Exact Solutions Of Einstein-Maxwell Equations Research Articles

General magnetized Weyl solutions: disks and motion of charged particles

We construct three families of general magnetostatic axisymmetric exact solutions of Einstein-Maxwell equations in spherical coordinates, prolate, and oblates. The solutions obtained are then presented in the system of generalized spheroidal coordinates which is a generalization of the previous systems. The method used to build such solutions is the well-known complex potential formalism proposed by Ernst, using as seed solutions vacuum solutions of the Einstein field equations. We show explicitly some particular solutions among them a magnetized Erez-Rosen solution and a magnetized Morgan-Morgan solution, which we interpret as the exterior gravitational field of a finite dislike source immersed in a magnetic field. From them we also construct using the well known "displace, cut and reflect" method exact solutions representing relativistic thin disks of infinite extension. We then analyze the motion of electrically charged test particles around these fields for equatorial circular orbits and we discuss their stability against radial perturbations. For magnetized Morgan-Morgan fields we find that inside of disk the presence of magnetic field provides the possibility of to find relativist charged particles moving in both prograde and retrograde direction.

Inhomogeneous two-fluid cosmologies with electromagnetic field

An algorithm for determining exact solutions of Einstein-Maxwell equations in Ruban's background is presented. In the most general case the cosmological constant is non-zero and the matter content is a mixture of two interacting simple fluids plus a sourceless electromagnetic field. By considering the case of a simple fluid, a class of expanding inhomogeneous solutions generalising the dust model found by Ruban (1982) and the Doroshkevich 'magnetic' universes is derived. The conditions under which the simple fluid may be interpreted as a two-fluid mixture are discussed. The influence of the field near the singularity and at the later stages of the expansion is also examined. A subclass of these models approaches homogeneity and isotropy for large cosmological times.

Some new exact solutions of Einstein-Maxwell equations with axial symmetry

Some new exact solutions of Einstein-Maxwell equations with axial symmetry

A class of axisymmetric stationary exact solutions of Einstein-Maxwell equations

Einstein-Maxwell vacuum field equations of an axially symmetric stationary charged rotating source are studied. A class of asymptotically flat solutions representing the exterior field of a stationary rotating charged oblate spheroidal source is obtained. By examining eigenvectors of Einstein tensor Gij, invariants RijRij and Petrov classification of Weyl's conformal tensor, it is proved that the metric potentials describe null electromagnetic fields.