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If anyone else takes a look here, note that these are not necessarily correct; there seems to be something wrong with my derivations, which is why I'm poking around here.

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My derivations

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- no guarantee over this, or that the here is the one equal to .

Old A

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- but see Weisstein's section below and New A section

New A

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Repeats

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- no guarantee over this, or that the here is the one equal to .

Reformulation

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- see Weisstein's section below

Damn, the different area formula is making things even worse?!? Maybe it's the definition of that's not what I'd expect? It needn't be the mass-energy equivalence of the entire mass of the black hole.

- Why this apparent equivalence? I have no idea. It could also be that .

Let's try a comparison with the gravitational binding energy formula. I doubt it has any relevance, but I'll see what it generates.

- Well, it's in the ballpark, and I'm pretty sure that binding energy formula doesn't allow for relativistic effects. But I still don't think it has anything to do with it.

Continued: emission

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Using my new S & T
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Using their S & T
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as in article

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(natural units)

examples in article

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derivations

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Odd, it does come out the same as the usual formula as surface area of a sphere. My mistake must lie elsewhere.

compared to my derivations

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For some reason, is coming out twice as large as . It naturally follows that this would lead to being 16 times larger than . I thought event horizons might have a surface area that was not equal to that of a conventional sphere, but that doesn't seem to explain it.

as in article

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(was Black hole entropy)

as in article

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(was Laws of black hole mechanics)

as in article

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(natural units)
(natural units)

as in article

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I noticed this in the table of equations with their nondimensionalized equivalents:

Thermal energy per particle per degree of freedom

This may be the key, if it's half of , much like threw me off with that half, when I was very young.

derivations

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, ,

as in article

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as in article

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- Here's where it's different! That's not the formula for an undistorted sphere.

Black Hole Radiation and Volume Statistical Entropy by Mario Rabinowitz

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as in article

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Examples

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SI units

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Solar-mass black hole

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or
or

1-second black hole

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or
or

Solar-mass black hole

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or
or

1-second black hole

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