Related papers: Stationary spacetimes and the Simon tensor
The Ricci and energy-momentum tensors have the same algebraic symmetries. In the Einstein equations they look ``dual'' to each other, in that interchanging them and inverting the gravitational coupling leaves the equations invariant. It may…
In this paper we propose a class of exact solutions (stationary and non-stationary) of Einstein's field equations. The energy-momentum tensors of the solutions describe dark energy.
It is known that de Sitter spacetime can be seen as the solution of field equation for completely isotropic matter. In the present paper a new class of exact solutions in spherical symmetry is found and discussed, such that the…
We prove several inequalities between the curvature invariants, which impose constraints on curvature singularities. Some of the inequalities hold for a family of spacetimes which include static, Friedmann--Lema\^itre--Robertson--Walker,…
In the paper we consider the energy and its flux in the Bonnor spacetime. We construct some non-local expressions from the Einstein canonical energy-momentum pseudotensor of the gravitational field which show that the gravitational energy…
It is shown in this article that if the Einstein Equivalence Principle is valid on a particular metric theory of gravitation in a spherically symmetric space-time, then the time metric component is not equal to the negative of the inverse…
The concept of Euclidean time is proposed which is dual to the usual Minkowski time. The De Sitter solution is shown to be dual to the anti-De Sitter solution under the dual transformation in which Euclidean time and Minkowski time are…
This paper introduces a new object called the momentum tensor. Together with the velocity tensor it forms a basis for establishing the tensorial picture of classical and relativistic mechanics. Some properties of the momentum tensor are…
Harmonic coordinate conditions in stationary asymptotically flat spacetimes with matter sources have more than one solution. The solutions depend on the degree of smoothness of the metric and its first derivatives, which we wish to impose…
Within the scope of a static cylindrically symmetric space-time we study the behavior of a nonlinear spinor field that depends on time and radial coordinates. It is found that the presence of nontrivial non-diagonal components of the…
We construct infinite dimensional families of non-singular stationary space times, solutions of the vacuum Einstein equations with a negative cosmological constant.
Several other factors, besides the intrinsic local geometry, contribute to give a meaning to a space-time model. The simplest example comes from comparing Minkowski's and Milne's model, that both have a null Riemann tensor. We add to these…
A combination of qualitative analysis and numerical study indicates that vacuum $T^2$ symmetric spacetimes are, generically, oscillatory.
A study is made of the possible holonomy group types of a space-time for which the energy-momentum tensor corresponds to a null or non-null electromagnetic field, a perfect fluid or a massive scalar field. The case of an Einstein space is…
Within the scope of Bianchi type-III spacetime we study the role of spinor field on the evolution of the Universe as well as the influence of gravity on the spinor field. In doing so we have considered a polynomial type of nonlinearity. In…
The static vacuum plane spacetimes are considered, which have two non-trivial solutions: The Taub solution and the Rindler solution. Imposed reflection symmetry, we find that the source for the Taub solution does not satisfy any energy…
The paper considers the problem of finding the metric of space time around a rotating, weakly gravitating body. Both external and internal metric tensors are consistently found, together with an appropriate source tensor. All tensors are…
A quantum mechanical formulation of de Sitter cosmological spacetimes still eludes string theory. In this paper we conjecture a potentially rigorous framework in which the status of de Sitter space is the same as that of a resonance in a…
A general formula is calculated for the connection of a central metric w.r.t.\ a noncommutative spacetime of Lie-algebraic type. This is done by using the framework of linear connections on central bi-modules. The general formula is further…
In this letter we discuss the possibility of treating the spacetime by itself as a kind of deformable body for which we can define an fundamental lattice, just like atoms in crystal lattices. We show three signs pointing in that direction.…