The BTZ spacetime as an algebraic embedding

Abstract

A simple algebraic global isometric embedding is presented for the nonrotating BTZ black hole and its counterpart of Euclidean signature. The image of the embedding, in Minkowski space of two extra dimensions, is the interection of two quadric hypersurfaces. Furthermore an embedding into $Ad{S}_4$ or $H_4$ is also obtained, showing that the spacetime is of embedding class one with respect to maximally symmetric space of negative curvature. The rotating solution of Euclidean signature is also shown to admit a quadratic algebraic embedding, but seemingly requires more than two extra dimensions.

arXiv comment15 pages, no figures. version 2: references and acknowledgements added, typos fixed, a paragraph on alternative global coordinates added

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Cited by in corpus (3)

• Global embeddings of BTZ and Schwarzschild-AdS type black holes in a flat space
• Lower-dimensional Regge-Teitelboim gravity
• Global embedding of BTZ spacetime using generalized method of symmetric embeddings construction