Related papers: Stationary Cylindrical Anisotropic Fluid
We present a detailed analysis of the general exact solution of Einstein's equation corresponding to a static and plane symmetric distribution of matter with density proportional to pressure. We study the geodesics in it and we show that…
We consider the compressible Navier--Stokes equation in a perturbed half-space with an outflow boundary condition as well as the supersonic condition. For a half-space, it has been known that a certain planar stationary solution exist and…
Using the conservation laws for charge, energy, momentum, and angular momentum, we derive hydrodynamic equations for the charge density, local temperature, and fluid velocity, as well as for the spin tensor, starting from local equilibrium…
We consider the Hamiltonian system consisting of scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subject to an external potential. The stationary solutions of the system are a Coulomb…
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…
Full self-consistent stationary Vlasov-Maxwell solutions of magnetically confined plasmas are built for systems with cylindrical symmetries. The stationary solutions are thermodynamic equilibrium solutions. These are obtained by computing…
This paper is devoted to investigate the cylindrical collapse of an anisotropic fluid in $f(R)$ gravity. For this purpose, the viscous charged anisotropic fluid dissipating energy with heat flow and shear is assumed. We use the perturbation…
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 prove the existence of nonradial classical solutions to the 2D incompressible Euler equations with compact support. More precisely, for any positive integer $k$, we construct compactly supported stationary Euler flows of class…
We prove that the vorticity or the expansion vanishes for any shear-free perfect fluid solution of the Einstein field equations where the pressure satisfies a barotropic equation of state and the spatial divergence of the electric part of…
Using a new metric for generating rotating solutions, we derive in a general fashion the solution of an imperfect fluid and that of its conformal homolog. We discuss the conditions that the stress-energy tensors and invariant scalars be…
Static spherically symmetric anisotropic source has been studied for the Einstein-Maxwell field equations assuming the erstwhile cosmological constant $ \Lambda $ to be a space-variable scalar, viz., $ \Lambda = \Lambda(r) $. Two cases have…
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 exact solutions of the Einstein-Maxwell equations for the interior gravitational field of static spherically symmetric charged compact spheres. The spheres consist of an anisotropic fluid with a charge distribution that gives rise…
We study stationary capillary-gravity waves in a two-dimensional body of water that rests above a flat ocean bed and below vacuum. This system is described by the Euler equations with a free surface. Our main result states that there exist…
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.…
By an argument similar to that of Gibbons and Stewart, but in a different coordinate system and less restrictive gauge, we show that any weakly-asymptotically-simple, analytic vacuum or electrovacuum solutions of the Einstein equations…
Herein we shall argue for the utility of "spacetime geodesy", a point of view where one delays as long as possible worrying about dynamical equations, in favour of the maximal utilization of both symmetries and geometrical features. This…
The general metric for conformally flat stationary cyclic symmetric noncircular spacetimes is explicitly given. In spite of the complexity introduced by the inclusion of noncircular contributions, the related metric is derived via the full…
We find a 4+1 dimensional stationary vacuum hyper-cylindrical solution solution which is spherically symmetric in $3-$dimensions and invariant under the translation along the fifth coordinate. The solution is characterized by three…