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I have recently read that by varying the string coupling adiabatically (hence the mass of the black hole as well), there is a transition going from a black hole to a single highly excited string. I would like to ask a few questions, and they are:

(i) What does it actually mean when we say we vary the string coupling adiabatically? Why is this an isentropic process?

(ii) What are the differences for black hole transition in the case of (a) extremal black holes, and (b) near-extremal black holes? Does the black hole evolve to a collection of free strings or one highly excited strings?

(iii) Why are strings the only object that remain to have finite energy in a compactified spatial dimension? Why couldn't we use other objects (say a membrane) to get involved in compactification?

(iv) I tried to look for related journals and review papers online (arxiv.org) but I couldn't find the derivation of the identification between string entropy and black hole entropy. Could anyone tell me where to find this derivation?

Thanks a lot!

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# String entropy and black hole entropy

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