New Black Hole Creation Feat Formula Proposal

[Epyriel]

I would like to propose a newly derived formula to be used for scaling black hole creation feats in cases where it has not been sufficiently substantiated that the black hole was constructed by directly creating the requisite mass from energy (and thus qualify for use of Einstein’s Mass-Energy equivalence formula). [Thread creation by non calc group member approved by Antvasima]

Currently the method used to quantify the low end for black hole creation feats is the one described here as discussed in this thread.

As has been pointed out, this essentially uses fictitious physics to get an estimate for what the GBE of a black hole would be (if it were possible for a black hole to have such a thing, which it isn’t) by using a ratio to the GBE of the Earth or Sun (whichever is closer). On top of the detriment of needing to cheat the physics to get an estimate, this method also suffers from the fact that it doesn’t proportionally scale as the size of the black hole further diverges from the two reference markers.

So how else might we might generate an estimate for this scenario without making up some physics? Well, if the mass isn’t being converted from energy, the only other option for actually assembling a black hole would be to displace existing mass and compress it past the Schwarzschild radius to collapse into a black hole.

If the black hole is created from what appears to be nothing and energy conversion isn’t responsible, I think it is fair to assume some fictitious means of summoning matter is at play. Now if the displacement of matter is handled by some summoning ability, the only thing left to calculate is the actual compression of the matter.

But before we can calculate the compression, we first must pick a building material. As far as a ‘default’ material might be considered, I think the best option would be hydrogen gas (H2). Since the Big Bang, the first wave of mass to spring forth in the universe was about three quarters hydrogen and one quarter helium. Since then, hydrogen remains the most abundant substance in the universe by far, and indeed the molecular gas clouds that form celestial objects are composed of hydrogen gas (H2).

If we assume the matter used to assemble our black hole is taken from one of these hydrogen gas clouds scattered throughout space, we can now calculate how much energy it would take to compress a sphere of such (held at equal density to the densest isolated molecular gas clouds to prevent complications arising from more imminent gravitational collapse at higher densities) of equal mass to the black hole in question down to its Schwarzschild radius.

This can be estimated by assuming the gas sphere operates as an ideal gas undergoing isothermal compression and integrating the work equation, which ultimately yields this formula:

E = -M * kB * T * ln[32π * M^2 * G^3 * nH2 * mH2 / (3c^6)] / mH2

This can be simplified by plugging in all the constants and the assumed values for our hydrogen gas cloud to get this final formula (accurate to four significant figures):

E = -(41,260 J * kg^-1) * M * ln[(4.593 x 10^-97 kg^-2) * M^2]

This ends up being a more conservative estimate than the currently accepted method (a 1 solar mass black hole only requires the equivalent energy of the GBE of a large planet to be created through gas compression) and has the benefit of following real physics without the need to invent a method to stick a GBE value to a black hole.

 

[Antvasima]

@DontTalkDT @Ultima_Reality @Executor_N0 @Spinosaurus75DinosaurFan @Mr. Bambu @Therefir @Ugarik @DMUA @Damage3245 @TheRustyOne @DemonGodMitchAubin @Jasonsith @Wokistan @Armorchompy @Migue79 @Psychomaster35 @CloverDragon03 @Dark-Carioca @AbaddonTheDisappointment @Aguywhodoesthings @Agnaa @Dalesean027 @DemiiPowa @Flashlight237 @SeijiSetto @Chariot190 @SunDaGamer

What do you think about this?

 

[Armorchompy]

I'd be in favor of a new method- the current one is essentially an arbitrary assumption to make it so BHs can have a rating, so any viable ones are automatically an improvement in my mind. As for whether there's issues with this one, I'll leave that to the CGMs that actually know what they're talking about (not me).

 

[CloverDragon03]

Yeah this is a case where I'm not too familiar with the workings of black hole feats, so provided the methodology actually works, I'd be on board with this rather than the approximation we currently have

 

[Ugarik]

The formula is correct but I'm not sure if it's reasonable to assume isothermal compression. Adiabatic seems to make much more sense to me

 

[Ugarik]

Hydrogen H2 is a two atomic gas to its internal energy is:
E = 3/2nRT
In adiobatic process temperature ratio is T2/T1 = (V1/V2)^(R/C)
so T2 = T1*(V1/V2)^(R/C)
E = 3/2nR*T1*(V1/V2)^(R/C)
From the calc above: V2 = 8πMG/c^2 and V1 = M/ρH2

E = 3/2nR*T1*((M/ρ)/(8πMG/c^2))^(R/C)

E = 3/2nR*T1*(c^2/8πρG)^(R/C)

 

[DontTalkDT]

Our current one is more in line with creation feats in general, where we don't really use physics at all but rule of thumb comparisions, based on what seems fair common sense like when you create something on the level of a star you're star level. The only reason we have formulas of some kind is that otherwise people will complain about lack of clear cut off points, not because we invent fictional physics.
Compression is appropriate if the black hole is created via compression, but not if it's magiced up from nothing. It would make little sense to assume that a 1 ton black hole bomb that explodes and creates a solar system sized black hole would work via compression of hydrogen. Heck, if you summon up matter then compression work doesn't really apply, as you don't need to work against pressure to teleport something into a highly compressed area.

