Science-based what-if questions

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Eebster the Great
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Re: Science-based what-if questions

Postby Eebster the Great » Sun Sep 03, 2017 2:01 am UTC

My understanding is that if the black hole is small enough, it will evaporate almost instantly, like setting off a small nuke in the core of the Sun. In other words, it would have no discernible effect. But maybe the intense pressure and gravity at the center of the Sun changes things.

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Re: Science-based what-if questions

Postby Soupspoon » Sun Sep 03, 2017 2:53 am UTC

(Would I be wrong in suggesting that there's no particularly notable local gravity at the centre of the Sun, i.e. shell theorem? Though I think I know what you mean. If I actually do think what I think I mean, that is.)

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Re: Science-based what-if questions

Postby andykhang » Sun Sep 03, 2017 10:03 am UTC

Well, I said inside, but I think it would be better anyway to just create it as the border of the sun (Maybe inside it abit for faster process). The opacity of the Sun is a problem though, but let said I used extreme Gamma ray's array as it.

Also, black hole last for waaaay longer than you think, even at microscopic size. A billion ton (...pretty much just all of the fish in the world, but pretty small for cosmic scale) black hole, with a radius of 1.484852e-15 (that's basically the size of an electron), would actually last for 2.335329e+16 hours, or around 2600 billion years.

Edit: According to http://xaonon.dyndns.org/hawking/

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Re: Science-based what-if questions

Postby Eebster the Great » Sun Sep 03, 2017 7:56 pm UTC

andykhang wrote:Well, I said inside, but I think it would be better anyway to just create it as the border of the sun (Maybe inside it abit for faster process). The opacity of the Sun is a problem though, but let said I used extreme Gamma ray's array as it.

Also, black hole last for waaaay longer than you think, even at microscopic size. A billion ton (...pretty much just all of the fish in the world, but pretty small for cosmic scale) black hole, with a radius of 1.484852e-15 (that's basically the size of an electron), would actually last for 2.335329e+16 hours, or around 2600 billion years.

Edit: According to http://xaonon.dyndns.org/hawking/

A billion tons of radiation is not exactly small in my mind. That's 21 trillion megatons of TNT equivalent all focused, as you said, on an area roughly that of the scattering cross-section of an electron.

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Re: Science-based what-if questions

Postby morriswalters » Sun Sep 03, 2017 10:11 pm UTC

If you could create a Black Hole at the surface, it would do what they do. Eat the sun. Just looking at the geometry, it would orbit in the sun in a descending spiral. Not knowing anything about black holes I would naively think that it would draw mass across the event horizon which I assume is spherical, as fast as it could, starting at whatever size. Sooner or later it would do whatever stars do when they take lunch with a black hole.

Having said that, I know nothing about black holes, or quantum mechanics. I simply play at it when it won't kill people.

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Re: Science-based what-if questions

Postby andykhang » Mon Sep 04, 2017 3:18 am UTC

Eebster the Great wrote:
andykhang wrote:Well, I said inside, but I think it would be better anyway to just create it as the border of the sun (Maybe inside it abit for faster process). The opacity of the Sun is a problem though, but let said I used extreme Gamma ray's array as it.

Also, black hole last for waaaay longer than you think, even at microscopic size. A billion ton (...pretty much just all of the fish in the world, but pretty small for cosmic scale) black hole, with a radius of 1.484852e-15 (that's basically the size of an electron), would actually last for 2.335329e+16 hours, or around 2600 billion years.

Edit: According to http://xaonon.dyndns.org/hawking/

A billion tons of radiation is not exactly small in my mind. That's 21 trillion megatons of TNT equivalent all focused, as you said, on an area roughly that of the scattering cross-section of an electron.


...True that. As 1.227203e+11, the heat that managed to get out would make it practically 12x hotter than a supernovae, and pretty much shine just as much too. Still, the mass would be draw in first before it could even get away. (...Or does it?)

That made me wonder though...as what size would the heat be hot enough so that it would delivered enough counterforce to the particle outside in compare to the gravitational force?

@morriswalter I know that, I just want to know as what size would the process be fast enough so that it would consume the sun in at least a month.

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Re: Science-based what-if questions

Postby p1t1o » Mon Sep 04, 2017 8:01 am UTC

Eebster the Great wrote:
andykhang wrote:Well, I said inside, but I think it would be better anyway to just create it as the border of the sun (Maybe inside it abit for faster process). The opacity of the Sun is a problem though, but let said I used extreme Gamma ray's array as it.

