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One question I had, prompted by a fever dream in which a black hole spawned in my house... If a black hole were to come into sustained existence, assume the sm

One question I had, prompted by a fever dream in which a black hole spawned in my house... If a black hole were to come into sustained existence, assume the smallest one. How long could we stand near it before being unable to escape? And how far is that distance?

helldritch 4y ago
The equation for escape velocity is: v = √(2GM/R) R = distance (radius, really) M = Mass of the body G = Universal gravitation constant We can modify this equation to find for the distance at which you can escape: r = 2GM/v^2 The answer is largely: it depends on how fast you can go, at the speed of light you can escape from further away, since the pull will increase the closer your are to the "event horizon". I'm in a car right now (as a passenger ofc) doing this from my phone so not in a situation where I can put together a model, but you should be able to plug in some numbers and estimate a result, just make sure you convert to SI units so you don't accidentally end up 3 orders of magnitude off. A black hole with the mass of the earth would have a radius of about 2cm, so things less massive than a planet start to get very small, very fast, and you end up fighting quantum effects which become less intuitive.
DJBunnies 4y ago
That's called the event horizon, which is proportional to its mass.
justsomeshmuck 4y ago
It's theorized that there is a grapefruit-sized black hole orbiting our sun in the outer reaches of our solar system with a mass of 5 to 10 earths. A black hole spontaneously appearing in your home small enough to not rip apart the entire planet immediately would probably be too small to notice without some sort of detection equipment.
- codethief 4y ago
  > It's theorized that there is a grapefruit-sized black hole orbiting our sun in the outer reaches of our solar system with a mass of 5 to 10 earths. Source: https://arxiv.org/abs/2004.14192 https://arxiv.org/abs/2004.14192 (There was also a pretty good discussion about it here on HN.) > would probably be too small to notice without some sort of detection equipment. What makes you think that?
  - justsomeshmuck 4y ago
    https://academic.oup.com/mnras/article/152/1/75/2604549?login=false https://academic.oup.com/mnras/article/152/1/75/2604549?logi... Theoretically, black holes can have a mass of the tiniest fraction of a gram which would be unimaginabley small. It's my own speculation that you wouldn't be able to detect that with a naked eye.
    - codethief 4y ago
      Thanks for the link! > you wouldn't be able to detect that with a naked eye. What if you touched it? No idea what the spacetime would look like near a gram-sized black hole with lots of heavier matter surrounding it but I suppose there would still be pretty severe tidal forces.
      - sliken 4y ago
        Anything coming anywhere close to the event horizon would be removed, and some fraction of that mass would be converted into energy an irradiate the surrounding. So the best you could hope for is that it's moving fast, leaves a hole in you and leaves fast before you die. Keep in mind that event horizon isn't a shell, just a point at which your future (which is in the singularity) is certain.
        codethief 4y ago
        > Keep in mind that event horizon isn't a shell, just a point at which your future (which is in the singularity) is certain. Yeah, exactly my thought. Then again, we're silently assuming here that spacetime would pretty much look like one of the vacuum black hole solutions plus some additional matter (our body) near it. That doesn't seem too likely, given that our body is much heavier and can't just be treated as a test particle. OTOH it doesn't seem too likely, either, that the actual spacetime would look completely different: There will surely still be a black hole and an event horizon.
