Well, I want to be clear that I’m specifically not asking that, but something even less well-defined: "is everywhere that curvature is large enough to make quantum gravitational effects significant hidden behind an event horizon?
Well, a Planck mass black hole would have its Schwartzschild radius at the Planck length, so any less massive BH would have a Schwartzschild radius less than the Planck length. That should be enough to produce “interesting” effects. Unfortunately, we can’t probe distances that small, so all the interesting effects will be hidden, anyway…
Hey, maybe that’s what elementary particles are! They’re mini-BHs, and things like spin, charge, and color are the quantum gravity effects of twisted spacetime! Now, where can I publish…?
Unfortunately I don’t think it’s new. A similar thing happened when I first grokked GR and thought that maybe just like there’s no “force” of gravity, that possibly all other “forces” can be reformulated as curvatures. This wasn’t the first time the idea came up, but unfortunately the quantum effects mean needing a quantized theory of geometry that isn’t really worked out yet and everyone ran off to thinking about other solutions while I was seduced by algebra.
The road not taken, eh?
No, it’s not new: 't Hooft was giving seminars ten years back about some highly speculative scheme where elementary particles were black holes, though I’m not sure he ever published anything on it. And I’ve forgotten the details.
I can’t be arsed to dig up the cite right now but somewhere in my reading of Quark Stars they mentioned the gravity well could be sufficicient to make light orbit it (some would still get away though I believe).
Considering that going not much further gets you a Black Hole I think that is about as close as you will get. Someone else will have to tell us if that is a sufficiently large curvature to make quantum garvitational effects sans an event horizon.
This is a complete hijack, but since the thread topic is somewhat related, and since the people gathered here may be best positioned to answer, let me ask:
Could the tidal forces near a black hole be sufficient to separate quark pairs into free quarks?
[most likley this is one of those questions that results from a naive “understanding”, or a totally inaccurate concept of what quarks (and other subatomic particles) really are]
As I understand it, no. Outside the event horizon it’s no more intense gravity than any other object of that mass would have at that distance from the center.
I guess the way I was looking at was that for sufficiently small radius, the tidal force should be infinite. No?
But the Schwartzchild radius is proportional to the mass inside. That is, as you get in closer you have to drop the mass to stay outside the event horizon. Maybe at a low enough mass you’d get the curvature high enough outside the radius to matter, but at that point you’d be looking at something the size of a subatomic particle anyhow.
Ah, that makes a lot of sense. Thank you.
The other part of the answer to this question is that, no matter HOW you try to pull quarks apart, the energy you put into pulling eventually becomes enough to pop a new quark-antiquark pair into existence. You don’t end up with free quarks, you end up with a couple of extra mesons.
{I won’t go into the problems of even *defining * a “particle” in an accelerated reference frame…}
First, a few observations:
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Do not, under any circumstances, misread the word “hadron” as “hardon” in sentences such as tim314’s “. . . the star just becomes like one big hadron.” It only leads to confusion.
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Since I’m sure someone else will point it out anyway, “Strange Quark Matter” would be a good name for a rock band.
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There is no such place as Meson, Arizona.
Now, regarding this contribution:
From the article:
How big would a one-tonne speck of SQM be?
RR
I haven’t been able to come across any figures for the density of SQM, but a 1-tonne speck of neutron-star matter would be about 15 microns across (this would be a blithe extrapolation from the neutron star’s mass, of course; without the gravity to hold it together, this chunk of neutronium would simply fly apart.) I assume that since SQM is supposed to be even denser than neutronium, it would be even smaller. If I find any specific numbers on the subject I’ll post them here.
Someone’s forgetting their GR: there’s no such thing as an accelerated reference frame.
Then again, this only transfers the difficulty to defining a particle in GR.
Ah, I’m sorry, I misunderstood you. I thought you were asking, given a black hole, is there guaranteed to be large curvature inside.
But a similar answer applies: Yes, you can have significant curvature outside of a black hole. Take a black hole, and let it evaporate for a long time. Eventually, one of two things will happen: Either it will stop evaporating, or it will pass the Planck mass. If it passes the Planck mass, then curvature at or a little outside the horizon will be Planck-scale curvature, which should be enough for something “interesting”. And if it stops evaporating before them, it would have to have been a quantum gravity effect which stopped it, in which case also the curvature at or outside the horizon would be interesting.
However, there is still no reason to suppose that there would be significant (in a quantum gravity sense) curvature in the vicinity of a quark star.
Also, the statement “there are no accelerated reference frames” is inconsistent with the statement “there is no gravitational force”. A non-freefalling reference frame must be said to either be accelerating, or to have a gravitational force. But in any case, defining a particle in a non-freefalling reference frame is nontrivial.
How can you define accelerated reference frames without nonaccelerated reference frames? All frames are “of the same type”. That’s what general covariance means, at least to a differential geometer.