#### Epyriel

He/Him- 87

- 110

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.

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.

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