Higher dimensional flat embeddings of (2+1)-dimensional black holes

We obtain the higher dimensional global hat embeddings of static, rotating, and charged Banados-Teitelboim-Zanelli (BTZ) black holes. On the other hand, we also study similar higher dimensional Aat embeddings of the (2+1)-dimensional de Sitter black holes which are the counterparts of the anti-de Sitter BTZ black holes. As a result, the charged de Sitter black hole is shown to be embedded in a (3+2)-dimensional GEMS, in contrast with the charged BTZ one having a (3+3)-dimensional GEMS structure.