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The general exact solution of the Einstein-matter field equations describing spherically symmetric shells satisfying an equation of state in closed form is discussed under general assumptions of physical reasonableness. The solutions split…

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 search for spherically symmetric, stationary solutions with a string gas shell as a source. The requirement of a uniform newtonian potential, or constancy of the 00 component of the metric, implies the existence of a "dual" radiation,…

We find solutions of Einstein's field equation for topologically stable strings associated with the breaking of a U(1) symmetry. Strings form in many GUTs and are expected whenever the homotopy group $\Pi_1(M_0)$ is non-trivial. The…

We consider a string model at one-loop related to a $\sigma$-model whose antisymmetric tensor field is constructed as complex structure on the background manifold, specially on a manifold $R\times N$ where $N$ is a complex manifold. As an…

In this paper we study regular cosmic string solutions of the non-Abelian Higgs model coupled with the Einstein gravity. In order to do that, we constructed a set of coupled differential ordinary equation. Because there is no closed…

We derive an exact solution to the Einstein's equations with a stress-energy tensor corresponding to an opposite-sign scalar field, and show that such a solution describes the internal region of a rotating wormhole. We also derive an static…

A solution of the vortex type is given in a six-dimensional $SU(2)\times U(1)$ pure gauge theory coupled to Einstein gravity in a compactified background geometry. We construct the solution of an effective abelian Higgs model in terms of…

We consider Einstein Gravity coupled to dynamical matter consisting of a gauge field with any compact gauge group and minimally coupled scalar fields. We investigate the conditions under which a free specification of a spatial field…

We consider a self-gravitating string generated by a global vortex solution in general relativity. We investigate the Einstein and field equations of a global vortex in the region of its central line and at a distance from the centre of the…

We review spherical and inhomogeneous analytic solutions of the field equations of Einstein and of scalar-tensor gravity, including Brans-Dicke theory, non-minimally (possibly conformally) coupled scalar fields, Horndeski, and beyond…

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 consider spherically symmetric higher-dimensional solutions of Einstein's equations with a bulk cosmological constant and n transverse dimensions. In contrast to the case of one or two extra dimensions we find no solutions that localize…

The paper is concerned with the Einstein equations for a spherically symmetric static distribution of anisotropic matter. The equations are cast into a system of Fuchsian type ODE for certain scalar invariants of the strain. And then the…

We present a particular solution to the Einstein field equations that could arise as a magnetic monopole in the strong field limit of the Born-Infeld electrodynamics. We solve its geodesics exactly and show that they can mimic the…

Einstein equations with $T_{\mu\nu} = k_\mu k_\nu + \ell_\mu \ell_\nu$ where $k, \ell$ are null are considered with spherical symmetry and staticity. The solution has naked singularity and is not asymptotically flat. However, it may be…

In this work, we give a general class of solutions of the spinning cosmic string in Einstein's theory of gravity. After treating same problem in Einstein Cartan (EC) theory of gravity, the exact solution satisfying both exterior and…

Schwarzschild's 'interior solution' is a space-time metric that satisfies Einstein's gravitational field equations with a source term that Einstein created on the basis of an unjustified identification of the conceptually distinct notions…

We study the behaviour of a specific system of relativistic elasticity in its own gravitational field: a static, spherically symmetric shell whose wall is of arbitrary thickness consisting of hyperelastic material. We give the system of…

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…