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Both mass and entropy behave differently for black holes than for normal matter.

For simple Schwarzschild black holes, mass is proportional to their radius. The Bekenstein-Hawing entropy is proportional to their surface.

Of course, the calculations for the two results can be found in the textbooks.

Is there a simple explanation for why the dependencies on the radius differ?

For example, fourfold surface implies fourfold entropy - but only twice the mass. In contrast, in normal matter, fourfold entropy implies fourfold mass.

What is the best way to explain that in black holes, entropy increases more than mass? Somehow, mass and entropy are decoupled.

What is the best way to explain this?

KlausK
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Watch carefully as I wave my hands:

My way naive way of looking at this is to think of the entropy of a black hole as residing at its event horizon- that in some way a black hole is an engine that separates out entropy from mass and stores them separately- at least from a viewpoint outside the EH.

But I have never managed to satisfy myself regarding the question of where the heck a black hole sequesters its mass. If it all fell straight into the singularity, then a black hole would not possess a moment of inertia because the radius of the mass distribution would be zero. So is it stored at the EH surface too? If it were, then the moment of inertia of a black hole would be that of a hollow spherical shell with the radius of the EH, which isn't right either.

I'm very interested in what the experts here can teach me about this.

niels nielsen
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