Related papers: Rigidly rotating dust in general relativity
We study a numerical solution to Einstein's equation for a compact object composed of null particles. The solution avoids quantum scale regimes and hence neither relies upon nor ignores the interaction of quantum mechanics and gravitation.…
An infinite family of new exact solutions of the Einstein vacuum equations for static and axially symmetric spacetimes is presented. All the metric functions of the solutions are explicitly computed and the obtained expressions are simply…
The gravitational wave solutions obtained from a perturbation about conformally flat backgrounds in Einstein gravity are investigated. A perturbation theory analysis of the Lesame, Ellis and Dunsby results, based on a covariant approach,…
The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. A simple derivation of the spin interaction with gravitational field is presented. The self-consistent description of the spin…
We investigate insterstellar gas spheres by determining the metric functions, the material distribution, and the features of particle orbits in terms of stability and geodesics. An exact solution of the Einstein's equations for interstellar…
We study thin shells of matter in (2+1)-dimensional F(R) theories of gravity with constant scalar curvature R. We consider a wide class of spacetimes with circular symmetry, in which a thin shell joins an inner region with an outer one. We…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
Static (not stationary) solutions of the Einstein-Klein-Gordon (EKG) equations including matter are obtained for real scalar fields. The scalar field interaction with matter is considered. The introduced coupling allows the existence of…
In this article, we present a gravitational collapse null dust solution of the Einstein field equations. The spacetime is regular everywhere except on the symmetry axis where it possesses a naked curvature singularity, and admits one…
General relativity is a set of physical and geometric principles, which lead to a set of (Einstein) field equations that determine the gravitational field, and to the geodesic equations that describe light propagation and the motion of…
A new approximate solution of vacuum and stationary Einstein field equations is obtained. This solution is constructed by means of a power series expansion of the Ernst potential in terms of two independent and dimensionless parameters…
Causal rigid particles whose action includes an {\it arbitrary} dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, including {\it causal tachyonic} ones. The Hamiltonian…
We show that a vector field non-minimally coupled to gravity reproduces exactly the dynamics of an Einstein cluster -- a large ensemble of non-interacting particles moving on circular geodesics under their collective gravitational field.…
A non-static solution of Einstein's field equations of General Relativity representing the gravitational field of an axisymmetric radiation flow is obtained using the Eddington or the Kerr-Schild form for the metric. A solution obtained…
The gravitational collapse of a thick cylindrical shell of dust matter is investigated. It is found that a spacetime singularity forms on the symmetry axis and that it is necessarily naked, i.e., observable in principle. We propose a…
The gravitation field of the flat plate was investigated. It have been shown that there exist the internal solution of Einstein equations sewed together with external one, which described a ''homogeneous'' gravitational field.
We prove that, given a stress-free, axially symmetric elastic body, there exists, for sufficiently small values of the gravitational constant and of the angular frequency, a unique stationary axisymmetric solution to the Einstein equations…
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 show that the equation of motion for a rigid one-dimensional elastic body (i.e. a rod or string whose speed of sound is equal to the speed of light) in a two-dimensional spacetime is simply the wave equation. We then solve this equation…
We derive global weak solutions of Einstein's equations for spherically symmetric dust-filled space-times which admit shell-crossing singularities. In the marginally bound case, the solutions are weak solutions of a conservation law. In the…