Related papers: A Spacetime in Toroidal Coordinates
We solve vacuum Einstein's field equations with the cosmological constant in space-times admitting 3-parameter group of isometries with 2-dimensional space-like orbits. The general exact solutions, which are represented in the advanced and…
Cylindrical-like coordinates for constant-curvature 3-spaces are introduced and discussed. This helps to clarify the geometrical properties, the coordinate ranges and the meaning of free parameters in the static vacuum solution of Linet and…
In the present article we find a new class of solutions of Einstein's field equations. It describes stationary, cylindrically symmetric spacetimes with closed timelike geodesics everywhere outside the symmetry axis. These spacetimes contain…
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…
The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical…
The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…
The static, apparently cylindrically symmetric vacuum solution of Linet and Tian for the case of a positive cosmological constant $\Lambda$ is shown to have toroidal symmetry and, besides $\Lambda$, to include three arbitrary parameters. It…
We construct self-similar, axisymmetric, time-independent solutions to Einstein's field equations for an isothermal gas with a flat rotation curve in the equatorial plane. The metric scales as $ds^2 \to a^2 ds^2$ under the transformation…
An exact solution of the vacuum Einstein equations with a cosmological constant is exhibited which can perhaps be used to describe the interior of compact rotating objects. The physical part of this solution has the topology of a torus,…
Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on…
We find exact static solutions of the Einstein equations in the spacetime with plane symmetry, where an infinite slab with finite thickness and homogeneous energy (mass) density is present. In the first solution the pressure is isotropic,…
A solution of the vacuum Einstein equations with a cosmological constant is exhibited which can perhaps be used to describe the interior of compact rotating objects, and may also provide a description of our universe on length scales…
In this work a class of interior solution for Einstein field equations corresponding to a spherically symmetric anisotropic fluid sphere has been obtained under the assumption that the cosmological constant is spatially variable. The…
In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well known cone solution, which is locally…
The solution of Einstein field equations for static spherically symmetric spacetime metric with anisotropic internal stresses has been obtained. The matter has vanishing complexity and a spacetime metric that satisfies the Karmarkar…
Spherically symmetric static solutions of the Einstein equations with a positive cosmological constant for the energy-momentum tensor of a barotropic perfect fluid are governed by the Tolman-Oppenheimer-Volkoff-de Sitter equation. Existence…
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…
A procedure to find static axially symmetric solutions to the Einstein field equations is presented. We obtained two general solutions and five particular solutions, which depend on the existence conditions for circular and $z$ direction…
We derive the general solution to the coupled Einstein and Dirac field equations in static and hyperplane-symmetric spacetime of arbitrary dimension including a cosmological constant of either sign. As a result, only a massful Dirac field…
The general stationary cylindrically symmetric solution of Einstein-massless scalar field system with a non-positive cosmological constant is presented. It is shown that the general solution is characterized by four integration constants.…