Related papers: Exact Solutions of Einstein's Field Equations
In the context of the braneworld, a method to find consistent solutions to Einstein's field equations in the interior of a spherically symmetric, static and non uniform stellar distribution with Weyl stresses is developed. This method,…
Two new classes of exact interior static solutions of the Einstein equations in homogeneous coordinates for a gravitating ball filled by a Pascal perfect fluid are obtained. Schwarzschild's interior solution of is a special case of these…
Static solutions of the electro-gravitational field equations exhibiting a functional relationship between the electric and gravitational potentials are studied. General results for these metrics are presented which extend previous work of…
We investigate all static spherically symmetric solutions in the context of general relativity surrounded by a minimally-coupled quintessence field, using dynamical system analysis. Applying the 1+1+2 formalism and introducing suitable…
The time independent spherically symmetric solutions of General Relativity (GR) coupled to a dynamical unit timelike vector are studied. We find there is a three-parameter family of solutions with this symmetry. Imposing asymptotic flatness…
It is known that the standard Schwarzschild interior metric is conformally flat and generates a constant density sphere in any spacetime dimension in Einstein and Einstein--Gauss--Bonnet gravity. This motivates the questions: In EGB does…
Schwarzschild's solution to the Einstein Field Equations was one of the first and most important solutions that lead to the understanding and important experimental tests of Einstein's theory of General Relativity. However, Schwarzschild's…
We study the exact solution of Einstein's field equations consisting of a ($n+2$)-dimensional static and hyperplane symmetric thick slice of matter, with constant and positive energy density $\rho$ and thickness $d$, surrounded by two…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…
Perfect-fluid, static, cylindrically symmetric solutions of Einstein's field equations are obtained for the equations of state $\rho+3p=0$ and $\rho=p$. In the former case, the density and the pressure turn out to be constant while in 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…
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…
It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle.…
Static spherically symmetric perfect-fluid solutions of Einstein's equations play a central role in relativistic astrophysics and stellar structure theory. While many exact solutions satisfy Einstein's equations mathematically, only a…
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…
The macroscopic model is formulated for a neutron star (NS) as a perfect liquid drop at the equilibrium. We use the leptodermic approximation $a/R\ll 1$, where $a$ is the crust thickness of the effective NS surface (ES), and $R$ is the mean…
Recent works by the second author and Maxwell et al. have shown that the Einstein-scalar field conformal constraint equations are highly complex and generally intractable, even in the vacuum case. In this article, to gain a clearer…
Certain exact solutions of the Einstein field equations over nonsimply-connected manifolds are reviewed. These solutions are spherically symmetric and have no curvature singularity. They provide a regularization of the standard…
We study exact solutions of the Einstein-Maxwell equations for the interior gravitational field of static spherically symmetric charged compact spheres. The spheres are composed of a perfect fluid with a charge distribution that creates a…
A static spherically symmetric metric in Einstein-scalar-tensor gravity theory with a scalar field potential $V[\phi]$ is non-singular for all real values of the coordinates. It does not have a black hole event horizon and there is no…