Related papers: Generating potentials via difference equations
We present solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes with a specified form of the electric field intensity. The condition of pressure isotropy yields…
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 special form of the isotropic metric in cylindrical coordinates is used to construct what may be interpreted as the General Relativistic versions of some wellknown potential-density pairs used in Newtonian gravity to model…
In this work, a spherically symmetric and static relativistic anisotropic fluid sphere solution of the Einstein field equations is provided. To build this particular model, we have imposed metric potential $e^{2\lambda(r)}$ and an equation…
A simple classification is given of the anisotropic relativistic star models, resembling the one of charged isotropic solutions. On the ground of this database, and taking into account the conditions for physically realistic star models, a…
The general exact solution of the Einstein-matter field equations describing spherically symmetric shells satisfying an equation of state in closed form is discussed under general assumptions of physical reasonableness. The solutions split…
We introduce a new type of generating theorems in General Relativity for anisotropic, static, spherically symmetric solutions of the Einstein field equations. The results are used to derive a class of solutions that can serve as new models…
In this article, an exact solution of Einstein's field equations for spherically symmetric anisotropic matter distributions in isotropic coordinates is obtained. For this, the solution has been obtained by using a generalized physically…
This paper formulates three different analytical solutions to the gravitational field equations in the framework of Rastall theory by taking into account the gravitational decoupling approach. For this, the anisotropic spherical interior…
We consider the general situation of a compact relativistic body with anisotropic pressures in the presence of the electromagnetic field. The equation of state for the matter distribution is linear and may be applied to strange stars with…
Static spherically symmetric solutions of the Einstein's field equations in isotropic coordinates representing perfect fluid matter distributions from Newtonian potential-density pairs are investigated. The approach is illustrated with…
Using the method of retarded potentials approximate formulas are obtained that describe the electromagnetic field outside the relativistic uniform system in the form of a charged sphere rotating at a constant speed. For the near, middle and…
We consider the Einstein-Maxwell system of equations in the context of isotropic coordinates for matter distributions with anisotropy in the presence of an electric field. We assume a polytropic equation of state for the matter…
This manuscript copes with the issue of analyzing the conditions to check the stability of the pressure isotropy condition by taking into account a spherically symmetric dissipative astrophysical configuration with the Palatini $f(R)$…
We study the gravitational potential generated by static, spherically symmetric matter distributions in a quadratic $f(R)$ gravity model. In the weak-field regime, the linearized field equations lead to a fourth-order modified Poisson…
In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are…
Due to R. Beig and W. Simon (1990) there is a uniqueness theorem for static solutions of the Einstein-Euler system which applies to fluid models whose equation of state fulfills certain conditions. In this article it is shown that this…
In this paper, we studied the behavior of relativistic objects with anisotropic matter distribution considering Tolman IV form for the gravitational potential Z. The equation of state presents a quadratic relation between the energy density…
We revisit the problem of the structure and physical properties of electrically charged static spherically symmetric solutions of the Einstein-Maxwell system of equations where the matter model is a polytropic gas. We consider a…
We establish a new algorithm that generates a new solution to the Einstein field equations, with an anisotropic matter distribution, from a seed isotropic solution. The new solution is expressed in terms of integrals of an isotropic…