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    Default Minimum Viable Size for a Black Hole?

    Some years ago, the press reported worries that the Large Hadron Collider could generate a black hole. People at CERN actually considered this possibility, and said that a micro-black hole "would disintegrate rapidly, in around 10^-27 seconds". They would have been able to track its existence, and the data would have been an important step towards new knowledge and unknown possibilities.

    Today I read that a black hole the size of a dime would need as much mass as the whole planet Earth. So how much mass do I need for a black hole that won't disappear for a few hours? What for one that will last as long as, let's say, a star (if that's possible for black holes)?
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    Default Re: Minimum Viable Size for a Black Hole?

    https://www.reddit.com/r/askscience/..._hole_that_is/

    According to them, 2/3 the size of the moon to sustain itself but it can't be generated by masses less than larger than the sun.
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    Default Re: Minimum Viable Size for a Black Hole?

    The thing is, the acceleration toward the eruption of Hawking radiation is exponential. A black hole would appear stable until it was almost small enough to begin erupting, then it would be gone in a titanic blast. As I understand it, it would be the whole mass as e=mc^2, which is to say much more than the biggest nuclear bomb ever made.
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    Default Re: Minimum Viable Size for a Black Hole?

    Theoretically once a black hole has the mass equal to the Planck mass it wouldn't be able to "evaporate" anymore since the radiating particle would need to have the mass energy equivalent of the Planck mass. The size would be the Planck length. It would be stable like this forever, and too small to actually ever absorb any energy (and if it did, just evaporate that again).
    This is because the hawkins radiation emitted from a black hole needs to have a wavelength equal to the diameter of a black hole, so big ones emit low energy waves, smaller ones emit higher energy waves.

    The sweet spot between "not radiating too fast" and "not radiating fast enough" seems to be around 606,000 metric tons if you want to use the Hawkins Radiation for something. It would be about 0.001 femtometer in diameter. (much smaller than an atom, the nucleus of an hydrogen atom is 1.7566 femtometer)
    Source: https://en.wikipedia.org/wiki/Black_hole_starship
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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by Tvtyrant View Post
    but it can't be generated by masses less than larger than the sun.
    I think it could if they were already very dense and smashed together at relativistic speeds
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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by Mastikator View Post
    Theoretically once a black hole has the mass equal to the Planck mass it wouldn't be able to "evaporate" anymore since the radiating particle would need to have the mass energy equivalent of the Planck mass. The size would be the Planck length. It would be stable like this forever, and too small to actually ever absorb any energy (and if it did, just evaporate that again).
    This is because the hawkins radiation emitted from a black hole needs to have a wavelength equal to the diameter of a black hole, so big ones emit low energy waves, smaller ones emit higher energy waves.
    Black holes can radiate particles larger than themselves.

    As the practical escapes, it becomes redshifted, increasing it's wavelength.
    Quote Originally Posted by Bohandas View Post
    I think it could if they were already very dense and smashed together at relativistic speeds
    I think TvTyrant meant generated naturally.
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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by Quizatzhaderac View Post
    Black holes can radiate particles larger than themselves.

    As the practical escapes, it becomes redshifted, increasing it's wavelength.
    I think TvTyrant meant generated naturally.
    Right when the particle appears it would be a photon and have the energy and size of the black hole it is escaping from. This photon would a) be a Kugelblitz and b) evaporate the black hole completely. The result would be that the black hole has just moved one Planck length to the side.
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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by Mastikator View Post
    Right when the particle appears it would be a photon and have the energy and size of the black hole it is escaping from. This photon would a) be a Kugelblitz and b) evaporate the black hole completely. The result would be that the black hole has just moved one Planck length to the side.
    There a few problems with this.

    First, there is no "right when the particle appears". The particle is virtual before it escapes. Virtual particles don't have energy the same way real particles do (which is to say, you can't use wavelength to determine their energy) . The particle doesn't become real until it's well away from the event horizon. The source of the virtual particle isn't even the event horizon, it's region of space that that ends in an event horizon; there is a pair of virtual particles outside the horizon (possibly bigger than the black hole) and one of two on falls in.