Also, black hole last for waaaay longer than you think, even at microscopic size. A billion ton (...pretty much just all of the fish in the world, but pretty small for cosmic scale) black hole, with a radius of 1.484852e-15 (that's basically the size of an electron), would actually last for 2.335329e+16 hours, or around 2600 billion years.

Edit: According to http://xaonon.dyndns.org/hawking/

A billion tons of radiation is not exactly small in my mind. That's 21 trillion megatons of TNT equivalent all focused, as you said, on an area roughly that of the scattering cross-section of an electron.


Thats still only an output of about 1GW though.

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Re: Science-based what-if questions

Postby Eebster the Great » Mon Sep 04, 2017 8:33 am UTC

p1t1o wrote:
Eebster the Great wrote:
andykhang wrote:Well, I said inside, but I think it would be better anyway to just create it as the border of the sun (Maybe inside it abit for faster process). The opacity of the Sun is a problem though, but let said I used extreme Gamma ray's array as it.

Also, black hole last for waaaay longer than you think, even at microscopic size. A billion ton (...pretty much just all of the fish in the world, but pretty small for cosmic scale) black hole, with a radius of 1.484852e-15 (that's basically the size of an electron), would actually last for 2.335329e+16 hours, or around 2600 billion years.

Edit: According to http://xaonon.dyndns.org/hawking/

A billion tons of radiation is not exactly small in my mind. That's 21 trillion megatons of TNT equivalent all focused, as you said, on an area roughly that of the scattering cross-section of an electron.


Thats still only an output of about 1GW though.

wat

Are you getting that by dividing 1012 kg * c2 by 2.6 * 1012 years? Because if so, I think you are missing the point. That is the average rate at which the black hole, having already been formed, would evaporate. The power required to form it is many orders of magnitude beyond what could be plausible for any species to ever produce via any physical mechanism. I calculate 1.8 * 1052 W.

EDIT: That calculation is also sort of meaningless, since you wouldn't have to form it all at once as I implied. If you want to form it gradually, you would only have to beat the rate of evaporation of a Planck mass black hole, which is a mere 2.3 * 1048 W. Far more reasonable.

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Re: Science-based what-if questions

Postby p1t1o » Mon Sep 04, 2017 10:36 am UTC

Eebster the Great wrote:
p1t1o wrote:
Eebster the Great wrote:
andykhang wrote:Well, I said inside, but I think it would be better anyway to just create it as the border of the sun (Maybe inside it abit for faster process). The opacity of the Sun is a problem though, but let said I used extreme Gamma ray's array as it.

Also, black hole last for waaaay longer than you think, even at microscopic size. A billion ton (...pretty much just all of the fish in the world, but pretty small for cosmic scale) black hole, with a radius of 1.484852e-15 (that's basically the size of an electron), would actually last for 2.335329e+16 hours, or around 2600 billion years.

Edit: According to http://xaonon.dyndns.org/hawking/

A billion tons of radiation is not exactly small in my mind. That's 21 trillion megatons of TNT equivalent all focused, as you said, on an area roughly that of the scattering cross-section of an electron.


Thats still only an output of about 1GW though.

wat

Are you getting that by dividing 1012 kg * c2 by 2.6 * 1012 years? Because if so, I think you are missing the point. That is the average rate at which the black hole, having already been formed, would evaporate. The power required to form it is many orders of magnitude beyond what could be plausible for any species to ever produce via any physical mechanism. I calculate 1.8 * 1052 W.

EDIT: That calculation is also sort of meaningless, since you wouldn't have to form it all at once as I implied. If you want to form it gradually, you would only have to beat the rate of evaporation of a Planck mass black hole, which is a mere 2.3 * 1048 W. Far more reasonable.


On second look, yes I think I was missing a few things :oops:

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Re: Science-based what-if questions

Postby andykhang » Mon Sep 04, 2017 1:56 pm UTC

Then again, again, I don't really care about the cost. Do you think the size of an electron would be enough? Or must you get it bigger?

