abstract: In the context of general relativity, static metrics describe canonical space-like slices of a static vacuum space-time. We present a new approach towards their classification both in the case of zero and non zero cosmological constant. For three dimensional static metrics with zero cosmological constant and connected horizon, we recover the well known black hole uniqueness theorem by Israel, Robinson et al. We will also discuss possibile extensions of such a theorem in the case of positive cosmological constant. The results are obtained in collaboration with V. Agostiniani and S. Borghini.