How Is Black Hole Entropy Calculated According to Bekenstein-Hawking?

[DuncanJames]

Homework Statement

Looking for help with a detailed explanation of the Bekenstein-Hawking black hole entropy equation, specifically where the variables and constants come from to form this particular arrangement. The pic shows one form of which I found several. Any insight is greatly appreciated.

Relevant Equations

see attached pic

none

 

[DuncanJames]

Anyone?

 

[256bits]

From where did you find the equation?
Isn't there a description in the write up?

 

[DuncanJames]

From where did you find the equation?
Isn't there a description in the write up?

Thank you for asking. I’ve found it in various forms with varying amounts of description. (This particular one I think came from wikipedia.) To clarify, I know what the factors are. What I’m looking for is an explanation on how they came to be in the same equation. The fact that piques my interest is what happened to pi? Surface area requires 4 pi, so one of the others had to come with pi in the numerator to cancel out pi in the denominator to leave 4 by itself.

 

[256bits]

Not that I know all that much of black hole entropy, but here is a short derivation
https://theoretical-physics-digest.fandom.com/wiki/Bekenstein-Hawking_entropy
do note that if you are looking for another pi, maybe this is it:
the Gh/ c^3 is the Planck length,
where h is the Planck constant - h/(2pi) - reduced by 2pi - or h_bar