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The conformal heat flow of harmonic maps is a system of evolution equations combined with harmonic map flow with metric evolution in conformal direction. It is known that global weak solution of the flow exists and smooth except at mostly…
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…
We obtain an exact simple solution of the Einstein equation describing a spherically symmetric cosmological model without the big-bang or any other kind of singularity. The matter content of the model is shear free isotropic fluid with…
A non-relativistic (Galilei-invariant) model of a perfect fluid coupled to a solenoidal field in arbitrary spatial dimension is considered. It contains an arbitrary parameter $\kappa$ and in the particular case of $\kappa=1$ it describes a…
Considering the evolution of a perfect fluid with self-similarity of the second kind, we have found that an initial naked singularity can be trapped by an event horizon due to collapsing matter. The fluid moves along time-like geodesics…
A Bianchi type -I metric of Kasner form is considered, when the space is filled with a viscous fluid. Whereas an ideal (nonviscous) fluid permits the Kasner metric to be anisotropic provided that the fluid satisfies the Zel'dovich equation…
Exact non-static spherically symmetric solutions of the Einstein equations for a null fluid source with pressure $P$ and density $\rho$ related by $P = k\rho^a$ are given. The $a=1$ metrics are asymptotically flat for $1/2<k\le 1$ and…
We study the evolution of a perfect--fluid sphere coupled to a scalar radiation field. By ensuring a Ricci invariant regularity as a conformally flat spacetime at the central world line we find that the fluid coupled to the scalar field…
The properties of some locally rotationally symmetric (LRS) perfect fluid space-times are examined in order to demonstrate the usage of the description of geometries in terms of the Riemann tensor and a finite number of its covariant…
Spherically symmetric static fluid sources are endowed with rotation and embedded in Kerr empty space-time up to an including quadratic terms in an angular velocity parameter using Darmois junction conditions. Einstein's equation's for the…
We present a general formulation of the theory for a non-minimally coupled perfect fluid in which both conformal and disformal couplings are present. We discuss how such non-minimal coupling is compatible with the assumptions of a perfect…
The problem of two stiff fluids (energy density = pressure) moving radially in spherical symmetry is treated. The metric ansatz is chosen spherically symmetric, conformally static with a multiplicative separation of variables. The first…
Lorentz proposed a classical model of electron in which electron was assumed to have only 'electromagnetic mass'. We modeled electron as charged anisotropic perfect fluid sphere admitting non static conformal symmetry. It is noticed that…
A method of solving perfect fluid Einstein equations with two commuting spacelike Killing vectors is presented. Given a spacelike 2-dimensional surface in the 3-dimensional nonphysical Minkowski space the field equations reduce to a single…
We construct models of static spherical distributions of perfect fluid in trace--free Einstein gravity theory. The equations governing the gravitational field are equivalent to the standard Einstein's equations however, their presentation…
Various models are under consideration with metric type flat FRW whose energy-momentum tensor is described by a perfect fluid whose generic equation state and taking into account the conservation principle, but considering some of the…
We present a singularity free class of inhomogeneous cylindrical universes filled with stiff perfect fluid $(\rho = p)$. Its matter free $ (\rho = 0)$ limit yield two distinct vacuum spacetimes which can be considered as analogues of Kasner…
All spherically symmetric Riemannian metrics of constant scalar curvature in any dimension can be written down in a simple form using areal coordinates. All spherical metrics are conformally flat, so we search for the conformally flat…
A simple group theoretic derivation is given of the family of space-time metrics with isometry group SO(2,1) X SO(2) X R first described by Godel, of which the Godel stationary cosmological solution is the member with a perfect-fluid…
We present a cosmological model constituted by three perfect fluids, cold dark matter, vacuum energy and radiation, which interacting with each other lead to an equivalent model of three self-preserved fluids that can be identified with the…