  - paulmd 4y ago
    Ah yes, the tachyon detection grid. ;) https://memory-alpha.fandom.com/wiki/Tachyon_detection_grid https://memory-alpha.fandom.com/wiki/Tachyon_detection_grid
Sharlin 4y ago
Well, if a black hole somehow appeared on Earth, with a low-ish velocity relative to the ground, it would immediately fall inside Earth so "standing" near it would be pretty difficult.
- serenitylater 4y ago
kqr 4y ago
Follow-up question: are black holes generally a question of density and not mass? If I could take a laptop and squeeze it hard enough to overcome various nuclear forces, would I get a black hole with an event horizon the size of a laptop's gravitational field? What would it take to get an event horizon on a human scale (a feet or two across?)
- codethief 4y ago
  > are black holes generally a question of density and not mass? Correct. Any mass M taking up a spherical volume of radius less than 2GM/c² (the Schwarzschild radius) will necessarily be a black hole. Black holes are thus the objects in the universe with the highest mass density and, coincidentally, the highest entropy density. > What would it take to get an event horizon on a human scale (a feet or two across?) A mass M = Lc²/2G, where L = 1ft for a black hole 2ft across.
- jfengel 4y ago
  Sort of. It depends on both density and mass. The more mass there is, the less density is required to make a black hole. A solar mass black hole is stupid dense. But a supermassive black hole is less dense than the earth, and can be less dense than water. That's still an insane amount of mass, but it's not really all that dense. A human scale black hole would be even denser than a solar mass black hole. It would require over 200 earth masses, though that's still a tiny fraction of a solar mass.
  - kqr 4y ago
    In this comment, are you defining density as mass per volume contained by event horizon? Or do we know how the mass is distributed inside the black hole? Does it even make sense to discuss distribution of mass in a black hole? Would clues about that leak out through dynamics like rotation?
    - jfengel 4y ago
      You only need total mass and total volume. No other details leak out. A non spinning black hole is an absolutely perfect sphere, with no "hair". A spinning black hole is flattened, or maybe even a torus, but is still mathematically perfect. Unless quantum mechanics intervenes in ways nobody has yet figured out.
TheDudeMan 4y ago
There is no "smallest one". The small ones evaporate to smaller and then nothing very quickly. "Evaporate" as in, emit huge amounts of radiation -- like a bomb.
- codethief 4y ago
  > The small ones evaporate to smaller and then nothing very quickly. This is not at all known, as we have no idea what a theory of quantum gravity would look like (which would necessarily enter the game here). We might end up with a black hole remnant, or Hawking radiation might behave differently for microscopic black holes etc.
InCityDreams 4y ago
You may enjoy The Aleph. https://en.m.wikipedia.org/wiki/The_Aleph_(short_story) https://en.m.wikipedia.org/wiki/The_Aleph_(short_story)
al2o3cr 4y ago
The event horizon is the least of your worries: the real problem is tidal forces. https://spacemath.gsfc.nasa.gov/blackh/4Page33.pdf https://spacemath.gsfc.nasa.gov/blackh/4Page33.pdf The calculation in that document is representative: for a solar-mass hole (event horizon radius 2.9km) the tidal forces on a human are 51000x Earth gravity at 100km away!

