The BTZ spacetime as an algebraic embedding

Details The BTZ spacetime as an algebraic embedding The BTZ spacetime as an algebraic embedding

2010-11-17

arxiv.org/abs/1011.3883v2

J.Math.Phys.52:042503,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, no figures. version 2: references and acknowledgements added, typos fixed, a paragraph on alternative global coordin

Scientific paper

10.1063/1.3579486

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 $AdS_4$ 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.

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