相关论文: Embedding the Reissner-Nordstrom spacetime in Eucl…

We consider embedding diagrams for the Reissner-Nordstr\"om spacetime. We embed the $(r-t)$ and $(r-\phi)$ planes into 3-Minkowski/Euclidean space and discuss the relation between the diagrams and the corresponding curvature scalar of the…

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…

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…

It is hard to imagine curved spacetimes of General Relativity. A simple but powerful way how to achieve this is visualizing them via embedding diagrams of both ordinary geometry and optical reference geometry. They facilitate to gain an…

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.…

Making use of the higher dimensional global embedding Minkowski spacetime (GEMS), we embed (3+1)-dimensional Schwarzschild and Reissner-Nordstr\"om (RN) black holes written by the Painlev\'e-Gullstrand (PG) spacetimes, which have…

A scheme is discussed for embedding n-dimensional, Riemannian manifolds in an (n+1)-dimensional Einstein space. Criteria for embedding a given manifold in a spacetime that represents a solution to Einstein's equations sourced by a massless…

Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an…

A simple algebraic global isometric embedding is presented for the nonrotating BTZ black hole and its counterpart of Euclidean signature. The image of the embedding, in Minkowski space of two extra dimensions, is the interection of two…

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

We find the spatial and dynamic embedding diagrams in some stationary spacetimes. The spatial embeddings include the NUT, pure NUT and Kerr spacetimes. In the case of pure NUT spacetime, the spatial embedding equations are solved in terms…

We obtain a (5+2)-dimensional global flat embedding of the (3+1)-dimensional curved RN-AdS space. Our results include the various limiting cases of global embedding Minkowski space (GEMS) geometries of the RN, Schwarzschild-AdS in…

We present a new solution in Einstein's theory of relativity, found through the use of the symmetries of the Ernst equations and in particular the Harrison and Ehlers transformations. The new metric represents a Reissner-Nordstr\"om black…

We study global flat embeddings inside and outside of event horizons of black holes such as Schwarzschild and Reissner-Nordstr\"{o}m black holes, and of de Sitter space. On these overall patches of the curved manifolds we investigate four…

In the framework of black hole spectroscopy, we extend the results obtained for a charged black hole in an asymptotically flat spacetime to the scenario with non vanishing negative cosmological constant. In particular, exploiting…

In this paper we propose a stationary solution of Einstein's field equations describing Reissner-Nordstrom black hole in dark energy background. It is to be regarded as the Reissner-Nordstrom black hole is embedded into the dark energy…

Recently, the phase space of black holes in a spherical cavity of radius $r_{B}$ has been extended by introducing a thermodynamic volume $V\equiv4\pi r_{B}^{3}/3$. In the extended phase space, we consider the thermodynamic geometry, which…

Properties of the optical reference geometry related to Kerr-Newman black-hole and naked-singularity spacetimes are illustrated using embedding diagrams of their equatorial plane. Among all inertial forces defined in the framework of the…

The event horizon of the Schwarzschild black hole has been well studied and the singular behavior of the Schwarzschild metric on horizon is understood as a coordinate singularity rather than an essential singularity. One demonstration of…

We discuss isometric embedding diagrams for the visualization of initial data for the problem of the head-on collision of two black holes. The problem of constructing the embedding diagrams is explicitly presented for the best studied…