Related papers: Type II Einstein spacetimes in higher dimensions
We consider expanding vacuum spacetimes with a CMC foliation by compact spacelike hypersurfaces. Under scale invariant a priori geometric bounds (type-III), we show that there are arbitrarily large future time intervals that are modelled by…
The fact that in Minkowski space, space and time are both quantized does not have to be introduced as a new postulate in physics, but can actually be derived by combining certain features of General Relativity and Quantum Mechanics. This is…
It is found the exact solution of the Poisson equation for the multidimensional space with topology $M_{3+d}=\mathbb{R}^3\times T^d$. This solution describes smooth transition from the newtonian behavior $1/r_3$ for distances bigger than…
In this paper, we deal with generalizations of real Einstein numbers to various spaces and dimensions. We search operations and their properties in generalized settings. Especially, we are interested in the generalized operation of…
Einstein's theory of general relativity models the physical universe using spacetimes which satisfy Einstein's gravitational field equations. To date, Einstein's theory has been enormously successful in modeling observed gravitational…
We review recent progress in taking the large dimension limit of Einstein's equations. Most of our analysis is classical in nature and concerns situations where there is a black hole horizon although we briefly discuss various extensions…
Bi-spinor and G-structure methods are used to classify the possible consistent truncations of type II supergravity to $d=6$ Einstein-Maxwell (gauged) supergravity, and its consistent sub-sectors. In the absence of R-symmetry gauging and a…
In this paper we give local and global parametric classifications of a class of Einstein submanifolds of Euclidean space. The highlight is for submanifolds of codimension two since in this case our assumptions are only of intrinsic nature.
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 analyze asymptotic properties of higher-dimensional vacuum spacetimes admitting a "non-degenerate" geodetic multiple WAND. After imposing a fall-off condition necessary for asymptotic flatness, we determine the behaviour of the Weyl…
When four-dimensional general relativity is embedded in an unconstrained man-ner in a fifth dimension, the physical quantities of spacetime can be interpreted as geometrical properties related to the extra dimension. It has become…
A class of 2-dimensional models including 2-d dilaton gravity, spherically symmetric reduction of d-dimensional Einstein gravity and other related theories are classically analyzed. The general analytic solutions in the absence of matter…
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…
Five classes of radiative solutions of Einstein's field equations are discussed in the light of some new developments. These are plane waves and their collisions, cylindrical waves, Robinson-Trautman and type N spacetimes, boost-rotation…
We present and analyze new exact gyraton solutions of algebraic type II on a background which is static, cylindrically symmetric Melvin universe of type D. For a vanishing electromagnetic field it reduces to previously studied gyratons on…
In order for spacetimes with static extra dimensions to have 4-dimensional de Sitter expansion they must have at least positive curvature, warping sourced by the 4-d expansion, or violate the null energy condition everywhere in the extra…
In this article we prove that a certain class of {\it smooth} Sasakian manifolds admits lifts to 4-dimensional quasi-Einstein shearfree spacetimes of Petrov type II or D. This is related to an analogous result by Hill, Lewandowski and…
We consider a thick brane model supported by two interacting scalar fields in 7D and 8D general relativity. Using the special type of a potential energy, we obtain numerically the regular asymptotically flat vacuum solutions. A possibility…
We investigate the Weyl tensor algebraic structure of a fully general family of D-dimensional geometries that admit a non-twisting and shear-free null vector field k. From the coordinate components of the curvature tensor we explicitly…
We classify all warped product space-times in three categories as i) generalized twisted product structures, ii) base conformal warped product structures and iii) generalized static space-times and then we obtain the Einstein equations with…