How much energy would be needed to compress a cubic meter of

>>8299820
What is the minimum mass of a black hole?

>>8299820
About as much energy your mom is storing.

>>8299840
My mom is about a cubic litre of ash.

>>8299820
you cant compress a fixed amount of water into a black hole, you would need to give the water enough mass to create a sufficiently large hole in space time

>>8299848
Then how is it that the LHC can supposedly make black holes from colliding individual particles?

>>8299848
>what is a Schwarzschild radius

>>8299836
There is no minimum mass of a black hole

>>8299855
At this radius, does gravity alone overpower all other attractive and repulsive forces?

>>8299836
There isnt one. Any amount of mass compressed beneath its Schwarzchild Radius becomes a black hole

>>8300072
No, its just the point at which escape velocity exceeds of C

>>8300074
Let's say I had a kg of electrons, could I make a black hole out of this?

>>8300093
Sure why not

>>8300093
Nope.

[math]r_s=\frac{2MG}{c^2}=\frac{2(1kg)(6.675\times10^{-11}\frac{N*m^2}{kg^2})}{(299792458\frac{m}{s})^2}=1.485\times10^{-27}m<2.818\times10^{-15}m=r_e[/math]

>>8300128
I dont speak math runes, what does this say

>>8300130
The Schwarzschild radius of 1 kg of electrons is smaller than the radius of one electron, so you can't compress 1 kg of electrons into a black hole.

>>8300133
Why not?

>>8300133
says who?

Anyone care to actually answer OP?

>>8300136
>>8300141
Okay, listen faggots.

The mass of electron is 9.109 x 10^-28 grams. That means that 1 kg's worth of electrons is 1098000000000000000000000000000 electrons.

Please tell me how you are going to fit 1098000000000000000000000000000 electrons into a space that is approximately 1000000000000 times smaller than the space a single electron occupies. I would love to know.

>>8300144
I'm also thinking about electric forces like that one french guy, so I thought to start with a material more simple than water

>>8300154
Magic. Also it's irrelevant, we are arguing the principle not the practicality

>>8300144
I'm working on it.

>>8300176
I'm talking about the practicality, since space watchers say these things are real

>>8300223
Space watchers say 1kg black holes made out of compressed electrons are real?

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What's the temperature of a black hole? -1K?

>>8300267
I'm not really sure the concept even makes sense for an infinitely dense point. It gets pretty fucking hot close to the event horizon though

>>8300272
>>8300267
Assuming there is an accretion disk I mean

>>8300272
Real black holes aren't infinitely dense, though, are they? Isn't that just an approximation?

>>8300277
No one really knows. Physics gets weird at those scales and we can get virtually no information from inside the event horizon (just Hawking Radiation)

I tried compressing a handful of water with, well my hand and it didn't work it just leaks from the cracks.
I deem it mathematically impossible from just that experiment.

>>8300287
Science wins again

>>8300277
If the singularity can actually have zero volume, then yes.

If there is a minimum non-zero volume, then the density can get arbitrarily large depending on how much matter goes into it.

We would have to wait until a verified theory of quantum gravity is developed to know which case applies.

>>8300317
We dont actually no that, although I agree it seems absurd. Every possibility we have thought up produces its own weirdness though

>>8300176
>we are arguing the principle
Sure. Theoretically, 1 kg of electrons compressed into its Schwarzschild radius would be a black hole. But, as far as I know, we can't fit more than one electron in the volume of one electron, so in practicality you can't make a black hole this way.

>>8300333
You can fit the mass of an electron into a space smaller than an electron. You start with 1kg of electrons and end up with kg of singularity

>>8299820
water is incompressible you moran

>>8300354
lol

>>8300333
>we can't fit more than one electron in the volume of one electron
just compress it man its not hard.

break it down into quarks if you have to.

Hydraulic press creates black hole! Scientists hate him!

how can you believe in black holes if it is just a theory (a gauss)?

>>8299836
>>8299871
>>8300074

Any black hole less massive than the Planck mass will have a Schwarzschild radius less than the Planck length.

If such a black hole could exist, there'd be no way we could fathom it with our knowledge of the universe.

>>8300154
i thought that was kind of what a black hole was
it magically compresses big amounts of things into a super small singularity

isn't a singularity of mindnumbingly large black hole still like less than the size of a proton?

>>8300400
How do we know black holes exist if we can't see them? XD

>>8300408
>isn't a singularity of mindnumbingly large black hole still like less than the size of a proton?
Well, a proton's radius is 1.535 x 10^-18 meters. We can find the mass whose Schwarzschild radius is the radius of a proton:

[math]M=\frac{r_sc^2}{2G}=\frac{(1.535\times10^{-18}m)(299792458\frac{m}{s})^2}{2(6.674\times10^{-11}\frac{N*m^2}{kg^2})}=1.034\times10^9kg.[/math]

For comparison, the earth's mass is 5.972 x 10^24 kg. So that's not an insignificant amount of mass, but I wouldn't call it mindnumbing. Of course, larger masses will have much larger Schwarzschild radii.

Keep in mind, though, that the Schwarzschild radius is only a maximum, so it's possible that a mindnumbing amount of mass could indeed occupy a very small volume. But we have no way of knowing that.

