Related papers: A New Solution of Einstein Vacuum Field Equations
In this paper, we introduce new methods for solving the vacuum Einstein constraints equations: the first one is based on Schaefer's fixed point theorem (known methods use Schauder's fixed point theorem) while the second one uses the concept…
The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical…
Einstein originally proposed a nonsymmetric tensor field, with its symmetric part associated with the spacetime metric and its antisymmetric part associated with the electromagnetic field, as an approach to a unified field theory. Here we…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
In this work we investigate analytic static and spherically symmetric solutions of a generalized theory of gravity in the Einstein-Cartan formalism. The main goal consists in analyzing the behavior of the solutions under the influence of a…
We derive a new class of exact solutions characterized by the Szekeres-Szafron metrics (of class I), admitting in general no isometries. The source is a fluid with viscosity but zero heat flux (adiabatic but irreversible evolution) whose…
In addition to the two standard solutions of the quantum field equations having the form e^{+/-(iwt-ikx)}, there exist two additional solutions of the form e^{+/-(iwt+ikx). By incorporating these latter solutions, deemed "supplemental…
We survey some results on scalar curvature and properties of solutions to the Einstein constraint equations. Topics include an extended discussion of asymptotically flat solutions to the constraint equations, including recent results on the…
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…
It is shown that all torsion-free vacuum solutions of the model of dS gauge theory of gravity are the vacuum solutions of Einstein field equations with the same positive cosmological constant. Furthermore, for the gravitational theories…
Cylindrical-like coordinates for constant-curvature 3-spaces are introduced and discussed. This helps to clarify the geometrical properties, the coordinate ranges and the meaning of free parameters in the static vacuum solution of Linet and…
We consider the Einstein-Dirac field equations describing a self-gravitating massive neutrino, looking for axially-symmetric exact solutions; in the search of general solutions, we find some that are specific and which have critical…
The solution of Einstein field equations for static spherically symmetric spacetime metric with anisotropic internal stresses has been obtained. The matter has vanishing complexity and a spacetime metric that satisfies the Karmarkar…
Both cosmological expansion and black holes are ubiquitous features of our observable Universe, yet exact solutions connecting the two have remained elusive. To this end, we study self-gravitating classical fields within dynamical…
In addition to the boosted static solution there are two other classes of stationary string-like solutions of the vacuum Einstein equation in (4+1)-dimensions. Each class is characterized by three parameters of mass, tension, and momentum…
In this work, we construct a modified version of the Einstein field equations for a vacuum and spherically symmetric spacetime in terms of the Riemann-Louville fractional derivative. The main difference between our approach and other works…
A new class of static plane symmetric solution of Einstein field equation, which is judged as the source of Taub solution, was presented in our previous work. In this letter the properties of geodesics of this solution are explored. It is…
We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary dimensions. We solve these constraints and show that they provide necessary and sufficient conditions so that a spacetime…
In this note we examine some recently proposed solutions of the linearized vacuum Einstein equations. We show that such solutions are {\it not} symmetries of the Einstein equations, because of a crucial integrability condition.
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…