But for feats that actually compress stuff to create black holes, sure.
As Ugarik said, isothermal is a weird assumption.
This probably would also depend on how the gas is compressed. Like, you could probably create a small black hole first and have it suck up the rest of the matter to grow.
And you have to calculate compression force against gravitational pull, as gravity aids you in compressing, especially for the hardest part at the end.
(And fairly sure there technically are other forces in the last stages to consider, but I guess compression does for a low-end)

Edit: Also which assumptions are we doing for initial density and temperature here?

 

[Agnaa]

To the OP; I'd like to know what happens if other materials are used instead. Perhaps, to keep it simple, how it differs if significantly denser gases are used. They're less prevalent, but most verses with black hole feats would still have those elements in sufficient abundance.

Although, even then, I do have similar concerns to DT (if we're assuming teleportation, they could use that power to create a black hole without actually compressing it; once a sufficiently dense object is formed, it would be easier to compress the rest of the mass in).

Still, if this method ends up lower, I'd be happy to have it supplant the current one as a safer estimate.

 

[Jasonsith]

[original message deleted]

So what Epyriel proposes is not even a black hole creation energy formula in your eyes?
What do others think?
If this is an incorrect formula even theoretically, then this could not be used for black hole creation feats.

 

[Agnaa]

So what Epyriel proposes is not even a black hole creation energy formula in your eyes?
What do others think?
If this is an incorrect formula even theoretically, then this could not be used for black hole creation feats.

No, I was responding to HammerStrikes219....

HammerStrikes and I have agreed to delete those, but I'll keep these two up to inform you, Jason.

 

[Flashlight237]

No comment.

 

[Antvasima]

Our current one is more in line with creation feats in general, where we don't really use physics at all but rule of thumb comparisions, based on what seems fair common sense like when you create something on the level of a star you're star level. The only reason we have formulas of some kind is that otherwise people will complain about lack of clear cut off points, not because we invent fictional physics.
Compression is appropriate if the black hole is created via compression, but not if it's magiced up from nothing. It would make little sense to assume that a 1 ton black hole bomb that explodes and creates a solar system sized black hole would work via compression of hydrogen. Heck, if you summon up matter then compression work doesn't really apply, as you don't need to work against pressure to teleport something into a highly compressed area.

But for feats that actually compress stuff to create black holes, sure.
As Ugarik said, isothermal is a weird assumption.
This probably would also depend on how the gas is compressed. Like, you could probably create a small black hole first and have it suck up the rest of the matter to grow.
And you have to calculate compression force against gravitational pull, as gravity aids you in compressing, especially for the hardest part at the end.
(And fairly sure there technically are other forces in the last stages to consider, but I guess compression does for a low-end)

Edit: Also which assumptions are we doing for initial density and temperature here?

Do any of you have any input regarding this?

 

[Agnaa]

I've said most of what I wanted to earlier:

Although, even then, I do have similar concerns to DT (if we're assuming teleportation, they could use that power to create a black hole without actually compressing it; once a sufficiently dense object is formed, it would be easier to compress the rest of the mass in).

Still, if this method ends up lower, I'd be happy to have it supplant the current one as a safer estimate.

While it's imperfect, and there are methods of black hole creation that wouldn't operate that way, we typically set our baselines for things like this based on what's most realistic (in this case, our current method isn't very realistic either) and on what's lower (so we don't accidentally rate feats higher than they are; we often rely on elaboration to clarify that a more power-intensive method is being used).

So I think this is a good starting point, at the very least.

 

[HammerStrikes219]

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4338837/

I share what I can find for alternatives for a formula of a creation of a black hole as this seems promising. However, as a note, this is a 2006 article so it is outdated, but seems to have formulas in relation to the formation of newly born black holes at least.

Different from the one formula being used currently.

 

[Epyriel]

To the OP; I'd like to know what happens if other materials are used instead. Perhaps, to keep it simple, how it differs if significantly denser gases are used. They're less prevalent, but most verses with black hole feats would still have those elements in sufficient abundance.

It depends on the exact material. If the natural logarithm of its mass density is proportionally greater than its molecular mass compared to H2 then it will require greater energy to isothermally compress. If the reverse is true it will take less energy to compress compared to hydrogen gas.

