Global embedding of BTZ spacetime using generalized method of symmetric embeddings construction

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 with symmetries into space higher dimension. While most the existing methods are based on Gauss-Codazzi-Mainardi-Peterson equations, we do not use and instead concentrate a system equations which connects metric manifold embedding function surface. Our group theoretical method separation variables that developed earlier (arXiv:1202.1204). The makes this more convenient simple use. allowed us simplify many known well obtain new ones. In particular, global spinning BTZ black hole 7-dimensional flat