Global embedding of BTZ spacetime using generalized method of symmetric embeddings construction
arXiv:2107.00752 · doi:10.1063/5.0062060
Abstract
It is often easier to study pseudo-Riemannian manifolds by presenting them as surfaces in some ambient space. We propose an algorithm for construction of explicit isometric embeddings of pseudo-Riemannian manifolds with symmetries into an ambient space of higher dimension. While most of the existing methods are based on Gauss-Codazzi-Mainardi-Peterson equations, we do not use them and instead concentrate on a system of equations which connects the metric on the manifold and the embedding function of the surface. Our algorithm is based on the group theoretical method of separation of variables that we developed earlier (arXiv:1202.1204). The algorithm makes this method more convenient and simple to use. It allowed us to simplify the construction of many known embeddings as well as obtain some new ones. In particular, we obtain explicit global embeddings of spinning BTZ black hole in 7-dimensional flat space.
arXiv comment16 pages
References in corpus (14)
- Geometry of the 2+1 Black Hole
- Godel metric as a squashed anti-de Sitter geometry
- Interior Structure of a Charged Spinning Black Hole in -Dimensions
- Gravity as a field theory in flat space-time
- Embeddings for Schwarzschild metric: classification and new results
- Global Embedding of the Reissner-Nordström Metric in the Flat Ambient Space
- Classification of global minimal embeddings for nonrotating black holes
- Global embeddings of BTZ and Schwarzschild-AdS type black holes in a flat space
- Embeddings of the black holes in a flat space
- The BTZ spacetime as an algebraic embedding
- Explicit isometric embeddings of collapsing dust ball
- Explicit isometric embeddings of pseudo-Riemannian manifolds: ideas and applications
- Canonical description for formulation of embedding gravity as a field theory in a flat spacetime
- Quasi-isometric embedding of Kerr poloidal sub-manifolds