 

[HammerStrikes219]

It depends on the exact material. If the natural logarithm of its mass density is proportionally greater than its molecular mass compared to H2 then it will require greater energy to isothermally compress. If the reverse is true it will take less energy to compress compared to hydrogen gas.

It is Solar Mass in case of black holes as it is well known in the scientific community that Black Holes are born from a collapsed dying Star and some other specific means


So it ain’t strictly Hydrogen if memories serve me right on this regard.

 

[Epyriel]

It is Solar Mass in case of black holes as it is well known in the scientific community that Black Holes are born from a collapsed dying Star and some other specific means


So it ain’t strictly Hydrogen if memories serve me right on this regard.

The proposal is a calculation of how much energy it would take to compress interstellar gas, not an active star.

Sure, black holes are naturally born from massive stars at the end of their fusion reserves but this isn’t really applicable to an artificial creation feat.

 

[HammerStrikes219]

The proposal is a calculation of how much energy it would take to compress interstellar gas, not an active star.

Sure, black holes are naturally born from massive stars at the end of their fusion reserves but this isn’t really applicable to an artificial creation feat.

Yes, but an artificial creation feat will not involve just one element. It will involve multiple elements on the periodic table as Outer Space is consist of many elements as we know it ain’t pure Hydrogen (It is one of the most common elements in Outer Space though).

 

[Epyriel]

Yes, but an artificial creation feat will not involve just one element. It will involve multiple elements on the periodic table as Outer Space is consist of many elements as we know it ain’t pure Hydrogen (It is one of the most common elements in Outer Space though).

If you are referring to supernova remnant gas clouds, those are a minority throughout space. Most molecular gas clouds remain as they were in the aftermath of the Big Bang - just hydrogen and helium.

It is in fact fairly typical for molecular gas clouds to be almost entirely either pure hydrogen, or a 3-1 hydrogen-helium mix. Either way, the math remains pretty accurate for a typical molecular gas cloud.

 

[HammerStrikes219]

If you are referring to supernova remnant gas clouds, those are a minority throughout space. Most molecular gas clouds remain as they were in the aftermath of the Big Bang - just hydrogen and helium.

It is in fact fairly typical for molecular gas clouds to be almost entirely either pure hydrogen, or a 3-1 hydrogen-helium mix. Either way, the math remains pretty accurate for a typical molecular gas cloud.

Gas clouds ain’t the same as a blackhole as I said earlier on Outer Space being made up of multiple elements. Even Nasa has that statement regarding the elements of the universe

https://www.nasa.gov/solar-system/five-weird-things-that-happen-in-outer-space/


However, Black Holes are still made out of matter so it would technically consist multiple elements of yet not at the same time due to its nature IIRC.

 

[Epyriel]

The formula is correct but I'm not sure if it's reasonable to assume isothermal compression. Adiabatic seems to make much more sense to me

As Ugarik said, isothermal is a weird assumption.

Isothermal compression was calculated under the assumption of a cooling mechanism in place to dispense induced heating in order to create a conservative estimate. Adiabatic compression with no cooling whatsoever produces some pretty insane highball estimates. I updated my blog with a sample derivation using such for reference.

Edit: Also which assumptions are we doing for initial density and temperature here?

Number density was set at 10,000 H2 molecules/cm^3 (essentially using the densest existing common stable isolated molecular gas clouds) and a temperature of 10K (the typical temperature for naturally occurring isolated molecular gas clouds).

Our current one is more in line with creation feats in general, where we don't really use physics at all but rule of thumb comparisions, based on what seems fair common sense like when you create something on the level of a star you're star level. The only reason we have formulas of some kind is that otherwise people will complain about lack of clear cut off points, not because we invent fictional physics.

I see where you are coming from and that is more or less what I was trying to do through a compression calc. Instead of needing to ratio of a separate celestial phenomenon not really applicable to black holes, instead we could get a reference marker from a purely classical compression equivalent. While in reality, most of these feats in fiction are essentially making up physics to perform these creation feats, I figured I’d give a crack at trying to parallel the closest we can get to scaling a corollary feat in reality.

Compression is appropriate if the black hole is created via compression, but not if it's magiced up from nothing.

I’d say it is as appropriate as the current method for the latter case, and has the benefit of scaling proportionally outside of ranges near the Sun and Earth.

Heck, if you summon up matter then compression work doesn't really apply, as you don't need to work against pressure to teleport something into a highly compressed area.

Although, even then, I do have similar concerns to DT (if we're assuming teleportation, they could use that power to create a black hole without actually compressing it; once a sufficiently dense object is formed, it would be easier to compress the rest of the mass in).

The idea was to try to make a reference mechanism as close as we can get to real world equivalent rather than trying to characterize a fictional teleportation method. The ‘summoning’ part of the explanation is more just for the sake of how such a thing can be rationalized in the fictional setting itself, but in reality most settings are just invoking magical physics that can’t really be translated in such a way.

