Related papers: Axisymmetric Stationary Solutions as Harmonic Maps
Beginning with a special form of the Einstein-Rosen metric, we find new cosmological solutions of the Einstein equations, having two hypersurface-orthogonal Killing vectors , with ideal fluid. The equation of state is in the most cases of…
We derive the general solution to the coupled Einstein and Dirac field equations in static and hyperplane-symmetric spacetime of arbitrary dimension including a cosmological constant of either sign. As a result, only a massful Dirac field…
A numerical solution scheme for the Einstein field equations based on generalized harmonic coordinates is described, focusing on details not provided before in the literature and that are of particular relevance to the binary black hole…
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…
The purpose of this paper is to demonstrate a new method of generating exact solutions to the Einstein's equations obtained by the Hamiltonian reduction. The key element to the successful Hamiltonian reduction is finding the privileged…
We present a mathematical framework for generating thick domain wall solutions to the coupled Einstein-scalar field equations which are (locally) plane symmetric. This approach leads naturally to two broad classes of wall-like solutions.…
Axially symmetric spacetimes are the only models for isolated systems with continuous symmetries that also include dynamics. For such systems, we review the reduction of the vacuum Einstein field equations to their most concise form by…
This paper presents a systematical study of stationary (rotating) cylindrical space-times of a Weyl form that are solutions to D=4 Einstein-Maxwell equations with cosmological constant. The corresponding equations of motion - with zero…
The Schwarzschild-deSitter metric is the known solution of Einstein field equations with cosmological constant term for vacuum spherically symmetric space around a point mass M. Recently it has been reported that in a $Lamda$-dominant world…
We study some geometric properties of Killing horizons in 4-dimensional stationary and axisymmetric space-times with electromagnetic field and cosmological constant. Using a $(1+1+2)$ space-time split, we construct relations between the…
All classes of spatially homogeneous space-time models are found that allow the integration of the equations of motion of test particles and the eikonal equation by the method of complete separation of variables according to type (2.1).…
We investigate the late-time asymptotics of future expanding, polarized vacuum Einstein spacetimes with T2-symmetry on T3, which, by definition, admit two spacelike Killing fields. Our main result is the existence of a stable asymptotic…
Using a new ansatz for solving the Einstein equations with a scalar field with the sign of the kinetic term inverted, I find a series of formulae to derive axial symmetric stationary exact solutions of the Phantom scalar field in general…
Methods and properties regarding the linear perturbations are discussed for some spatially closed (vacuum) solutions of Einstein's equation. The main focus is on two kinds of spatially locally homogeneous solution; one is the Bianchi III…
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…
We seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been…
We demonstrate a technique to generate new class of exact solutions to the Einstein-Maxwell system describing a static spherically symmetric relativistic star with anisotropic matter distribution. An interesting feature of the new class of…
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…
Certain features associated with the symmetry reduction of the vacuum Einstein equations by two commuting, space-like Killing vector fields are studied. In particular, the discussion encompasses the equations for the Gowdy $T^3$ cosmology…
In this note, we generalize biharmonic equation for rotationally symmetric maps ([4], [16], [10]) to equivariant maps between model spaces and use it to give a complete classification of rotationally symmetric conformal biharmonic maps from…