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Solutions of the stationary axisymmetric Einstein equations describing the interior of circularly rotating dust are investigated in order to study their potential applicability as galaxy models. It is shown that such interior solutions…
An infinite family of new exact solutions of the Einstein vacuum equations for static and axially symmetric spacetimes is presented. All the metric functions of the solutions are explicitly computed and the obtained expressions are simply…
We obtain a general five dimensional (5D) quasispherical solutions of irrotational dust in Einstein gravity with the Gauss-Bonnet combination of quadratic curvature terms. These solutions are generalization, to Einstein-Gauss-Bonnet…
In this paper, solutions to the Ernst equation are investigated that depend on two real analytic functions defined on the interval [0,1]. These solutions are introduced by a suitable limiting process of Backlund transformations applied to…
The second order perturbation calculations for gravity wave and Einstein equation for space time and matter are presented for the FRW metric cosmological model. While exact equations are found, suitable approximations are made to obtain…
We constructed a simple cosmological model which approximates the Einstein-de Sitter background with periodically distributed dust inhomogeneities. By taking the metric as a power series up to the third order in some perturbative parameter…
Recent Planck observations of dust polarization in the Galaxy have revealed that the power in $E$ mode is twice that in $B$ mode. Caldwell et. al. have formulated a theoretical model in the context of magnetohydrodynamic (MHD) turbulence…
Applying the method of conformal metric to a given static axially symmetric vacuum solution of the Einstein equations, we have shown that there is no solution representing a cosmic ideal fluid which is asymtotically FLRW. Letting the cosmic…
Bertrand space-times (BSTs) are static, spherically symmetric solutions of Einstein's equations, that admit stable, closed orbits. Starting from the fact that to a good approximation, stars in the disc or halo regions of typical galaxies…
This paper is concerned with the global existence and blowup of the classical solution to the Cauchy problem of the relativistic Euler equation with $ p=0 $ in a fixed Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) spacetime. The aim of…
We present a comprehensive investigation of cosmological constraints on the class of vector field formulations of modified gravity called Generalized Einstein-Aether models. Using linear perturbation theory we generate cosmic microwave…
We review explicit solutions to the stationary axisymmetric Einstein-Maxwell equations which can be interpreted as disks of charged dust. The disks of finite or infinite extension are infinitesimally thin and constitute a surface layer at…
We present a method for solving the constraint equations in the Hassan-Rosen bimetric theory to determine the initial data for the gravitational collapse of spherically symmetric dust. The setup leads to equations similar to those for a…
The hypothesis about possible existence of new class of particles able to travel faster then light as a source of dark matter, recently formulated by L. Gonzalez-Mesters, is analyzed. To this end the general geometrical model for several…
The Lense--Thirring spacetime describes a 4-dimensional slowly rotating approximate solution of vacuum Einstein equations valid to a linear order in rotation parameter. It is fully characterized by a single metric function of the…
We try to solve the dark matter problem in the fit between theory and the Hubble diagram of supernovae by allowing for torsion via Einstein-Cartan's gravity and for anisotropy via the axial Bianchi I metric. Otherwise we are conservative…
An effective action of ghost condensate with higher derivatives creates a source of gravity and mimics a dark matter in spiral galaxies. We present a spherically symmetric static solution of Einstein--Hilbert equations with the ghost…
We study the dynamics of a 2+1 dimensional relativistic viscous conformal fluid in Minkowski spacetime. Such fluid solutions arise as duals, under the "gravity/fluid correspondence", to 3+1 dimensional asymptotically anti-de Sitter (AAdS)…
If we consider the spacetime manifold as product of a constant curvature 2-sphere (hypersphere) and a 2-space, then solution of the Einstein equation requires that the latter must also be of constant curvature. There exist only two…
The vorticity equation stemming from the modified Navier-Stokes equation gives a solution for a flat profile of the orbital speed of spiral galaxies. Solutions disclose existence of the Gaussian vortex clouds, the coherent vortices with…