Related papers: Fundamental domains in the Einstein Universe
In this paper, we study the inverse surfaces in 3-dimensional Euclidean space $\mathbb{E}^{3}$. We obtain some results relating Christoffel symbols, the normal curvatures, the shape operators and the third fundamental forms of the inverse…
A novel class of discrete integrable surfaces is recorded. This class of discrete O surfaces is shown to include discrete analogues of classical surfaces such as isothermic, `linear' Weingarten, Guichard and Petot surfaces. Moreover,…
It is shown that any two-dimensional spacetimes with compact Cauchy surfaces can be causally isomorphically imbedded into the two-dimensional Einstein's static universe. Also, it is shown that any two-dimensional globally hyperbolic…
We present a general formalism for describing singular hypersurfaces in the Einstein theory of gravitation with a Gauss--Bonnet term. The junction conditions are given in a form which is valid for the most general embedding and matter…
In a recent important breakthrough D. Christodoulou has solved a long standing problem of General Relativity of evolutionary formation of trapped surfaces in the Einstein-vacuum space-times. He has identified an open set of regular initial…
We prove several theorems concerning the connection between the local CR embeddability of 3-dimensional CR manifolds, and the existence of algebraically special Maxwell and gravitational fields. We reduce the Einstein equations for…
In this paper, we investigate the differential geometric properties of lightcone framed surfaces in Lorentz-Minkowski 3-space. In general, a mixed type surface is a connected regular surface with non-empty spacelike and timelike point sets.…
We prove the Morrison-Kawamata cone conjecture for klt Calabi-Yau pairs in dimension 2. That is, for a large class of rational surfaces as well as K3 surfaces and abelian surfaces, the action of the automorphism group of the surface on the…
An action principle of singular hypersurfaces in general relativity and scalar-tensor type theories of gravity in the Einstein frame is presented without assuming any symmetry. The action principle is manifestly doubly covariant in the…
In this paper we constructed a semi-realistic cosmological model in a dynamic domain wall framework. Our universe is considered to be a (3+1) dimensional dynamic domain wall in a higher dimensional Einstein-Maxwell-Born-Infeld background.…
We consider a dynamical membrane world in a space-time with scalar bulk matter described by domain walls. Using the solutions to Einstein field equations and Israel conditions we investigate the possibility of having shortcuts for gravitons…
The flows of phase trajectories of cosmological models based on the vacuum classical Higgs field and their behavior on the Einstein-Higgs surface near singular points of a dynamical system are investigated by numerical simulation. The…
We suggest a mechanism which leads to 3+1 space-time dimensions. The Universe assumed to have nine spatial dimensions is regarded as a special nonlinear oscillatory system -- a kind of Einstein solid. There are p-brane solutions which…
The unique Nature of the Lorentz group in four dimensions is the root cause of the many remarkable properties of the Einstein spacetimes, in particular their operational structure on the 2-forms. We show how this operational structure can…
We reformulate the Einstein equations as equations for families of surfaces on a four-manifold. These surfaces eventually become characteristic surfaces for an Einstein metric (with or without sources). In particular they are formulated in…
K fields, that is, fields with a non-standard kinetic term, allow for soliton solutions with compact support, i.e., compactons. Compactons in 1+1 dimensions may give rise to topological defects of the domain wall type and with finite…
In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by…
We study the domain walls which form when Bose condensates acquire a double-well dispersion. Experiments have observed such domain walls in condensates driven across a $\mathbb{Z}_2$ symmetry-breaking phase transition in a shaken optical…
The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analysed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and…
It has been argued that a Universe governed by Eddington-Born-Infeld gravity can be compatible with current cosmological constraints. The extra fields introduced in this theory can behave both as dark matter and dark energy, unifying the…