Related papers: On an Extension of a Static Ball Solution
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…
Seven new solutions to the interior static and spherically symmetric Einstein's field equations (EFE) are found and investigated. These new solutions are a generalisation of the quadratic density fall-off profile of the Tolman VII solution.…
The first exact interior solution to Einstein's field equations for a static and non-uniform braneworld star with local and non-local bulk terms is presented. It is shown that the bulk Weyl scalar ${\cal U}(r)$ is always negative inside the…
The theoretical description of compact structures that share some key features with mass varying particles allows for a simple analysis of equilibrium and stability for massive stellar bodies. We investigate static, spherically symmetric…
Schwarzschild's 'interior solution' is a space-time metric that satisfies Einstein's gravitational field equations with a source term that Einstein created on the basis of an unjustified identification of the conceptually distinct notions…
Interior solutions of Einstein's equations with a non-zero cosmological constant are given for static and spherically symmetric configurations of uniform density. The metric tensor and pressure are determined for both positive and negative…
Via a straightforward integration of the Einstein equations with cosmological constant, all static circularly symmetric perfect fluid 2+1 solutions are derived. The structural functions of the metric depend on the energy density, which…
We study Einstein static universes in the context of generic f(R) models. It is shown that Einstein static solutions exist for a wide variety of modified gravity models sourced by a barotropic perfect fluid with equation of state w=p/rho,…
We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in ref. [20] which should be fulfilled by any static and spherically symmetric solution in the state of hydrostatic…
In the field equations of Einstein-Cartan theory with cosmological constant a static spherically symmetric perfect fluid with spin density satisfying the Weyssenhoff restriction is considered. This serves as a rough model of space filled…
We obtain well behaved interior solutions describing hydrostatic equilibrium of anisotropic relativistic stars in scale-dependent gravity, where Newton's constant is allowed to vary with the radial coordinate throughout the star. Assuming…
We investigate the interior Einstein's equations in the case of a static, axially symmetric, perfect fluid source. We present a particular line element that is specially suitable for the investigation of this type of interior gravitational…
This paper deals with the evolution of the Einstein gravitational fields which are coupled to a perfect fluid. We consider the Einstein--Euler system in asymptotically flat spacestimes and therefore use the condition that the energy density…
In the process of protostar formation, astrophysical gas clouds undergo thermodynamically irreversible processes and emit heat and radiation to their surroundings. Due the emission of this energy one can envision an idealized situation in…
The stability properties of the Einstein Static solution of General Relativity are altered when corrective terms arising from modification of the underlying gravitational theory appear in the cosmological equations. In this paper the…
We construct exact static inhomogeneous solutions to Einstein's equations with counter flow of particle fluid and a positive cosmological constant by using the Sasaki metrics on three-dimensional spaces. The solutions, which admit an…
We prove existence of solutions for an elastic body interacting with itself through its Newtonian gravitational field. Our construction works for configurations near one given by a self-gravitating ball of perfect fluid. We use an implicit…
Einstein field equations for anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities.…
Various profiles of matter distribution in galactic halos (such as Navarro-Frenk-White, Burkert, Hernquist, Moore, Taylor-Silk and others) are considered here as the source term for the Einstein equations. We solve these equations and find…
The exact general solution to the Einstein equations in a homogeneous Universe with a full causal viscous fluid source for the bulk viscosity index $m=1/2$ is found. We have investigated the asymptotic stability of Friedmann and de Sitter…