Related papers: General Exact Solution of Einstein Field Equations…
We summarize some our recent results on encoding exact solutions of field equations in Einstein and modified gravity theories into solitonic hierarchies derived for nonholonomic curve flows with associated bi-Hamilton structure. We argue…
The interpretations of solutions of Einstein field's equations led to the prediction and the observation of physical phenomena which confirm the important role of general relativity, as well as other relativistic theories in physics. In…
Spherically symmetric static empty space solutions are studied in f(R) theories of gravity. We reduce the set of modified Einstein's equations to a single equation and show how one can construct exact solutions in different f(R) models. In…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple two layers star model: a self-gravitating ball built up by two layers of perfect fluid having different linear…
Einstein's field equations for a spherically symmetric metric coupled to a massless scalar field are reduced to a system effectively of second order in time, in terms of the variables $\mu=m/r$ and $y=(\alpha/ra)$, where $a$, $\alpha$, $r$…
We study the pages in Albert Einstein's 1916 landmark paper in the Annalen der Physik where he derived his field equations for gravity. Einstein made two heuristic and physically insightful steps. The first was to obtain the field equations…
Extended gravitational models have gained large attention in the last couple of decades. In this work, we examine the solution space of vacuum, static, and spherically symmetric spacetimes within $F(R)$ theories, introducing novel methods…
This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with…
We review and strengthen the arguments given by Einstein to derive his first gravitational field equation for static fields and show that, although it was ultimately rejected, it follows from General Relativity (GR) for negligible pressure.…
We show how the Einstein equations with cosmological constant (and/or various types of matter field sources) can be integrated in a very general form following the anholonomic deformation method for constructing exact solutions in four and…
Contents: 1) Introduction and a few excursions [A word on the role of explicit solutions in other parts of physics and astrophysics. Einstein's field equations. "Just so" notes on the simplest solutions: The Minkowski, de Sitter and anti-de…
In this article, we construct explicit analytical exact solutions to the six and higher dimensional Einstein-Maxwell theory. In all solutions, a subspace of the metric is the Eguchi-Hanson space where the metric functions are completely…
We consider the 3-dimensional formulation of Einstein's theory for spacetimes possessing a non-null Killing field $\xi^a$. It is known that for the vacuum case some of the basic field equations are deducible from the others. It will be…
In the famous textbook written by Landau and Lifshitz all the vacuum metrics of the general theory of relativity are derived, which depend on one coordinate in the absence of a cosmological constant. Unfortunately, when considering these…
We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a…
We show that the tree dimensional Einstein vacuum field equations with cosmological constant are integrable. Using the $sl(2,R)$ valued soliton connections we obtain the metric of the spacetime in terms of the dynamical variables of the…
As an example of the unification of gravitation and particle physics, an exact solution of the five-dimensional field equations is studied which describes waves in the classical Einstein vacuum. While the solution is essentially 5D in…
We study some exact and approximate solutions of Einstein's equations that can be used to describe the gravitational field of astrophysical compact objects in the limiting case of slow rotation and slight deformation. First, we show that…
I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled…
In multi-scalar field cosmologies new dynamical degrees of freedom are introduced which can explain the observational phenomena. Unlike the usual scalar field theory where a single scalar field is considered, the multi-scalar field…