Related papers: Analytic Solutions for Geodesic Motion in Static A…
In this work we present an approximate solution of the Einstein equations describing a global model for the gravitational field generated by a bounded, self-gravitating stationary and axisymmetric body rotating rigidly with constant angular…
In the standard Einstein's theory the exterior gravitational field of any static and axially symmetric stellar object can be described by means of a single function from which we obtain a metric into a four-dimensional space-time. In this…
The Einstein equations for a plane-symmetric gravitational field coupled to an arbitrary nonlinear sigma model (NSM) are shown to be represented in the form of dynamical equations of a {\it generalized effective NSM}. The gravitational…
We study the geodesic motion in a space-time describing a swirling universe. We show that the geodesic equations can be fully decoupled in the Hamilton-Jacobi formalism leading to an additional constant of motion. The analytical solutions…
The exact axisymmetric and static solution of the Einstein equations coupled to axisymmetric and static gravitating scalar (or phantom) field is presented. The spacetimes modified by the scalar field are explicitly given for the so called…
First we review some of the attempts made to find exact spherically symmetric solutions of Einstein field equations in the presence of scalar fields .Wyman solution in both static and non static scalar field is discussed briefly and it is…
In this work, we have obtained exact solutions of Einstein equations for static and axially symmetric magnetized matter, specifically in plane-symmetric and almost-plane symmetric cases. Although these solutions impose constraints on the…
Exact time-dependent solutions of Einstein's gravitational field equation for a spherical mass moving with arbitrarily high constant velocity are derived and analyzed. The threshold conditions required for gravitational repulsion of…
This work is focused in the study of analytic anisotropic solutions to Einstein's field equations, describing spherically symmetric and static configurations by way of the gravitational decoupling through the method of Minimal Geometric…
In this paper, we develop a new method to find the exact solutions of the Einstein's field equations by using which we construct time-periodic solutions. The singularities of the time-periodic solutions are investigated and some new…
Dirac's constraint analysis and the symplectic structure of geodesic equations are obtained for the general cylindrically symmetric stationary spacetime. For this metric, using the obtained first order Lagrangian, the geodesic equations of…
In this article we find the general, exact solution for the gravitational field equations for diagonal, vacuum, separable metrics. These are metrics each of whose terms can be separated into functions of each space-time variable separately.…
The fundamental metrics, which describe any static three-dimensional Einstein-Maxwell spacetime (depending only on a unique spacelike coordinate), are found. In this case there are only three independent components of the electromagnetic…
In recent years, interest in extra dimensions has experienced a dramatic increase. A common practice has been to look for higher-dimensional generalizations of four-dimensional solutions to the Einstein equations. In this vein, we have…
We present a new numerical code designed to solve the Einstein field equations for axisymmetric spacetimes. The long term goal of this project is to construct a code that will be capable of studying many problems of interest in axisymmetry,…
We study a static spherically symmetric problem with a black hole and radially directed geodesic flows of dark matter. The obtained solutions have the following properties. At large distances, the gravitational field produces constant…
We consider the motion of test particles and light rays in a static cylindrically symmetric conformal spacetime given by Said et al [1]. We derive the equations of motion and present their analytical solutions in terms of the Weierstrass…
We study spherically symmetric solutions to the Einstein field equations under the assumption that the space-time may possess an arbitrary number of spatial dimensions. The general solution of Synge is extended to describe systems of any…
A d-dimensional spacetime is "axisymmetric" if it possesses an SO(d-2) isometry group whose orbits are (d-3)-spheres. In this paper, algebraically special, axisymmetric solutions of the higher dimensional vacuum Einstein equation (with…
In this paper we show that any static and spherically symmetric anisotropic solution of the Einstein field equations can be thought as a system sourced by certain deformed isotropic system in the context of Minimal Geometric…