This week's physics puzzler.

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This question is prompted by a passage from Brian Greene's Fabric of the Cosmos. Greene is discussing the fact that in our usual experience entropy is proportional to volume (other things being equal) whereas for black holes the entropy is proportional to the area of the horizon. On page 479 of chapter 16 he says
Were you to double the radius of a black hole, its volume would increase by a factor of 8 while its surface area would only increase by a factor of 4.
This is misleading. His radius, area, volume relations are only valid for flat space, in curved space the ratios are different. The radius circumference relations for a circle on the surface of a two sphere illustrate the point.

So here's the question, in two parts:

a) What are the radius, area, volume relations (for a surface r=constant) in a Schwarzschild space-time?

b) Do the notions of radius and volume even make sense for a black hole?

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