Related papers: Exact Static Axially Symmetric Thin Annular Dust D…
We consider a system representing self-gravitating balls of dust in an expanding Universe. It is demonstrated that one can prescribe data for such a system at infinity and evolve it backward in time without the development of shocks or…
Applying the Horsk\'y-Mitskievitch conjecture to the empty space solutions of Morgan and Morgan due to the gravitational field of a finite disk, we have obtained the corresponding solutions of the Einstein-Maxwell equations. The resulting…
We solve a class of boundary value problems for the stationary axisymmetric Einstein equations corresponding to a disk of dust rotating uniformly around a central black hole. The solutions are given explicitly in terms of theta functions on…
We construct infinite-dimensional families of non-singular static space times, solutions of the vacuum Einstein-Maxwell equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with…
We adapt the well known "displace, cut and reflect" method to construct exact solutions of the Einstein-Maxwell equations corresponding to infinitesimally thin disks of matter endowed with dipole magnetic fields, which are entirely…
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…
The exact global solution of the Einstein equations [Neugebauer & Meinel, Phys. Rev. Lett. 75 (1995) 3046] describing a rigidly rotating, self-gravitating disk is discussed. The underlying matter model is a perfect fluid in the limit of…
We present a three-parameter family of solutions to the stationary axisymmetric Einstein equations that describe differentially rotating disks of dust. They have been constructed by generalizing the Neugebauer-Meinel solution of the problem…
A general procedure to find static and axially symmetric, interior solutions to the Einstein equations is presented. All the so obtained solutions, verify the energy conditions for a wide range of values of the parameters, and match…
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…
We construct static axially symmetric solutions of SU(2) Einstein-Yang-Mills-dilaton theory. Like their spherically symmetric counterparts, these solutions are nonsingular and asymptotically flat. The solutions are characterized by the…
In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to…
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…
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…
We provide exact solutions to the Einstein equations when the Universe contains vacuum energy plus a uniform arrangements of magnetic fields, strings, or domain walls. Such a universe has planar symmetry, i. e., it is homogeneous but, not…
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…
Using the well-known ``displace, cut and reflect'' method used to generate disks from given solutions of Einstein field equations, we construct static disks made of perfect fluid based on vacuum Schwarzschild's solution in isotropic…
The time independent spherically symmetric solutions of General Relativity (GR) coupled to a dynamical unit timelike vector are studied. We find there is a three-parameter family of solutions with this symmetry. Imposing asymptotic flatness…
We consider two exact solutions of Einstein's field equations corresponding to a cylinder of dust with net zero angular momentum. In one of the cases, the dust distribution is homogeneous, whereas in the other, the angular velocity of dust…
We present new numerical cosmological solutions of the Einstein Field Equations. The spacetime is spherically symmetric with a source of dust and radiation approximated as a perfect fluid. The dust and radiation are necessarily non-comoving…