Global embeddings of BTZ and Schwarzschild-AdS type black holes in a flat space

Abstract

We study the problem of construction of global isometric embedding for spherically symmetric black holes with negative cosmological constant in various dimensions. Firstly, we show that there is no such embedding for 4D RN-AdS black hole in 6D flat ambient space, completing the classification which we started earlier. Then we construct an explicit embedding of non-spinning BTZ black hole in 6D flat ambient space. Using this embedding as an anzats, we then construct a global explicit embedding of (d)-dimensional Schwarzschild-AdS black hole in a flat (d+3)-dimensional ambient space.

15 pages

References in corpus (3)

• Embeddings for Schwarzschild metric: classification and new results
• General Relativity à la string: a progress report
• The BTZ spacetime as an algebraic embedding

Cited by in corpus (6)

• On energy for accelerating observers in black hole spacetimes
• Global embedding of BTZ spacetime using generalized method of symmetric embeddings construction
• GEMS embeddings of Schwarzschild and RN black holes in Painlevé-Gullstrand spacetimes
• Explicit isometric embeddings of pseudo-Riemannian manifolds: ideas and applications
• Nontrivial isometric embeddings for flat spaces
• GEMS embeddings of Hayward regular black holes in massless and massive gravities