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Re: Science-based what-if questions

Postby Eebster the Great » Mon Sep 04, 2017 2:13 pm UTC

The black hole will definitely eat the star, or at least the parts of it that don't get ejected as a result of pressure from fusion or neutron degeneracy or whatever happens as the star starts to collapse. A billion tons isn't much, but it should grow exponentially. I don't know how long it would take, but my gut feeling is that it wouldn't be as long as you would expect.

On the other hand, there is a definite possibility that the black hole itself ends up getting ejected, while the star is just fine. I have no idea how to evaluate the probability of that.

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Re: Science-based what-if questions

Postby gmalivuk » Mon Sep 04, 2017 3:48 pm UTC

I'm not sure if it would eat the star at that size, because the (Hawking) radiation pressure coming out of it is too high to let anything in.

(By my calculation a billion-ton black hole is strong enough to pull matter through a luminosity of 100MW, but this one puts out 350MW, so it would only need to be slightly bigger to work.)
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Re: Science-based what-if questions

Postby Eebster the Great » Mon Sep 04, 2017 4:59 pm UTC

That said, if you build it in the star's core, that won't be a problem, right?

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Re: Science-based what-if questions

Postby gmalivuk » Mon Sep 04, 2017 9:50 pm UTC

Why wouldn't it be a problem there? The star's own gravity has no net effect at its center so it's not going to make a difference.
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Re: Science-based what-if questions

Postby Eebster the Great » Mon Sep 04, 2017 9:58 pm UTC

gmalivuk wrote:Why wouldn't it be a problem there? The star's own gravity has no net effect at its center so it's not going to make a difference.

I was thinking more about the star's pressure than it's gravity. The pressure at the center of the Sun is 27 PPa. Surely that's a significant contribution. Though the scale here is so confusing, it's impossible for me to tell intuitively whether this is huge or negligible.

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Re: Science-based what-if questions

Postby morriswalters » Tue Sep 05, 2017 12:08 am UTC

Instead of starting it in the sun, start it in orbit close to the sun. Put it out where it can eat, and let gravity take care of everything else. Not even close to a Physicist.

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Re: Science-based what-if questions

Postby gmalivuk » Tue Sep 05, 2017 12:15 am UTC

I don't imagine pressure in the usual sense matters at all to something the size of an electron, whether or not that tiny thing is also extremely luminous.

I also think in this case that pressure is negligible. I don't know if the math really works this way, but the power emitted by the billion ton black hole would produce a bit more than one newton of thrust if those photons all went in the same direction. The area of the event horizon is on the order of 10^-29 square meters, so it amounts to about 13 orders of magnitude more radiation pressure outward than the star's own pressure inward.

morriswalters wrote:Instead of starting it in the sun, start it in orbit close to the sun. Put it out where it can eat, and let gravity take care of everything else. Not even close to a Physicist.
Doesn’t matter where you start it, this black hole is too luminous to eat.
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Re: Science-based what-if questions

Postby andykhang » Tue Sep 05, 2017 12:57 am UTC

Not even with 3.026414e+31 m/s/s surface gravity?

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Re: Science-based what-if questions

Postby gmalivuk » Tue Sep 05, 2017 4:11 am UTC

While the equation I have for Eddington luminosity uses Newtonian potential, given that atomic distances are a few orders of magnitude larger than the black hole you're talking about, that's a reasonable enough approximation even if it is only an approximation.

Electrons are so small that even a minuscule force is enough to accelerate them a great deal, and this black hole is putting out more than a newton of total pressure. Right at the event horizon maybe it actually could suck another electron in, but it has to get close enough first, and I don't think that can happen.

(And right at the event horizon of an electron-sized black hole, I don't think we can say at all what would happen to an individual electron, without a quantum theory of gravity. But conveniently for us I doubt more than a few electrons would be able to get close enough for that to happen, and meanwhile the black hole is shedding quintillions of electron-masses worth of energy every second.)
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Re: Science-based what-if questions

Postby andykhang » Tue Sep 05, 2017 6:26 am UTC

Make sense. I supposed it should at least be as large as a proton then?

Edit:...I just tried to calculate this myself and found a nifty trick: an Eddington Limit is approximately equal to the mass in kg*6.321809415. If I follow that, this electron-size black hole would actually be magnitude away from reaching it (10^8 compare to 10^12, so 10000 times). Pretty much enough then.

Edit2: Though whether the electron themselves could reach them or not, is up to debate...

Edit 3: Then again, the Eddington limit is specifically to compare radiation pressure with gravitational force anyway...


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