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Let us assume for the moment that the water somehow manages to retain the intrinsic thermodynamic properties it has at STP. This is obviously unrealistic, but with the magnitudes of pressure we're talking about, it will be close enough.

If the water were compressed adiabatically:
[eqn]
\Delta Q = 0 \\
\Delta U = -\Delta W \\
\mathrm{d}\left( p V^\gamma \right) = 0
[/eqn]
Expanding out that total derivative:
[eqn]
V^\gamma \mathrm{d}p + pV^{\gamma - 1} \gamma \mathrm{d}V = 0
[/eqn]
Now by using the fundamental thermodynamic relation:
[eqn]
\mathrm{d}U = T \mathrm{d} S - p \mathrm{d} V
[/eqn]
Place it under isentropic conditions and rewrite it slightly:
[eqn]
\Delta W = p \mathrm{d} V
[/eqn]
Isentropic compressibility is defined as:
[eqn]
\beta_S = - \frac{1}{V} \left. \frac{\partial V}{\partial p} \right|_{\mathrm{d} S = 0}
[/eqn]
Therefore:
[eqn]
\frac{1}{V \beta_S} = -\frac{\partial p}{\partial V} \wedge p(V_0) = p_0 \\
p(V) = p_0 - \beta^{-1}_S \left( \ln V - \ln V_0 \right)
[/eqn]
Now with that done, we have to see what is the volume we need to compress the water to.

Assuming we start at STP, the amount of water in the OP has a mass of [math]998.207 \mathrm{kg}[/math]. The Schwarzschild radius is therefore:
[eqn]
r_s = \frac{2mG_C}{c^2} \approx 1.48247 \mathrm{ym}
[/eqn]
For reference, that yoctometer is [math]10^{-24}[/math] meters.

I assume you're not children, so how we go from that to a volume of [math]13.6472 \mathrm{ym}^3[/math] should be obvious.

The isentropic compressibility of water does not appear to be in the usual sources, but it can be calculated from the speed of sound [math]v[/math] and the density [math]\rho[/math]:
[eqn]
\beta_S = \frac{1}{\rho v^2} \approx 0.00456 \mathrm{MPa}^{-1}
[/eqn]

We conclude by integrating the work done to get from STP to this final volume:
[eqn]
W = \int_{V_0}^{V_1} p(V)\mathrm{d} V = \\
\left[ p_0 V - V \frac{\ln \frac{V}{V_0} - 1}{\beta} \right]^{V_1}_{V_0} \approx \\
4386.92\mathrm{MJ}
[/eqn]
...Maybe?

>>8300449
I forgot that the density is obviously variable in this case:
[eqn]
\rho = \frac{m}{V}
[/eqn]
Which brings us up to [math]29.558\mathrm{TJ}[/math]. Still seems kinda low though, even for a naive calculation such as this one.

>>8300407
>If such a black hole could exist, there'd be no way we could fathom it with our knowledge of the universe
Fair point, but thats not the same thing as it not existing

>>8299848
That makes literally no sense.

>>8300154
The whole point of compressing it is that it would take up less space.

>>8300449
I'm not sure how relevant that is, since you actually have to compress the water into neutrons and then the neutrons into quarks. I don't think it makes much difference if we're talking about water or anything else.

>>8300664
It's a purely classical thermodynamic analysis. Which goes to show just how much that breaks down at these scales.

>>8300081
No. That's the Event Horizon. The Schwarzchild radius, were such a thing even to exist would describe the singularity itself.

>>8300650
What is there to compress, retard?

>>8299820
12

>>8300965
No, the Schwarzschild radius IS the radius of the event horizon sphere for a given mass. We don't know what size the actual singularity would be, assuming it has a property we could even call a size in the conventional sense.

>>8300513
Yes, but assuming the laws of physics are correct, it could never possibly exist. It would be like saying how much energy is required to make a unicorn like house music?

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>>8300357
>break electrons down into quarks

>>8300154
But the electron is a point particle with no radius

what have you been smoking?

>>8299843
Liter is already a volume measurement, you didn't need to add cubic. Unless the urn is a cube.

>>8301585
>models of the real world are exactly how the real world actually works

Underageb&

>>8301589
I believe he meant a cubic litre of ash in 4-space.

>>8301589
A cubic liter would actually be 1*10^-9 m^9
>>8301591
As far as we know, it's not a model. Electrons are literally point particles.

>>8301593
wouldn't a cubic litre actually be 9-space?

>>8301591
So what makes you think the electron has a radius?

>>8301599
4D cube with 3D cubes as "surfaces"

i'll give you some bounds:
at least 2 pascals and infinite energy.

>>8300965
The event horizon is identical to the schwartzchild radius once the black hole forms

>>8301570
The laws of physics dont preclude objects smaller than the planck length. Its a limit on human investigation not reality

>>8301601
so what makes you think that electron exist?

>>8299836
I did some research on black holes for my senior research paper last year and there isn't a minimum mass for a black hole to be created and they're created all the time but they're so small that they burn themselves out before they're even noticed. They don't need much mass to be stable but I'm not sure if OP's idea is feasible

https://www.youtube.com/watch?v=7e5-0t0pTF0

>>8300074
>Any amount of mass compressed beneath its Schwarzchild Radius becomes a black hole
It's never been done, how do you know that? Yet more guesswork from /x/.