helldritch 4y ago

The equation for escape velocity is: v = √(2GM/R) R = distance (radius, really) M = Mass of the body G = Universal gravitation constant We can modify this equation to find for the distance at which you can escape: r = 2GM/v^2 The answer is largely: it depends on how fast you can go, at the speed of light you can escape from further away, since the pull will increase the closer your are to the "event horizon". I'm in a car right now (as a passenger ofc) doing this from my phone so not in a situation where I can put together a model, but you should be able to plug in some numbers and estimate a result, just make sure you convert to SI units so you don't accidentally end up 3 orders of magnitude off. A black hole with the mass of the earth would have a radius of about 2cm, so things less massive than a planet start to get very small, very fast, and you end up fighting quantum effects which become less intuitive.

DJBunnies 4y ago

That's called the event horizon, which is proportional to its mass.

justsomeshmuck 4y ago

It's theorized that there is a grapefruit-sized black hole orbiting our sun in the outer reaches of our solar system with a mass of 5 to 10 earths. A black hole spontaneously appearing in your home small enough to not rip apart the entire planet immediately would probably be too small to notice without some sort of detection equipment.

codethief 4y ago
> It's theorized that there is a grapefruit-sized black hole orbiting our sun in the outer reaches of our solar system with a mass of 5 to 10 earths. Source: https://arxiv.org/abs/2004.14192 https://arxiv.org/abs/2004.14192 (There was also a pretty good discussion about it here on HN.) > would probably be too small to notice without some sort of detection equipment. What makes you think that?
- justsomeshmuck 4y ago
  https://academic.oup.com/mnras/article/152/1/75/2604549?login=false https://academic.oup.com/mnras/article/152/1/75/2604549?logi... Theoretically, black holes can have a mass of the tiniest fraction of a gram which would be unimaginabley small. It's my own speculation that you wouldn't be able to detect that with a naked eye.
  - codethief 4y ago
    Thanks for the link! > you wouldn't be able to detect that with a naked eye. What if you touched it? No idea what the spacetime would look like near a gram-sized black hole with lots of heavier matter surrounding it but I suppose there would still be pretty severe tidal forces.
    - sliken 4y ago
      Anything coming anywhere close to the event horizon would be removed, and some fraction of that mass would be converted into energy an irradiate the surrounding. So the best you could hope for is that it's moving fast, leaves a hole in you and leaves fast before you die. Keep in mind that event horizon isn't a shell, just a point at which your future (which is in the singularity) is certain.
      - codethief 4y ago
        > Keep in mind that event horizon isn't a shell, just a point at which your future (which is in the singularity) is certain. Yeah, exactly my thought. Then again, we're silently assuming here that spacetime would pretty much look like one of the vacuum black hole solutions plus some additional matter (our body) near it. That doesn't seem too likely, given that our body is much heavier and can't just be treated as a test particle. OTOH it doesn't seem too likely, either, that the actual spacetime would look completely different: There will surely still be a black hole and an event horizon.
- paulmd 4y ago
  Ah yes, the tachyon detection grid. ;) https://memory-alpha.fandom.com/wiki/Tachyon_detection_grid https://memory-alpha.fandom.com/wiki/Tachyon_detection_grid

Sharlin 4y ago

Well, if a black hole somehow appeared on Earth, with a low-ish velocity relative to the ground, it would immediately fall inside Earth so "standing" near it would be pretty difficult.

serenitylater 4y ago

kqr 4y ago

Follow-up question: are black holes generally a question of density and not mass? If I could take a laptop and squeeze it hard enough to overcome various nuclear forces, would I get a black hole with an event horizon the size of a laptop's gravitational field? What would it take to get an event horizon on a human scale (a feet or two across?)

codethief 4y ago
> are black holes generally a question of density and not mass? Correct. Any mass M taking up a spherical volume of radius less than 2GM/c² (the Schwarzschild radius) will necessarily be a black hole. Black holes are thus the objects in the universe with the highest mass density and, coincidentally, the highest entropy density. > What would it take to get an event horizon on a human scale (a feet or two across?) A mass M = Lc²/2G, where L = 1ft for a black hole 2ft across.
jfengel 4y ago
Sort of. It depends on both density and mass. The more mass there is, the less density is required to make a black hole. A solar mass black hole is stupid dense. But a supermassive black hole is less dense than the earth, and can be less dense than water. That's still an insane amount of mass, but it's not really all that dense. A human scale black hole would be even denser than a solar mass black hole. It would require over 200 earth masses, though that's still a tiny fraction of a solar mass.
- kqr 4y ago
  In this comment, are you defining density as mass per volume contained by event horizon? Or do we know how the mass is distributed inside the black hole? Does it even make sense to discuss distribution of mass in a black hole? Would clues about that leak out through dynamics like rotation?
  - jfengel 4y ago
    You only need total mass and total volume. No other details leak out. A non spinning black hole is an absolutely perfect sphere, with no "hair". A spinning black hole is flattened, or maybe even a torus, but is still mathematically perfect. Unless quantum mechanics intervenes in ways nobody has yet figured out.

TheDudeMan 4y ago

There is no "smallest one". The small ones evaporate to smaller and then nothing very quickly. "Evaporate" as in, emit huge amounts of radiation -- like a bomb.

codethief 4y ago
> The small ones evaporate to smaller and then nothing very quickly. This is not at all known, as we have no idea what a theory of quantum gravity would look like (which would necessarily enter the game here). We might end up with a black hole remnant, or Hawking radiation might behave differently for microscopic black holes etc.

InCityDreams 4y ago

You may enjoy The Aleph. https://en.m.wikipedia.org/wiki/The_Aleph_(short_story) https://en.m.wikipedia.org/wiki/The_Aleph_(short_story)

al2o3cr 4y ago

The event horizon is the least of your worries: the real problem is tidal forces. https://spacemath.gsfc.nasa.gov/blackh/4Page33.pdf https://spacemath.gsfc.nasa.gov/blackh/4Page33.pdf The calculation in that document is representative: for a solar-mass hole (event horizon radius 2.9km) the tidal forces on a human are 51000x Earth gravity at 100km away!