    Second, you're ignoring potential energy. As accounted by the distant observer, that particle doesn't change it's total energy during it's journey. At infinity, the photon has zero energy. Infinitely close to the event horizon, the photon would have negatively infinite potential energy.
    The thing is the Azurites don't use a single color; they use a single hue. The use light blue, dark blue, black, white, glossy blue, off-white with a bluish tint. They sky's the limit, as long as it's blue.

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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by Mastikator View Post
    Theoretically once a black hole has the mass equal to the Planck mass it wouldn't be able to "evaporate" anymore since the radiating particle would need to have the mass energy equivalent of the Planck mass. The size would be the Planck length. It would be stable like this forever, and too small to actually ever absorb any energy (and if it did, just evaporate that again).
    This is because the hawkins radiation emitted from a black hole needs to have a wavelength equal to the diameter of a black hole, so big ones emit low energy waves, smaller ones emit higher energy waves.

    The sweet spot between "not radiating too fast" and "not radiating fast enough" seems to be around 606,000 metric tons if you want to use the Hawkins Radiation for something. It would be about 0.001 femtometer in diameter. (much smaller than an atom, the nucleus of an hydrogen atom is 1.7566 femtometer)
    Source: https://en.wikipedia.org/wiki/Black_hole_starship
    Would it be possible to extract further energy from the planck black hole by lifting its energy just above planck mass?

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    Default Re: Minimum Viable Size for a Black Hole?

    All the energy you could possibly get out would be identical to the energy you put in.
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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by Yora View Post
    All the energy you could possibly get out would be identical to the energy you put in.
    Why? If the black hole is at .8 h (h being planck mass), and you put it up to, say 1.2 h, couldn't it then radiate away h to end up at .2 h?

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    Default Re: Minimum Viable Size for a Black Hole?

    If that is the case, the energy you gain would literally be one of the smallest possible amounts amounts you'd ever get. Probably get a lot more energy from collecting the Cosmic Microwave Background.
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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by Rydiro View Post
    Would it be possible to extract further energy from the planck black hole by lifting its energy just above planck mass?
    It would be virtually impossible to add any energy to it, the cross-hair is literally the smallest meaningful length. The uncertainty principle says no.

    It's also possible that no such black hole actually exists, it would have to been created in the big bang. AFAIK there's no evidence that they exist. A stellar mass black hole wouldn't become this light, a) the universe isn't old enough and b) it would gain much more energy just from the CBR than it would lose to Hawkins radiation.
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    Default Re: Minimum Viable Size for a Black Hole?

    Quoth Mastikator:

    Theoretically once a black hole has the mass equal to the Planck mass it wouldn't be able to "evaporate" anymore since the radiating particle would need to have the mass energy equivalent of the Planck mass. The size would be the Planck length. It would be stable like this forever, and too small to actually ever absorb any energy (and if it did, just evaporate that again).
    It's more accurate to say that our current theories concerning black holes break down in the vicinity of the Planck mass, and thus we have no idea how such a hole would behave. For that matter, it's quite possible that our theories break down long before that point, but we're absolutely certain that they break down by then.

    And while there's no known mechanism in the current Universe that could produce black holes smaller than a few times the mass of the Sun, it's quite possible that smaller holes might have been formed during the very early stages of the Universe, and some of those might still be around. And of course, it's also possible that there are mechanisms in the current Universe that we don't know of. So it would be very exciting, but no great surprise, to discover black holes of sub-stellar size.
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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by Yora View Post
    If that is the case, the energy you gain would literally be one of the smallest possible amounts amounts you'd ever get. Probably get a lot more energy from collecting the Cosmic Microwave Background.
    A quick application of E=mc² gives about 180 000 000 000 Joule for one planck mass, if I'm not mistaken.
    Which would power a fridge for four years.
    Sure, small on an industrial scale, let alone on an astronomical. But pretty sure beats the CMB.
    Last edited by Rydiro; 2021-06-18 at 07:24 AM.

