Related papers: Generating Generalized $G_{D-2}$ solutions
The vacuum Einstein equations in 5+1 dimensions are shown to admit solutions describing naked singularity formation in gravitational collapse from nonsingular asymptotically locally flat initial data that contain no trapped surface. We…
In recent years, interest in extra dimensions has experienced a dramatic increase. A common practice has been to look for higher-dimensional generalizations of four-dimensional solutions to the Einstein equations. In this vein, we have…
A D-dimensional gravitational model with Gauss-Bonnet and cosmological term is considered. When ansatz with diagonal cosmological metrics is adopted, we overview recent solutions for zero cosmological term and find new examples of solutions…
By means of a simple model we investigate the possibility that spacetime is a membrane embedded in higher dimensions. We present cosmological solutions of d-dimensional Einstein-Maxwell theory which compactify to two dimensions. These…
A new method of construction of integral varieties of Einstein equations in three dimensional (3D) and 4D gravity is presented whereby, under corresponding redefinition of physical values with respect to anholonomic frames of reference with…
The vacuum cosmological model on the manifold $R \times M_1 \times \ldots \times M_n$ describing the evolution of $n$ Einstein spaces of non-zero curvatures is considered. For $n = 2$ the Einstein equations are reduced to the Abel (ordinary…
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 consider four-dimensional, Riemannian, Ricci-flat metrics for which one or other of the self-dual or anti-self-dual Weyl tensors is type-D. Such metrics always have a valence-2 Killing spinor, and therefore a Hermitian structure and at…
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 algebraically classify some higher dimensional spacetimes, including a number of vacuum solutions of the Einstein field equations which can represent higher dimensional black holes. We discuss some consequences of this work.
The classification of certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is performed in $d\geq5$ dimensions. The class of metrics under consideration is such that the spacelike section is a warped product of…
It is shown that four dimensional vacuum Einstein solutions simply embedded in five dimensions obey the Gauss-Bonnet-Einstein field equations: $G_{ab}+\alpha GB_{ab}+\delta^{55}_{ab}\alpha\exp(-2\chi/\sqrt{\alpha})GB_4=0$ and the…
We study time-dependent compactification of extra dimensions. We assume that the spacetime is spatially homogeneous, and solve the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally…
We use solution-generating techniques to construct interpolating geometries between general asymptotically flat, charged, rotating, non-extremal black holes in four and five dimensions and their subtracted geometries. In the…
We construct new solutions of the vacuum Einstein field equations with cosmological constant. These solutions describe spacetimes with non-trivial topology that are asymptotically dS, AdS or flat. For a negative cosmological constant these…
We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein's equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie…
As an extension of the Robinson-Trautman solutions of D=4 general relativity, we investigate higher dimensional spacetimes which admit a hypersurface orthogonal, non-shearing and expanding geodesic null congruence. Einstein's field…
More than thirty years passed since the first discoveries of various aspects of integrability of the symmetry reduced vacuum Einstein equations and electrovacuum Einstein - Maxwell equations were made and gave rise to constructions of…
In this paper, we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish, keep finite or take the infinity at some points in these space-times, respectively.…
We construct solutions of higher-dimensional Einstein gravity coupled to nonlinear $\sigma$-model with cosmological constant. The $\sigma$-model can be perceived as exterior configuration of a spontaneously-broken $SO(D-1)$ global…