Related papers: Integrability of Three Dimensional Gravity Field E…
In this work, we have obtained exact solutions of Einstein equations for static and axially symmetric magnetized matter, specifically in plane-symmetric and almost-plane symmetric cases. Although these solutions impose constraints on the…
We consider the classical equations of the Einstein-Yang-Mills model in five space-time dimensions and in the presence of a cosmological constant. We assume that the fields do not depend on the extra dimension and that they are spherically…
We continue recent work and formulate the gravitational vacuum Einstein equations over a locally finite spacetime by using the basic axiomatics, techniques, ideas and working philosophy of Abstract Differential Geometry. The whole…
We show how the Einstein equations with cosmological constant (and/or various types of matter field sources) can be integrated in a very general form following the anholonomic deformation method for constructing exact solutions in four and…
Certain features associated with the symmetry reduction of the vacuum Einstein equations by two commuting, space-like Killing vector fields are studied. In particular, the discussion encompasses the equations for the Gowdy $T^3$ cosmology…
The explicit relationship is determined between the interior properties of a static cylindrical matter distribution and the metric of the exterior space-time according to Einstein gravity for space-time dimensionality larger or equal to…
We investigate the possibility of inducing the cosmological constant from extra dimensions by embedding our four-dimensional Riemannian space-time into a five-dimensional Weyl integrable space. Following approach of the induced matter…
The equations of motion describing all physical systems, except gravity, remain invariant if a constant is added to the Lagrangian. In the conventional approach, gravitational theories break this symmetry exhibited by all other physical…
We investigate the (conformally coupled) scalar field on a general Carrollian spacetime in arbitrary dimension. The analysis discloses electric and magnetic dynamics. For both, we provide the energy and the momenta of the field, accompanied…
The solution of Einstein field equations for static spherically symmetric spacetime metric with anisotropic internal stresses has been obtained. The matter has vanishing complexity and a spacetime metric that satisfies the Karmarkar…
The complete non-linear three-dimensional Einstein gravity with gravitational Chern-Simons term and cosmological constant are studied in dreibein formulation. The constraints and their algebras are computed in an explicit form. From…
Some theoretic results related to the cosmological constant, obtained in the 80's and 90's of last century, are reviewed. These results exhibit some interesting underlying pattern when viewed from a category-theoretic perspective. In doing…
We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on…
The field equations of the recent nonlocal generalization of Einstein's theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of…
We study the Riemann geometric approach to be aimed at unifying soliton systems. The general two-dimensional Einstein equation with constant scalar curvature becomes an integrable differential equation. We show that such Einstein equation…
In this paper we study non-singular vacuum static space-times with non-zero cosmological constant. We introduce new integral quantities, and under suitable assumptions we prove their monotonicity along the level set flow of the static…
A formulation of Einstein's gravitational field equations in four space-time dimensions is presented using generalized differential forms and Cartan's equations for metric geometries. Cartan's structure equations are extended by using…
We investigate a class of cosmological solutions of Einstein's field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject…
It is shown that all torsion-free vacuum solutions of the model of dS gauge theory of gravity are the vacuum solutions of Einstein field equations with the same positive cosmological constant. Furthermore, for the gravitational theories…
We solve vacuum Einstein's field equations with the cosmological constant in space-times admitting 3-parameter group of isometries with 2-dimensional space-like orbits. The general exact solutions, which are represented in the advanced and…