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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by Rydiro View Post
    A quick application of E=mc² gives about 180 000 000 000 Joule for one planck mass, if I'm not mistaken.
    That looks high to me. They're expecting the emissions from any micro-blackholes produced in the LHC to be containable, which I don't think that would be.
    Last edited by halfeye; 2021-06-18 at 07:30 AM.
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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by Rydiro View Post
    A quick application of E=mc² gives about 180 000 000 000 Joule for one planck mass, if I'm not mistaken.
    Which would power a fridge for four years.
    Sure, small on an industrial scale, let alone on an astronomical. But pretty sure beats the CMB.
    The Plank length is on the order of 10-35 meters. What's the order of a plank mass in grams? I confess I do not know.

    E = m c2 => m = E/c2

    c = 299,792,458 m/s.

    c2 = 8.98755 x 1016 m2/s2 ~ 1.0 x 1017 m2/s2

    180 billion joules is roughly 2.0 x 1011 kg m2/s2

    m = (2.0 x 1011 kg m2/s2) / (1.0 x 1017 m2/s2)

    The m2/s2 cancel out, and you're left with 2 x 10-6 kg. Or about 2 mg. I'm... pretty sure that's a good bit heavier than a Plank mass.
    Last edited by Lord Torath; 2021-06-18 at 08:36 AM. Reason: Typos
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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by Lord Torath View Post
    Or about 2 mg. I'm... pretty sure that's a good bit heavier than a Plank mass.
    Yeah, I was off by a factor of 100. Planck mass is 20 micro grams. I did get that right, but was off on c by a factor of 10.
    Guess you can run that 1000 Watt fridge just for some weeks.

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    Default Re: Minimum Viable Size for a Black Hole?

    Our current understanding of physics would not allow for the LHC to produce black holes. Which would mean that if it did produce black holes, that would be a sign that our current understanding was incomplete. But in any event, any black hole (or in fact, anything at all) produced by the LHC would have a mass much, much lower than the Planck mass. The only energy you'll ever get out of anything produced in a particle accelerator is the energy you put in, which won't be much.
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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by Rydiro View Post
    Planck mass is 20 micro grams.
    What's the meaning of the Planck mass? I understand that the Planck length is the smallest possible lenght, but that mass is relatively huge, neutrinos are much smaller, and photons allegedly have no rest mass at all.
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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by halfeye View Post
    What's the meaning of the Planck mass? I understand that the Planck length is the smallest possible lenght, but that mass is relatively huge, neutrinos are much smaller, and photons allegedly have no rest mass at all.
    Planck units are units derived from fundamental constants: gravtional (G), speed of light in a vaccum (c), Planck (h), and Boltzmann (kb) normalized to 1. They have the advatange of being 'natural' units rather than human defined. The kg was originally a defined standard, a human designated amount of material, if you use the Planck definition of mass mp=Sqrt( (h*c)/G)) everything is in terms of physical constants and thus less changeable/ subject to error.

    The Planck mass works out to be relatively huge in terms of sub-atomic particles.

    EDIT: Or rather, subatomic particles happen to REALLY small in terms of the 'natural' scale of mass.
    Last edited by Thomas Cardew; 2021-07-26 at 07:51 PM.

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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by Quizatzhaderac View Post
    I think TvTyrant meant generated naturally.
    Naturally occurring cosmic ray particles can be quite energetic
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    Default Re: Minimum Viable Size for a Black Hole?

    Have a look at the Hawking Radiation Calculator, which you'll have to search for yourself since I evidently haven't made enough posts yet to post links.

    You can plug in a value for whatever parameter you'd care to investigate and see how it affects everything else. If you want a black hole that lasts for a few hours, that's a mass of around six million kg. If you want one that lasts around ten billion years, that would correspond to a mass of around 190 billion kg.

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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by McGarnagle View Post
    Have a look at the Hawking Radiation Calculator, which you'll have to search for yourself since I evidently haven't made enough posts yet to post links.
    That clearly doesn't work. I plugged in one for seconds, got a mass, doubled the mass, got two seconds for the answer, and that's obviously mistaken.
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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by halfeye View Post
    That clearly doesn't work. I plugged in one for seconds, got a mass, doubled the mass, got two seconds for the answer, and that's obviously mistaken.
    Yeah, the lifetime of a black hole before it evaporates due to Hawking radiation scales with the cube of its mass, so something definitely not right there.

