Remarks on conserved quantities and entropy of BTZ black hole solutions. I. The general setting

The Bañados-Teitelboim-Zanelli (BTZ) stationary black hole solution is considered and its mass and angular momentum are calculated by means of the Nöther theorem. In particular, relative conserved quantities with respect to a suitably fixed background are discussed. Entropy is then computed in a geometric and macroscopic framework, so that it satisfies the first principle of thermodynamics. In order to compare this more general framework to the prescription of Wald and co-workers, we construct the maximal extension of the BTZ horizon by means of Kruskal-like coordinates. A discussion about the different features of the two methods for computing entropy is finally developed.