Black hole entropy calculations based on symmetries

Symmetry-based approaches to the black hole entropy problem have a number o f attractive features; in particular, they are very general and do not depe nd on the details of the quantization method. However, we point out that, o f the two available approaches, one faces conceptual problems (also emphasi zed by others), while the second contains certain technical flaws. We corre ct these errors and, within the new, improved scheme, calculate the entropy of three-dimensional black holes. We find that, while the new symmetry vec tor fields are well defined on the 'stretched horizon', and lead to well de fined Hamiltonians satisfying the expected Lie algebra, they fail to admit a well defined limit to the horizon. This suggests that, although the forma l calculation can be carried out at the classical level, its real, conceptu al origin probably lies in the quantum theory.