Related papers: A new algorithm for anisotropic solutions
This paper formulates some new exact solutions to the field equations by means of minimal gravitational decoupling in the context of $f(\mathbb{R},\mathbb{T})$ gravity. For this purpose, we consider anisotropic spherical matter distribution…
Einstein's spherically symmetric interior gravitational equations are investigated. Following Synge's procedure, the most general solution of the equations is furnished in case $T^{1}_{1}$ and $T^{4}_{4}$ are prescribed. The existence of a…
We establish the existence of a class of asymptotically Euclidean solutions to Einstein's constraint equations, whose asymptotic behavior at infinity is arbitrarily prescribed. The proposed seed-to-solution method relies on iterations based…
It is formulated a new 'anholonomic frame' method of constructing exact solutions of Einstein equations with off--diagonal metrics in 4D and 5D gravity. The previous approaches and results are summarized and generalized as three theorems…
In this work, an exact solution of Einstein's field equations in isotropic coordinates for anisotropic matter distribution is obtained by considering a particular metric choice of metric potential $g_{rr}$. To check the feasibility of the…
In this paper, we present new axisymmetric and reflection symmetric vacuum solutions to the Einstein field equations. They are obtained using the Hankel integral transform method and all three solutions exhibit naked singularities. Our…
In this work, we present a class of relativistic and well-behaved solution to Einstein's field equations for anisotropic matter distribution. We perform our analysis by using the Buchdahl ansatz for the metric function grr. Three different…
A general procedure to find static and axially symmetric, interior solutions to the Einstein equations is presented. All the so obtained solutions, verify the energy conditions for a wide range of values of the parameters, and match…
We present a general method to obtain static anisotropic spherically symmetric solutions, satisfying a nonlocal equation of state, from known density profiles. This equation of state describes, at a given point, the components of the…
We find a reconstruction algorithm able to generate all the static spherically symmetric interior solutions in the framework of Ho\v{r}ava gravity and Einstein-\ae ther theory in presence of anisotropic fluids. We focus for simplicity on…
We present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the…
This work is focused in the study of analytic anisotropic solutions to Einstein's field equations, describing spherically symmetric and static configurations by way of the gravitational decoupling through the method of Minimal Geometric…
In this article, we provide a discussion on a composite class of exact static spherically symmetric vacuum solutions of Einstein's equations. We construct the composite solution of Einstein field equation by match the interior vacuum metric…
We present a method for generating exact interior solutions of Einstein's equations in the case of static and axially symmetric perfect-fluid spacetimes. The method is based upon a transformation that involves the metric functions as well…
We present exact solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields with a specified form of the electric field intensity. The condition of pressure isotropy yields a difference equation with…
The known static isotropic metric of Schwarzschild solution of Einstein equation cannot cover with the range of r<2MG, a new isotropic metric of Schwarzschild solution is obtained. The new isotropic metric has the characters: (1) It is…
We present new exact solutions for the Einstein-Maxwell system in static spherically symmetric interior spacetimes. For a particular form of the gravitational potentials and the electric field intensity, it is possible to integrate the…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two…
We find new classes of exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is…