Entropy calculation for a toy black hole

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In this note we carry out the counting of states for a black hole in loop quantum gravity, however assuming an equidistant area spectrum. We find that this toy-model is exactly solvable, and we show that its behavior is very similar to that of the correct model. Thus this toy-model can be used as a nice and simplifying `laboratory' for questions about the full theory.
18 pages, 4 figures. v2: Corrected mistake in bibliography, added appendix with further results

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