Related papers: Exact Vacuum Solutions to the Einstein Equation
Assuming that universe is the object of point rotation at a frequency, the relationship is established between this frequency and the cosmological constant. Using the transformation for point-like rotating coordinate systems, an unusual…
A solution of the Einstein vacuum field equations is constructed within the contex of perturbation theory. The solution possesses a graphical representation in terms of diagrams.
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…
In this work, we have obtained exact solutions of Einstein equations for static and axially symmetric magnetized matter, specifically in plane-symmetric and almost-plane symmetric cases. Although these solutions impose constraints on the…
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…
It is formulated a new 'anholonomic frame' method of constructing exact solutions of Einstein equations with off--diagonal metrics in 4D and 5D gravity. The previous approaches and results are summarized and generalized as three theorems…
We construct exact static inhomogeneous solutions to Einstein's equations with counter flow of particle fluid and a positive cosmological constant by using the Sasaki metrics on three-dimensional spaces. The solutions, which admit an…
Axisymmetric Solutions of the vacuum Einstein equations are found in the Papapetrou-Weyl gauge. The solutions depend on two pairs of functionals, each pair of two functions depends on a different arbitrarily chosen function of one variable.…
We ask the following question: Of the exact solutions to Einstein's equations extant in the literature, how many could represent the field associated with an isolated static spherically symmetric perfect fluid source? The candidate…
We construct low regularity solutions of the vacuum Einstein constraint equations. In particular, on 3-manifolds we obtain solutions with metrics in $H^s\loc$ with $s>{3\over 2}$. The theory of maximal asymptotically Euclidean solutions of…
In this work, we introduce a method for finding exact solutions to the vacuum Einstein field equations in higher dimensions from a given solution to the chiral equation. When considering a $n + 2$-dimensional spacetime with $n$ commutative…
We express the vacuum Einstein constraints in terms of differential forms - the forms include one-forms constituting an orthonormal coframe of the spatial metric. We show that if the metric is real-analytic, then the constraints can be…
We present the solution space of the field equations in the Einstein-aether theory for the case of a vacuum Bianchi Type V space-time. We also find that there are portions of the initial parameters space for which no solution is admitted by…
Exact time-dependent solutions of Einstein's gravitational field equation for a spherical mass moving with arbitrarily high constant velocity are derived and analyzed. The threshold conditions required for gravitational repulsion of…
Assuming conformally flat metric we obtain inhomogeneous solutions of Einstein equations with the energy-momentum of a viscous fluid. We suggest that the viscous solution can be applied as a model of an expanding inhomogeneous dark energy.
We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two…
This paper presents solutions to Einstein's equation -- and the numerical methods used to construct them -- that describe simple cosmological models on manifolds with compact non-orientable spatial slices. These solutions have been…
The solutions of vacuum Einstein's field equations, for the class of Riemannian metrics admitting a non Abelian bidimensional Lie algebra of Killing fields, are explicitly described. They are parametrized either by solutions of a…
The classification of certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is presented. The spacelike section of the class of metrics under consideration is a warped product of the real line with a nontrivial…
Let $(M,g)$ be a compact Riemannian manifold on which a trace-free and divergence-free $\sigma \in W^{1,p}$ and a positive function $\tau \in W^{1,p}$, $p > n$, are fixed. In this paper, we study the vacuum Einstein constraint equations…