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We introduce a technique to solve numerically the relativistic Euler's equations in scenarios with spherical symmetry using the standard Smoothed Particles Hydrodynamics method in cartesian coordinates. This implementation allow us to…
We study spherically symmetric geometries made of anisotropic perfect fluid based on general relativity. The purpose of the work is to find and classify black hole solutions in closed spacetime. In a general setting, we find that a static…
Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on…
Presented are two results on the formation of finite time singularities of solutions to the compressible Euler equations in two and three space dimensions for isentropic, polytropic, ideal fluid flows. The initial velocity is assumed to be…
The aim of the present paper is to obtain the condition under which a pseudosymmetric spacetime to be a perfect fluid spacetime. It is proven that a pseudosymmetric generalized Robertson-Walker spacetime is a perfect fluid spacetime.…
By imposing suitable junction conditions on a space-like hyper-surface, we obtain a two-parameter family of possible static configurations from gravitational collapse. These exemplify a new class of naked singularities. We show that these…
The equations of the 1+3 orthonormal frame approach are explicitly presented and discussed. Natural choices of local coordinates are mentioned. A dimensionless formulation is subsequently given. It is demonstrated how one can obtain 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…
We present several different classes of selfdual Yang-Mills instantons in all even d backgrounds with Euclidean signature. In d=4p+2 the only solutions we found are on constant curvature dS and AdS backgrounds, and are evaluated in closed…
In this paper we give some two-dimensional and some three-dimensional examples for the shape of the symmetric solution set of a linear complementarity problem where the given data are not explicitly known but can only be enclosed in…
The general metric for N-dimensional spherically symmetric and conformally flat spacetimes is given, and all the homogeneous and isotropic solutions for a perfect fluid with the equation of state $p = \alpha \rho$ are found. These solutions…
We present a new non-diagonal G2 inhomogeneous perfect-fluid solution with barotropic equation of state p=rho and positive density everywhere. It satisfies the global hyperbolicity condition and has no curvature singularity anywhere. This…
We consider two exact solutions of Einstein's field equations corresponding to a cylinder of dust with net zero angular momentum. In one of the cases, the dust distribution is homogeneous, whereas in the other, the angular velocity of dust…
In a recent series of papers new exact analytical interior spacetimes sourced by stationary rigidly rotating cylinders of fluids have been displayed. A fluid with an axially directed pressure has been first considered, then a perfect fluid,…
A modified version of the conditional symmetry method, together with the classical method, is used to obtain new classes of elliptic solutions of the isentropic ideal compressible fluid flow in (3+1) dimensions. We focus on those types of…
We discuss spherically symmetric perfect fluid solutions of Einstein's equations which have equation of state ($p=\alpha \mu$) and which are self-similar in the sense that all dimensionless variables depend only upon $z\equiv r/t$. For each…
We investigate the two-dimensional ($2$D) inviscid compressible flow equations in axisymmetric coordinates, constrained by an ideal gas equation of state (EOS). Beginning with the assumption that the $2$D velocity field is space-time…
The existence and multiplicity of similarity solutions for the steady, incompressible and fully developed laminar flows in a uniformly porous channel with two permeable walls are investigated. We shall focus on the so-called asymmetric case…
Einstein's field equations for spatially self-similar locally rotationally symmetric perfect fluid models are investigated. The field equations are rewritten as a first order system of autonomous ordinary differential equations.…
The main purpose of this paper is to investigate the exact solutions of cylindrically symmetric spacetime in the context of $f(R,T)$ gravity [1], where $f(R,T)$ is an arbitrary function of Ricci scalar $R$ and trace of the energy momentum…