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We discuss the physical features of two recent classes of analytical solutions of the Einstein equations sourced by an exotic perfect fluid with equation of state $ P=-\rho/5$. These geometries depend on up to four parameters and are static…
In this note the velocity field and the associated tangential stress corresponding to the rotational flows of a generalized second grade fluid within an infinite circular cylinder are determined by means of the Laplace and Hankel…
We investigate solutions of Einstein field equations for the non-static spherically symmetric perfect fluid case using different equations of state. The properties of an exact spherically symmetric perfect fluid solutions are obtained which…
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…
We present an exact solution for the time-dependent Stokes problem of an infinite cylinder of radius r=a in a fluid with harmonic boundary conditions at infinity. This is a 3-dimensional problem but, because of translational invariance…
Via a straightforward integration of the Einstein equations with cosmological constant, all static circularly symmetric perfect fluid 2+1 solutions are derived. The structural functions of the metric depend on the energy density, which…
We consider the existence of radially symmetric stationary solutions of the compressible viscous and heat-conductive polytropic ideal fluid on the unbounded exterior domain of a sphere where the boundary and far-field conditions are…
We introduce a physical characterization of the static and stationary perfect fluid solutions of the Einstein field equations with a single or 2-component perfect fluid sources, according to their gravitoelectric and gravitomagnetic fields.…
We carry on a comprehensive study on static fluid distributions endowed with hyperbolical symmetry. Their physical properties are analyzed in detail. The energy density appears to be necessarily negative, which suggests that any possible…
We study the general properties of dissipative fluid distributions endowed with hyperbolical symmetry. Their physical properties are analyzed in detail. It is shown that the energy density is necessarily negative and the fluid distribution…
In this paper we utilize symmetries in order to exhibit exact solutions to Einstein's equation of a perfect fluid on a static manifold all of whose spatial factor belongs to the conformal class of a Riemannian space of constant curvature.
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…
In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to…
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…
Static spherically symmetric perfect fluid solutions are studied in metric $f(R)$ theories of gravity. We show that pressure and density do not uniquely determine $f(R)$ ie. given a matter distribution and an equation state, one cannot…
The explicit relationship is determined between the interior properties of a static cylindrical matter distribution and the metric of the exterior space-time according to Einstein gravity for space-time dimensionality larger or equal to…
In a recent series of papers new exact analytical solutions of the field equations of General Relativity representing interior spacetimes sourced by stationary rigidly rotating cylinders of fluids with various equations of state have been…
We investigate relativistic spherically symmetric static perfect fluid models in the framework of the theory of dynamical systems. The field equations are recast into a regular dynamical system on a 3-dimensional compact state space,…
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…
We consider the three-dimensional steady Navier-Stokes system in the exterior of an infinite cylinder under the action of an external force. We construct solutions in the class of vertically uniform flows which vanish at horizontal…