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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by factotum View Post
    Yeah, the lifetime of a black hole before it evaporates due to Hawking radiation scales with the cube of its mass, so something definitely not right there.
    I made a mistake. I thouight the "time to singularity" was the time to evaporation. It seems what that means is the time from the event horizon to the singularity in the centre, in whatever way you might want to measure that with all the time dilation going on.

    The "lifetime" parameter is much more well behaved, double mass gives us 8.00003 seconds lifetime. Cubed, more or less, as you said.

    https://www.vttoth.com/CMS/physics-n...ion-calculator
    Last edited by halfeye; 2021-09-02 at 07:34 PM.
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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by Thomas Cardew View Post
    Planck mass works out to be relatively huge in terms of sub-atomic particles.

    EDIT: Or rather, subatomic particles happen to REALLY small in terms of the 'natural' scale of mass.
    The Planck Mass isn't just huge. It's another extreme limit. It's the mass required for a black hole with a diameter of a planck length. That means, the mass for tbe smallest imaginable black hole. Any mass smaller than that could never be a black hole under any imaginary circumstances as the black hole would be smaller than a planck length.

    I guess we never see it mentioned much, as it's relevant to black holes, which tend to be considerably larger when studied.
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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by Yora View Post
    The Planck Mass isn't just huge. It's another extreme limit. It's the mass required for a black hole with a diameter of a planck length. That means, the mass for tbe smallest imaginable black hole. Any mass smaller than that could never be a black hole under any imaginary circumstances as the black hole would be smaller than a planck length.

    I guess we never see it mentioned much, as it's relevant to black holes, which tend to be considerably larger when studied.
    Interesting.

    I wonder whether that means that the last particle out of an evaporating black hole has to have at least that much energy, because that would be quite some gamma ray.
    Last edited by halfeye; 2021-09-06 at 05:35 AM.
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    Default Re: Minimum Viable Size for a Black Hole?

    It's a common misconception that "the Planck Length is the smallest possible length". There are multiple layers of ignorance between us and any sort of statement like that.

    First, it's possible that spacetime is quantized. I think most physicists would say that it's plausible or even likely, but we don't actually know it is, and certainly we don't know the details.

    Then, if spacetime is quantized, it's possible that it's quantized in such a way that there's a minimum possible length... but not everything that's quantized has a minimum possible value, so it's also possible that there isn't such a minimum length.

    If there is a minimum possible length, then we don't know what it would be. We know that it must be smaller than what we've probed, but we don't know how much smaller. Something in the vicinity of the Planck length is certainly plausible, since it is indeed much smaller than what we've probed, and it bears a natural relation to constants of the Universe that we do know about... but that's just our best guess; it could be something completely different.

    And even if there is a minimum possible length and it's in the vicinity of the Planck length, that doesn't mean it's the Planck length exactly. Nobody would be in the least surprised if it turned out that the minimum possible length were half the Planck length, or pi times it, or whatever.

    Now, one situation where we do know that the Planck scales have relevance is in the final stages of the evaporation of a black hole. If what we know about black holes extrapolates smoothly down to those scales (and that's a VERY big if), then a black hole with a mass comparable to the Planck mass would be radiating particles with an energy comparable to the Planck energy, which would indeed seem to set a limit of the Planck mass as the smallest possible size for a black hole. Actually, it'd mean a smallest possible size of many times that, as such a hole would be radiating a very great many particles. Of course, it's also quite possible, likely even, that what we know of black holes doesn't extrapolate that far, and that there's some new physics that we don't know that becomes relevant before then, but then the Planck scale is still relevant, as it provides a scale to let us know when we must be approaching that new physics.
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    Default Re: Minimum Viable Size for a Black Hole?

    Quote Originally Posted by halfeye View Post
    I made a mistake. I thouight the "time to singularity" was the time to evaporation. It seems what that means is the time from the event horizon to the singularity in the centre, in whatever way you might want to measure that with all the time dilation going on.
    Time to singularity is the proper time of an observer moving from the event horizon to the singularity.

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