Accuracy of Black Hole Radiation Equation on Wikipedia

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SUMMARY

The discussion centers on the accuracy of the black hole radiation equation presented on Wikipedia, specifically for a nonrotating, non-charged Schwarzschild black hole. The equation estimates the power emitted as Hawking radiation, utilizing the Schwarzschild radius, Stefan-Boltzmann law, and the surface area of the event horizon. Participants confirm that the energy outflow, denoted as P, is indeed measured in watts, equivalent to joules per second, despite initial confusion regarding unit cancellation. The formula has not been derived within the framework of semiclassical gravity, indicating ongoing research in this area.

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kuahji
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Was just curious as to if this equation on wikipedia was accurate.

The link on wiki states
The power emitted by a black hole in the form of Hawking radiation can easily be estimated for the simplest case of a nonrotating, non-charged Schwarzschild black hole of mass M. Combining the formulae for the Schwarzschild radius of the black hole, the Stefan-Boltzmann law of black-body radiation, the above formula for the temperature of the radiation, and the formula for the surface area of a sphere (the black hole's event horizon) we get:

http://upload.wikimedia.org/math/9/1/e/91ead79dbf75e21b618af5d067458717.png

where P is the energy outflow, \hbar is the reduced Planck constant, c is the speed of light, and G is the gravitational constant. It is worth mentioning that the above formula has not yet been derived in the framework of semiclassical gravity.

So what I'm wondering is, exactly what units would P or rather the energy outflow be represented as. I was thinking joules, but for some reason couldn't get all the units to cancel out, which is probably just a mistake on my part. Anyway, anyone have any thoughts or input on this subject?
 
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The units in the formula match for watt (joules per second).
 

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