Related papers: Solving the Einstein field equations
Solutions of classical and quantum equations of motion in spinor electrodynamics are constructed within the context of perturbation theory. The solutions possess a graphical representation in terms of diagrams.
Exact solutions to the Einstein field equations may be generated from already existing ones (seed solutions), that admit at least one Killing vector. In this framework, a space of potentials is introduced. By the use of symmetries in this…
A vacuum solution of the Einstein gravitational field equation is given that follows from a general ansatz but fails to follow from it if a certain symmetric matrix is assumed to be in diagonal form from the beginning.
For a wide class of nonlinear equations a perturbative solution is constructed. This class includes equations of motion of field theories. The solution possesses a graphical representation in terms of diagrams. To illustrate the formalism…
Schwarzschild's solution of Einstein's field equations in vacuum can be written in many different forms. Unfortunately Schwarzschild's own original form is less nice looking and simple than that latter derived by Droste and Hilbert. We…
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 obtain the perturbed components of affine connection and Ricci tensor using algebraic computation. Naturally, the perturbed Einstein field equations for the vacuum can be written. The method can be used to obtain perturbed equations of…
In this article, we provide a discussion on a composite class of exact static spherically symmetric vacuum solutions of Einstein's equations. We construct the composite solution of Einstein field equation by match the interior vacuum metric…
A new solution of Einstein's vacuum field equations is discovered which appears as a generalization of the well-known Ozsvath-Schucking solution and explains its source of curvature which has otherwise remained hidden. Curiously, the new…
In this paper we provide a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field. All spacetimes of this type which are symmetric with respect to a…
This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to…
The first step in the building of a spacetime solution of Einstein's gravitational field equations via the initial value formulation is finding a solution of the Einstein constraint equations. We recall the conformal method for constructing…
In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well known cone solution, which is locally…
In this paper we construct a new kind of solutions of the Einstein's field equations with non-vanishing cosmological constant, which possess some interesting physical properties. The singularities of this kind of solutions are investigated.…
We discuss the exact solution of Einstein's equation corresponding to a static and plane symmetric distribution of matter with constant positive density located below $z=0$ matched to vacuum solutions.
We present a simple method to obtain vacuum solutions of Einstein's equations in parabolic coordinates starting from ones with cylindrical symmetries. Furthermore, a generalization of the method to a more general situation is given together…
We study self-consistent cosmological solutions for an Einstein Universe in a graph-based induced gravity model. The graph-based field theory has been proposed by the present authors to generalize dimensional deconstruction. In this paper,…
Mathematical modeling of gravitating configurations of physical fields is one of the priority directions of the modern theory of gravity. Most of the exact solutions constructed within the framework of the general relativity are static or…
In this work we present an approximate solution of the Einstein equations describing a global model for the gravitational field generated by a bounded, self-gravitating stationary and axisymmetric body rotating rigidly with constant angular…
In this paper, we present a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can…