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Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…
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.
Using the differential calculus on discrete group, we study the general relativity in the space-time which is the product of a four dimensional manifold by a two-point space. We generalize the usual concept of frame and connection in our…
We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is…
In this paper, we prove that Linearization Stability of Einstein Field Equations is a Generic Property in the sense that within the class $\mathcal{V}$ of space-times which admit a compact Cauchy hypersurface of constant mean curvature, the…
In this article we provide a new class of interior solutions of a five dimensional compact star in Einstein Gauss-Bonnet (EGB) gravity within the framework of Finch-skea space time. The Exterior space time is described by the EGB…
We study the exact solution of Einstein's field equations consisting of a ($n+2$)-dimensional static and hyperplane symmetric thick slice of matter, with constant and positive energy density $\rho$ and thickness $d$, surrounded by two…
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…
In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for…
We derive Einstein's equations from a linear theory in flat space-time using free-field gauge invariance and universal coupling. The gravitational potential can be either covariant or contravariant and of almost any density weight. We adapt…
The gravitational field of an idealized plane-wave solution of the Maxwell equations can be described in closed form. After discussing this particular solution of the Einstein-Maxwell equations, the motion of neutral test particles, which…
The linearized form of the metric of a Finsler - Randers space is studied in relation to the equations of motion, the deviation of geodesics and the generalized Raychaudhuri equation are given for a weak gravitational field. This equation…
Einstein gravity at $D\rightarrow 2$ limit can be obtained from the Kaluza-Klein procedure by taking the dimensions of the internal space to zero while keeping only the breathing mode. The resulting scalar-tensor theory can be further…
We present a relativistic model describing a thin disk surrounded by a halo in presence of an electromagnetic field. The model is obtained by solving the Einstein-Maxwell equations on a particular conformastatic spacetime background and by…
On a spacetime $(M,g)$ endowed with a density function $h$, we consider the vacuum weighted Einstein field equations: \[h\rho-\operatorname{Hes}_h+\Delta h g=0.\] First, it is shown that the equation characterizes critical metrics for an…
In the search for exact solutions to Einstein's field equations the main simplification tool is the introduction of spacetime symmetries. Motivated by this fact we develop a method to write the field equations for general matter in a form…
The solutions of $U(1)$ gauge-gravity coupling is one of the interesting models for analyzing the semi-classical nature of spacetime. In this regard, different well-known singular and nonsingular solutions have been taken into account. The…
Einstein's spherically symmetric interior gravitational equations are investigated. Following Synge's procedure, the most general solution of the equations is furnished in case $T^{1}_{1}$ and $T^{4}_{4}$ are prescribed. The existence of a…
A tensor description of perturbative Einsteinian gravity about an arbitrary background spacetime is developed. By analogy with the covariant laws of electromagnetism in spacetime, gravito-electromagnetic potentials and fields are defined to…
We discuss dynamical aspects of gravitational plane waves in Einstein theory with massless scalar fields. The general analytic solution describes colliding gravitational waves with constant polarization, which interact with scalar waves…