Asymptotically AdS spacetimes and isometric embeddings

Abstract: We present a simple isometric embedding of the nonrotating BTZ black hole spacetime into (3+2)-dimensional Minkowski space and (3+1)-dimensional mathematical AdS space. A one parameter family of embeddings of the physical (2+1) AdS space (i.e. the universal covering of AdS) is obtained by a double Wick rotation from the BTZ case. The continuous parameter is an example of "isometric bending" and corresponds to the temperature of the Euclidean spacetime. The embeddings take a particularly elegant form in terms of Klein's projective model. More generally, we find that the falloff conditions for asymptotically AdS spacetimes such as black holes take a simple form in the projective model.

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