Duality in the BTZ Black Hole and the Statistical Entropy

In Strominger’s proposal for the computation of the statistical entropy of black holes based on the asymptotic symmetry analysis of Brown and Henneaux a fundamental role is played by the asymptotic conditions that the considered metric must satisfy at infinity. Here it is shown that $T$-duality does not preserve such conditions. This observation is used to discuss a possible reformulation of the proposal.