Related papers: Static and stationary dark fluid universes: A grav…
In this article, a cylindrical symmetry and static solution of the Einstein's field equations, was presented. The space-time is conformally flat, regular everywhere except on the symmetry axis where it possesses a naked curvature…
Perfect-fluid, static, cylindrically symmetric solutions of Einstein's field equations are obtained for the equations of state $\rho+3p=0$ and $\rho=p$. In the former case, the density and the pressure turn out to be constant while in the…
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.
We ask the following question: Of the exact solutions to Einstein's equations extant in the literature, how many could represent the field associated with an isolated static spherically symmetric perfect fluid source? The candidate…
A new class of static plane symmetric solution of Einstein field equation generated by a perfect fluid source is put forward. A special family of this new solution is investigated in detail. The constraints on the parameters by different…
Locally rotationally symmetric perfect fluid solutions of Einstein's gravitational equations are matched along the hypersurface of vanishing pressure with the NUT metric. These rigidly rotating fluids are interpreted as sources for the…
Perfect fluid with kinematic self-similarity is studied in 2+1 dimensional spacetimes with circular symmetry, and various exact solutions to the Einstein field equations are given. In particular, these include all the solutions of dust and…
The staid subject of exact static spherically symmetric perfect fluid solutions of Einstein's equations has been reinvigorated in the last decade. We now have several solution generating techniques which give rise to new exact solutions.…
In a recent series of papers new exact analytical solutions of the Einstein equations representing interior spacetimes sourced by stationary rigidly rotating cylinders of different kinds of fluids have been displayed, [Phys. Rev. D {\bf…
We investigate the gravitational field of static perfect-fluid in the presence of electric field. We adopt the equation of state $p(r)=-\rho(r)/3$ for the fluid in order to consider the closed ($S_3$) or the open ($H_3$) background spatial…
Einstein's field equations for stationary Bianchi type II models with a perfect fluid source are investigated. The field equations are rewritten as a system of autonomous first order differential equations. Dimensionless variables are…
We review the problem of describing the gravitational field of compact stars in general relativity. We focus on the deviations from spherical symmetry which are expected to be due to rotation and to the natural deformations of mass…
In this paper we provide a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field. All spacetimes of this type which are symmetric with respect to a…
In this work we study static perfect fluid stars in 2+1 dimensions with an exterior BTZ spacetime. We found the general expression for the metric coefficients as a function of the density and pressure of the fluid. We found the conditions…
Dark energy with the usually used equation of state $p=w\rho$, where $w=const<0$ is hydrodynamically unstable. To overcome this drawback we consider the cosmology of a perfect fluid with a linear equation of state of a more general form…
In Newton's and in Einstein's theory we give criteria on the equation of state of a barotropic perfect fluid which guarantee that the corresponding one-parameter family of static, spherically symmetric solutions has finite extent. These…
A main issue in cosmology and astrophysics is whether the dark sector phenomenology originates from particle physics, then requiring the detection of new fundamental components, or it can be addressed by modifying General Relativity.…
This paper examines the inhomogeneous Einstein equation for a static spherically symmetric metric with a source term corresponding to a perfect fluid with p=-rho. By a careful treatment of the equation near the origin we find an analytic…
We consider cosmological solutions to general relativity with a single barotropic fluid, where the pressure is a general function of the density, $p = f(\rho)$. We derive conditions for static and oscillating solutions and provide examples,…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…