Related papers: On linearised vacuum constraint equations on Einst…
Apart from the flat space with an angular deficit, Einstein general relativity possesses another cylindrically symmetric solution. Because this configuration displays circles whose "circumferences" tend to zero when their "radius" go to…
In this paper we recall a simple formulation of the stationary electrovacuum theory in terms of the famous complex Ernst potentials, a pair of functions which allows one to generate new exact solutions from known ones by means of the…
We derive the `exact' Newtonian limit of general relativity with a positive cosmological constant $\Lambda$. We point out that in contrast to the case with $\Lambda = 0 $, the presence of a positive $\Lambda$ in Einsteins's equations…
Starting with a subclass of the four-dimensional spaces possessing two commuting Killing vectors and a non-trivial Killing tensor, we fully integrate Einstein's vacuum equation with a cosmological constant. Although most of the solutions…
This essay elucidates recent achievements of the "nongravitating vacuum energy" (NGVE) theory" which has the feature that a shift of the Lagrangian density by a constant does not affect dynamics. In the first order formalism, a constraint…
In this paper, we study generalized $m$-quasi-Einstein $(M^n,g,X,\lambda)$ under natural conditions on the potential vector field. We show that, under suitable integral assumptions, the potential vector field is Killing, extending earlier…
In this note we construct self-dual cosmic strings from a gauge field theory with a generalized linear formation of potential energy density. By integrating the Einstein equation, we obtain a nonlinear elliptic equation which is equal with…
In this paper we construct a new kind of solutions of the Einstein's field equations with non-vanishing cosmological constant, which possess some interesting physical properties. The singularities of this kind of solutions are investigated.…
The general relativistic treatment of gravitation can be extended by preserving the geometrical nature of the theory but modifying the form of the coupling between curvature and stress tensors. The gravitation constant is thus replaced by…
We survey elementary features of Lovelock gravity and its maximally symmetric vacuum solutions. The latter is solely determined by the real roots of a dimension-dependent polynomial. We also recover the static spherically symmetric (black…
A tensor description of perturbative Einsteinian gravity about an arbitrary background spacetime is developed. By analogy with the covariant laws of electromagnetism in spacetime, gravito-electromagnetic potentials and fields are defined to…
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
A formalism for analyzing the complete set of field equations describing Macroscopic Gravity is presented. Using this formalism, a cosmological solution to the Macroscopic Gravity equations is determined. It is found that if a particular…
We consider static, spherically symmetric, electrically or/and magnetically charged configurations of a minimally coupled scalar field with an arbitrary potential $V(\phi)$ in general relativity. Using the inverse problem method, we obtain…
In standard general relativity the universe cannot be started with arbitrary initial conditions, because four of the ten components of the Einstein's field equations (EFE) are constraints on initial conditions. In the previous work it was…
We investigate the properties of a fairly large class of boundary conditions for the linearised Einstein equations in the Riemannian setting, ones which generalise the linearised counterpart of boundary conditions proposed by Anderson.…
We investigate some cylindrically symmetric nonstationary and nonstatic solutions of Einstein field equations. We first study some physical properties of a solution which can be considered as Kasner generalization of static Levi-Civita…
We consider 1 spacelike Killing vector field reductions of 4-d vacuum general relativity. We restrict attention to cases in which the manifold of orbits of the Killing field is $R^{3}$. The reduced Einstein equations are equivalent to those…
I propose an alternative $f(R)$ theory of gravity constructed by applying the function $f$ directly to the Ricci tensor instead of the Ricci scalar. The main goal of this study is to derive the resulting modified Einstein equations for the…
A broad class of generalized Einstein's gravity can be cast into Einstein's gravity with a minimally coupled scalar field using suitable conformal rescaling of the metric. Using this conformal equivalence between the theories, we derive the…