up in an instant ( or three ).

Cheers, Mike.

( edit ) This also explains the prediction that 'at the end of the universe', assuming it is 'open' and expands 'forever', the large black holes will evaporate too as the CMB temperature goes less than theirs. So the black holes will then be sitting in a bath that is at a temperature less than millionth of a degree above absolute zero. I forget the exact timescale, but I think it was 10^(70-ish) years. As we are about 10^10 years now, this won't be any time soon. :-)

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## RE: RE: Great Scott

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So for a black hole that takes a whole second to evaporate, how much mass would it start out with? About 228,270.5 kilograms â€“ according to this nifty Hawking Radiation Calculator. That seems like a lot of mass, even for the LHC ...

The arXiv article mentioned in the Fox News article is On the Possibility of Catastrophic Black Hole Growth in the Warped Brane-World Scenario at the LHC. In this scenario it does look like a more compete treatment of accretion/evaporation rates ... and that a black hole formed in the LHC that travels inside the earth would still evaporate faster than it could gain mass from the surroundings ...

edit- using the calculator (above) for a black hole in thermal equilibrium with the cosmic background (at 2.75 deg. K), the black hole would have only about 0.0075 times the mass of the earth, it would be only about 132 microns in diameter, and it would have an unbelievably long lifetime (over 2x10^35 gigayears) ...

After some reading about how buckyballs also exhibit light-like interference (from the antimatter thread), it's a wonder anything collides at all ... and that's about how much I know for certain :))

## RE: So for a black hole

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And according to that calculator, it would have a luminosity of 6.8e+21 watts ... now, that would be kind of a problem, right? So I guess the calculator isn't really applicable for the Black Holes in question here.

CU

Bikeman

## RE: RE: So for a black

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Right, the calculator doesn't apply to the black holes formed in the LHC in a warped-brane scenario, and of course the main question is what exactly does apply to black holes that might be created by the higher-energy and heavier-particle collisions made possible in the LHC, apart from the other main question on the exact nature of black hole radiation rates ... and now this question: In a warped-brane scenario (as a basis for an amplitude), how many black holes with mass greater than the critical mass would have been formed from cosmic-ray events in the atmosphere during the last 4.5 billion years?

I don't know if that answers that or not :))

## RE: RE: RE: So for a

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CERN: ask an expert---->LHC and black holes?

С Новым Годом!

## RE: ...CERN: ask an

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Hmm, so maybe the comparison to the energy of cosmic rays isn't valid - the center-of-mass collision energy for the colliding beams in the LHC is just the sum of the energy in each beam, so for colliding protons at 7 TeV per beam the center-of-mass energy is 14 TeV. For lead ions at 575 TeV per beam, the center-of-mass energy is 1150 TeV ... while for cosmic rays the center-of-mass energy is proportional to the square root of the cosmic ray's energy (if the particle it collides with is taken to be more or less stationary â€“ see the 'Why collider?' and 'What is the collision energy at the LHC and what's so special about it?' sections on this page), and so with the highest energy cosmic ray yet observed at over 10^20 eV (see here), it gives a center-of-mass energy of sqrt(10^20) eV = 10^10 eV, and 10^10 eV = 10 GeV = 0.01 TeV. Did I do that right? :-0

## (Last post

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(Last post continued)

Getting a bit more on-topic regarding the 1-second black holes referred to in the thread's original post, quoting from the 'Is there an intention to create black holes with the LHC?' section of the link provided by Dirk,

That certainly makes the source of the mystery noise in the GEO600 gravitational wave detector (and prediction of it from a version of M-theory, mentioned in this thread) all the more exciting!

## It's a domain thingy. That is

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It's a domain thingy. That is do theories like GR ( plus whatever Mr Hawking added in ) when yielding holes, radiation, horizons etc still remain applicable to much smaller scales? This is the $64K question. Hence what is the correct form of 'quantum gravity' ?

It's interesting to note there hasn't been much direct measurement of gravity below certain scales. The incredibly relatively low strength of gravity, ~ 10^(-41), compared with other forces ( ie. the ones we are doing the measuring with ) restrains this. Of course we assume that it is a universal force, in that all forms of matter/energy participate but I find it interesting that maybe it doesn't hold all the way down in size/separation.

This is not unreasonable to have scale dependence, after all the strong/weak nuclear forces have abrupt or quasi-exponential decay with distance respectively. Can we conceive of a force, the coupling constant ( G ) of which goes to zero effectively below a certain separation? Could that neatly solve the thorny issues of central singularities, infinities and whatnot with highly bound/massive bodies? Perhaps beneath the horizon of the black hole is a very dense, but not infinitely so, central core of matter. If so, then perversely : when it is within some volume, if gravity did not apply below that scale then there would be no force ( of gravity ) binding it! However if any extension beyond that scale occurred gravity would kick in over some separation threshold and yank it back it in!

Ha! What a Catch-22 that would be ...... or a Hotel California maybe ..... :-)

Cheers, Mike.

( edit ) NB. If one has a thin uniformly dense spherical shell of matter, then the gravitational field anywhere within is zero ( a test body is acted upon to produce no nett force ). However outside the shell gravity will act as if that shell was replaced by a point mass ( equal to the entire shell's mass ) at the centre. Interesting analogy perhaps ..... and this a purely Newtonian picture.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## RE: This is not

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That sounds like a good idea ... like a gamma factor in front of G(m1m2/r^2), where R is the minimum separation and gamma might look something like (1 â€“ R^2/r^2)^(1/2) ? Like a multi-lobed blob with Brownian undulation sort of ...

Although I think on such small scales, well beyond the distances where principles of uncertainty and exclusion are in full swing, that it's a competition between the principles, and of course between symmetries â€“ I've heard the phrase 'competing orders' used before but I don't know enough about it to say it applies here. Seems to apply in a general way, though.

Speaking of domain thingys, and extra dimensions, what about the domain of complex numbers as a dimension? Seriously, to ask the question another way, if something is universal, does that mean it is also nonlocal? Or does each minimum interval of spacetime have its own independent abstract chalkboard upon which to resolve the local mechanics? Or is the minimum interval of spacetime the chalkboard itself?

## I've been thinking a lot

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I've been thinking a lot about your idea, Mike, and it occurred to me that such a modification of the gravitational force produces a regime where it behaves just like the strong nuclear force â€“ where the force of attraction increases with increasing distance between the objects, up to a point. You don't suppose ... ? Naw, it couldn't be the same force ... could it?

Anyway, I wanted to know where the modified force would be at a maximum, so using the suggestion of 'gamma' to produce the effect of your idea, where R is the distance at which two point-masses will feel no gravitational attraction, then as the distance r between the masses increases, the gravitational force will shoot up to a maximum and level off, and as the distance increases more, the gravitational force will decrease from the maximum just like it does for the standard (Newtonian) equation â€“ so if m_1 is at the origin with m_2 some distance r away, at what distance r is the modified force at a maximum, in terms of R?

If I did the math right, the maximum attraction would be at a distance r = 1.225 R. I sure hope I did the math right, and am certainly grateful for anyone to look it over:

(Click the thumbnail for full size image)

Hopefully that's just what the good doctor ordered :)