Geometry of generic isolated horizons

Geometrical structures intrinsic to non-expanding, weakly-isolated and isolated horizons are analysed and compared with structures which arise in other contexts within general relativity, e.g. at null infinity. In particular, we address in detail the issue of singling out the preferred normals to these horizons required in various applications. This study provides powerful tools to extract invariant, physical information from numerical simulations of the near-horizon, strong-field geometry. While it complements the previous analysis of laws governing the mechanics of weakly-isolated horizons, prior knowledge of those results is not assumed.