Related papers: Global embedding of the Kerr black hole event hori…

In previous work, we developed tools for quantifying the tidal distortion of a black hole's event horizon due to an orbiting companion. These tools use techniques which require large mass ratios (companion mass $\mu$ much smaller than black…

We study the horizon geometry of Kerr black holes (BHs) with scalar synchronised hair, a family of solutions of the Einstein-Klein-Gordon system that continuously connects to vacuum Kerr BHs. We identify the region in parameter space…

We obtain a global embedding of the surface of a rapidly rotating Kerr-Newman black hole in an Euclidean 4-dimensional space.

In this paper, we study the smooth isometric immersion of a complete, simply connected surface with a negative Gauss curvature into the three-dimensional Euclidean space. A fundamental and longstanding problem is to find a sufficient…

We discuss generalizations of the well-known theorem of Hilbert that there is no complete isometric immersion of the hyperbolic plane into Euclidean 3-space. We show that this problem is expressed very naturally as the question of the…

We study the old problem of isometrically embedding a 2-dimensional Riemannian manifold into Euclidean 3-space. It is shown that if the Gaussian curvature vanishes to finite order and its zero set consists of two Lipschitz curves…

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 conditions of the existence of Hawking into Unruh mapping for hyperbolic (Fronsdal-type) embeddings of metric into the Minkowski space, for which timelines are hyperbolas. Many examples are known for global embeddings into the…

The geometry of a two-dimensional surface in a curved space can be most easily visualized by using an isometric embedding in flat three-dimensional space. Here we present a new method for embedding surfaces with spherical topology in flat…

We prove that the isometric embedding of any metric of differentiability class C1 in E3 exists. We use simplified notation for the given metric, namely geodesic parameters, and level parameters for the embedded surface in E3. Central to our…

For any H in [0,1), we construct complete, non-proper, stable, simply-connected surfaces with constant mean curvature H embedded in hyperbolic 3-space.

We study the problem of isometrically embedding a two-dimensional Riemannian manifold into Euclidean three-space. It is shown that if Gaussian curvature vanishes to finite order and its zero set consists of two smooth curves tangent at a…

We give a necessary and sufficient condition for a 2-dimensional Riemannian manifold to be locally isometrically immersed into a 3-dimensional homogeneous manifold with a 4-dimensional isometry group. The condition is expressed in terms of…

This preliminary report studies immersed surfaces of constant mean curvature in $H^3$ through their {\it adjusted Gauss maps} (as harmonic maps in $S^2$) and their {\it adjusted frames} in SU(2). Lawson's correspondence between Euclidean…

We prove rigidity results involving the Hawking mass for surfaces immersed in a $3$-dimensional, complete Riemannian manifold $(M,g)$ with non-negative scalar curvature (resp. with scalar curvature bounded below by $-6$). Roughly, the main…

We study isometric embeddings of non-extremal Reissner-Nordstr\"om metric describing a charged black hole. We obtain three new embeddings in the flat ambient space with minimal possible dimension. These embeddings are global, i.e.…

In this paper we prove the conjecture of Alexander and Currier that states, except for covering maps of equidistant surfaces in hyperbolic 3-space, a complete, nonnegatively curved immersed hypersurface in hyperbolic space is necessarily…

The superintegrability of several Hamiltonian systems defined on three-dimensional configuration spaces of constant curvature is studied. We first analyze the properties of the Killing vector fields, Noether symmetries and Noether momenta.…

We show that there exists a precise kinematical notion of holography for the Euclidean warped $AdS_3$ black hole. This follows from the fact that the Euclidean warped $AdS_3$ black hole spacetime is a geometrically finite hyperbolic…

The generalization of (super)integrable Euclidean classical Hamiltonian systems to the two-dimensional sphere and the hyperbolic space by preserving their (super)integrability properties is reviewed. The constant Gaussian curvature of the…