Related papers: On an Extension of a Static Ball Solution
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…
By assuming a particular mass function we find new exact solutions to the Einstein field equations with an anisotropic matter distribution. The solutions are shown to be relevant for the description of compact stars. A distinguishing…
The universe is viewed as a dust gas filling a sphere and floating in infinite empty space. Einstein's gravitational equations are applied to this case together with appropriate boundary values. The equations are solved for initial…
We carry on a comprehensive study on static fluid distributions endowed with hyperbolical symmetry. Their physical properties are analyzed in detail. The energy density appears to be necessarily negative, which suggests that any possible…
We present new results concerning the existence of static, electrically charged, perfect fluid spheres that have a regular interior and are arbitrarily close to a maximally charged black-hole state. These configurations are described by…
The classification of certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is performed in $d\geq5$ dimensions. The class of metrics under consideration is such that the spacelike section is a warped product of…
Static spherically symmetric solution of the Einstein's equations is found representing averaged properties of an infinite self-gravitating gas in the dynamical equilibrium. It depends upon three parameters: the core radius, the…
We study the solutions of the Einstein equations in the presence of a thick infinite slab with constant energy density. When there is an isotropy in the plane of the slab, we find an explicit exact solution that matches with the Rindler and…
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
We obtain an exact solution for the Einstein's equations with cosmological constant coupled to a scalar, static particle in static, "spherically" symmetric background in 2+1 dimensions.
We study the properties of compact objects in a particular 4D Horndeski theory originating from higher dimensional Einstein-Gauss-Bonnet gravity. Remarkably, an exact vacuum solution is known. This compact object differs from general…
We have found exact constant solutions for the cosmological density parameter using a generalization of general relativity that incorporates a cosmic time-variation of the velocity of light in vacuum and the Newtonian gravitation constant.…
The purpose of this paper is to analyze the existence of static stable Einstein universe using inhomogeneous linear perturbations in the context of $f(R,T)$ gravity ($R$ and $T$ denote the scalar curvature and trace of the stress-energy…
The paper is concerned with the Einstein equations for a spherically symmetric static distribution of anisotropic matter. The equations are cast into a system of Fuchsian type ODE for certain scalar invariants of the strain. And then the…
We look for "static" spherically symmetric solutions of Einstein's Equations for perfect fluid source with equation of state $p=w\rho$. In order to include the possibilities of recently popularized dark energy and phantom energy possibly…
Stationary perfect-fluid configurations of Einstein's theory of gravity are studied. It is assumed that the 4-velocity of the fluid is parallel to the stationary Killing field, and also that the norm and the twist potential of the…
We propose a revised formulation of General Relativity for cosmological settings, in which the Einstein constant varies with the energy density of the Universe. We demonstrate that this modification has only phenomenological impact of…
Owing to the quadratic nature of the theory, Einstein-Gauss-Bonnet gravity generically permits two distinct vacuum solutions. One solution (the "Einstein" vacuum) has a well defined limit as the Gauss-Bonnet coupling goes to zero, whereas…
The Einstein equations with a positive cosmological constant are coupled to the pressureless perfect fluid matter in plane symmetry. Under suitable restrictions on the initial data, the resulting Einstein-dust system is proved to have a…
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…