Holographic Horizons

We examine how the (2+1)-dimensional AdS space is covered by the Fefferman-Graham system of coordinates for Minkowski, Rindler and static de Sitter boundary metrics. We find that, in the last two cases, the coordinates do not cover the full AdS space. On a constant-time slice, the line delimiting the excluded region has endpoints at the locations of the horizons of the boundary metric. Its length, after an appropriate regularization, reproduces the entropy of the dual CFT on the boundary background. The horizon can be interpreted as the holographic image of the line segment delimiting the excluded region in the vicinity of the boundary.