It would make little sense to assume that a 1 ton black hole bomb that explodes and creates a solar system sized black hole would work via compression of hydrogen.

Pretty sure something like that would qualify for a mass-energy equivalence calculation as a kind of Kugelblitz so neither method would really apply.

This probably would also depend on how the gas is compressed. Like, you could probably create a small black hole first and have it suck up the rest of the matter to grow.
And you have to calculate compression force against gravitational pull, as gravity aids you in compressing, especially for the hardest part at the end.
(And fairly sure there technically are other forces in the last stages to consider, but I guess compression does for a low-end)

Yeah there would be a whole host of factors at play if we consider a scenario of a compression characterization of natural astronomical scaled interactions, from the quantum mechanical effects of degeneracy pressure to the atomic effects of radiative pressure caused by nuclear reactions induced by the extreme outside pressure, both of which would cause opposing forces against gravitational collapse.

The idea I had for this was to create a reference purely in consideration of the classical effects at play from just what you would need to induce for a simple model of how much work you would need to overcome a given pressure at any scale. This wouldn’t be super accurate for a real world model of a gradual induced collapse, but I figured it would be worth a shot as an attempt to characterize the input energy for fictional creation feats that tend to just be on an instantaneous timeframe - something that would bypass the numerous possible complications raised above.

But for feats that actually compress stuff to create black holes, sure.

I’m fine with settling for just that, but I thought I might as well offer this as a general solution since the existing method is kind of arbitrary - although to be fair that is relatively par for the course for the current standards of non mass-energy equivalence creation feats.

 

[Epyriel]

Gas clouds ain’t the same as a blackhole as I said earlier on Outer Space being made up of multiple elements. Even Nasa has that statement regarding the elements of the universe

https://www.nasa.gov/solar-system/five-weird-things-that-happen-in-outer-space/


However, Black Holes are still made out of matter so it would technically consist multiple elements of yet not at the same time due to its nature IIRC.

Black holes don’t really have a composition as is typically understood. Once anything is introduced into a black hole, the current understanding is that such is stripped down to its three fundamental properties of mass, charge, and spin.

Regardless, this calc is about artificially creating a black hole through compressing H2 gas, not attempting to replicate common collapse methods and compositions of stars in nature.

 

[HammerStrikes219]

Black holes don’t really have a composition as is typically understood. Once anything is introduced into a black hole, the current understanding is that such is stripped down to its three fundamental properties of mass, charge, and spin.

Regardless, this calc is about artificially creating a black hole through compressing H2 gas, not attempting to replicate common collapse methods and compositions of stars in nature.

Compression of H2 gas doesn’t seem to account for the other elements in my opinion as since this is fiction we talking about, they could easily, in theory, made that black hole from creating matter and then turn it into a black hole which will consist of not pure H2 gas to begin with, but with other elements in it.

 

[Agnaa]

It depends on the exact material. If the natural logarithm of its mass density is proportionally greater than its molecular mass compared to H2 then it will require greater energy to isothermally compress. If the reverse is true it will take less energy to compress compared to hydrogen gas.

So are you saying that some elements/molecules would take more energy, and some would take less?

Because if, between different materials, it's a crapshoot that jumps all over the place, we may as well go with hydrogen. But if hydrogen is a real outlier compared to the rest (being particularly difficult or particularly easy), we might wanna look for something else.

 

[Agnaa]

@HammerStrikes219 That doesn't answer my question.

If you make another unhelpful post I'll thread-ban you. CGMs are only meant to post here when they've got helpful information; you've been posting things that misunderstand the topic of this thread the whole time.

 

[Epyriel]

So are you saying that some elements/molecules would take more energy, and some would take less?

Because if, between different materials, it's a crapshoot that jumps all over the place, we may as well go with hydrogen. But if hydrogen is a real outlier compared to the rest (being particularly difficult or particularly easy), we might wanna look for something else.

Yes. And its actually more complicated than that as it depends not only on the specific molecule, but also in what context that molecule is found, as many often exist stably at multiple different densities of varying rarity depending on where exactly you are taking it from.

Although luckily all the most common elements have math that works out very similar to hydrogen - my guess is that it would only significantly diverge if you start looking for substances that only tend to exist in a lab or have too diluted a concentration throughout space to make this scenario practical.

If we consider real world gas clouds that we could source from, the only two substances we could realistically take from in large enough quantities would be hydrogen or helium, or a mix of the two. From the two, hydrogen is three times as abundant as helium, but ultimately the math is very similar.

 

[Agnaa]

Ye, as I said if hydrogen isn't an outlier, we may as well just go with it due to its abundance. I'm fine with this method.