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We establish rigorously the existence of a three-parameter family of self-similar,globally bounded, and continuous weak solutions in two space dimensions to the compressible Euler equations with axisymmetry for gamma-law polytropic gases…
In this paper, we present a formalism to generate a family of interior solutions to the Einstein-Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner-Nordstr\"om…
In recent works we have constructed axisymmetric solutions to the Euler-Poisson equations which give mathematical models of slowly uniformly rotating gaseous stars. We try to extend this result to the study of solutions of the…
This paper uses the definition of complexity for a static spherically symmetric spacetime and extends it to the case of charged distribution. We formulate the Einstein-Maxwell field equations corresponding to the anisotropic interior and…
For any configuration of a static plane-symmetric distribution of matter along space-time, there are coordinates where the metric can be put explicitly as a functional of the energy density and pressures. It satisfies Einstein equations as…
Approximate solutions representing the gravitational-electrostatic balance of two arbitrary point sources in general relativity have led to contradictory arguments in the literature with respect to the condition of balance. Up to the…
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We…
In this work, we study the implications of nonlinearity in general relativistic spherically symmetric inviscid irrotational accretion flow in a stationary non-rotating spacetime. It has been found that the perturbation scheme leads to a…
In a previously work, we undertook a static and anisotropic content in $f(T)$ theory and obtained new spherically symmetric solutions considering a constant torsion and some particular conditions for the pressure. In this paper, still in…
A procedure to find static axially symmetric solutions to the Einstein field equations is presented. We obtained two general solutions and five particular solutions, which depend on the existence conditions for circular and $z$ direction…
In this paper, we explore instability regions of non-static axial reflection symmetric spacetime with anisotropic source in the interior. We impose linear perturbation on the Einstein field equations and dynamical equations to establish the…
We complete the intrinsic characterization of spherically symmetric solutions partially accomplished in a previous paper [Class.Quant.Grav. (2010) 27 205024]. In this approach we consider every compatible algebraic type of the Ricci tensor,…
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…
The full set of equations governing the structure and the evolution of self--gravitating spherically symmetric dissipative fluids with anisotropic stresses, is written down in terms of five scalar quantities obtained from the orthogonal…
The present paper has the purpose to illustrate the importance of the ideas and constructions of the Non-Euclidean (Lobachevsky) Geometry, which can be applied even today for solving some conceptually important problems. We study the static…
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…
The structure of the Einstein field equations describing the gravitational collapse of spherically symmetric isotropic fluids is analyzed here for general equations of state. A suitable system of coordinates is constructed which allows us,…
In this work, we explore wormhole solutions in $f(R,T)$ theory of gravity, where $R$ is the scalar curvature and $T$ is the trace of stress-energy tensor of matter. To investigate this, we consider static spherically symmetric geometry with…
We attempt to a physical interpretation of some known static vacuum solutions of Einstein's equations, namely, the A and B metrics of Ehlers and Kundt. All of them have axial symmetry, so they can be transformed to the Weyl form. In Weyl…
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…