Is there a limit to information storage on the surface of a black hole?

[binaryverse]

Hello,

I'll try to explain this as well as I can...

I was watching NOVA's special on The Fabric of the Cosmos and the segment on how information is both lost in the black hole and stored on the surface got me wondering "Is there a limit to how much information can be stored on the surface of a black hole?"

Any insight or feedback is appreciated.

 

[Physics Monkey]

The standard answer is one bit per "Planck area". This estimate comes from the expression for black entropy which says $S = A/G_N$ (S is the entropy, A is the area, and G is Newton's constant). In 4d Newton's constant is related to the Planck length by $G_N = L_p^2$. Hence the entropy is $S = A/L_p^2$. Since it is argued that a black hole is the most compact object possible, the maximal possible entropy should be that of a black hole, and hence the maximal amount of information that can be stored is roughly one bit per Planck area.

Does that help?

 

[gendou2]

Actually, it's 4 bits per plank area, but you get the idea.
$S = A/4 L_p^2$
http://www.scholarpedia.org/article/Bekenstein-Hawking_entropy

 

[Ynaught?]

Actually, it's 4 bits per plank area, but you get the idea.
$S = A/4 L_p^2$
http://www.scholarpedia.org/article/Bekenstein-Hawking_entropy

Don't you mean 1 bit per 4 Planck areas, as shown in the picture on your link?

 

[gendou2]

Oops, yes! Algebra.