Related papers: The BTZ spacetime as an algebraic embedding
An algebraic global isometric embedding of the nonrotating BTZ black hole is presented. The ambient spacetime is $\mathbb{M}^{2,3}$, the 3+2 dimensional flat spacetime. We also present the analogous embedding for the Euclidean BTZ spacetime…
We consider static circularly symmetric solution of three-dimensional Einstein's equations with negative cosmological constant (the BTZ black hole). The case of zero cosmological constant corresponding to the interior region of a black hole…
Under certain conditions, a $(1+1)$-dimensional slice $\hat{g}$ of a spherically symmetric black hole spacetime can be equivariantly embedded in $(2+1)$-dimensional Minkowski space. The embedding depends on a real parameter that corresponds…
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…
The regular black hole solution arising as a spherically symmetric vacuum solution of Born-Infeld gravity possesses an asymptotic interior structure which is very well described by a four dimensional generalization of the non-rotating BTZ…
It is shown that 2+1 dimensional anti-de Sitter spacetimes are Lorentz-flat. This means, in particular, that any simply-connected patch of the BTZ black hole solution can be endowed with a Lorentz connection that is locally pure gauge. The…
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…
We analyze the double Wick rotated BTZ black hole with the Euclidean signature, which is a Riemannian manifold. We calculate thermodynamics, total energy of spacetime, and holographic two point functions in the double Wick rotated…
We show that it is possible to embed the 1+1 dimensional reduction of certain spherically symmetric black hole spacetimes into 2+1 Minkowski space. The spacetimes of interest (Schwarzschild de-Sitter, Schwarzschild anti de-Sitter, and…
We show that the 1+1 dimensional reduction (i.e., the radial plane) of the Kruskal black hole can be embedded in 2+1 Minkowski spacetime and discuss how features of this spacetime can be seen from the embedding diagram. The purpose of this…
Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x(t). This…
We investigate a class of semi-Riemannian manifolds characterized by smooth metric signature changes with a transverse radical. This class includes spacetimes relevant to cosmological models such as the Hartle-Hawking "no boundary"…
We examine embedding diagrams of hypersurfaces in the Reissner-Nordstrom black hole spacetime. These embedding diagrams serve as useful tools to visualize the geometry of the hypersurfaces and of the whole spacetime in general.
We study the wave equation for a massive scalar in three-dimensional AdS-black hole spacetimes to understand the unitarity issues in a semiclassical way. Here we introduce four interesting spacetimes: the non-rotating BTZ black hole (NBTZ),…
We obtain a global embedding of the surface of a rapidly rotating Kerr-Newman black hole in an Euclidean 4-dimensional space.
Spacetime singularities represent a fundamental challenge in gravitational physics. We present a mathematically consistent framework for signature-changing black holes based on the $(2+1)$-dimensional BTZ metric, where the signature…
The generic rotating BTZ black hole, obtained by identifications in AdS3 space through a discrete subgroup of its isometry group, is investigated within a Lie theoretical context. This space is found to admit a foliation by two-dimensional…
We consider a $(2+1)$-dimensional spacetime whose two-dimensional space part is Weyl-related to a surface of arbitrary negative constant Gaussian curvature with symmetries of two-dimensional Lie algebra. It is shown that the geometry is a…
A large variety of spacetimes---including the BTZ black holes---can be obtained by identifying points in 2+1 dimensional anti-de Sitter space by means of a discrete group of isometries. We consider all such spacetimes that can be obtained…
This paper is a sequel of "Solvable symmetric black hole in anti de Sitter spaces" [arXiv:math.DG/0510442]. In the latter, we described the BTZ black hole in every dimension by defining the singularity as the closed orbits of the Iwasawa…