Related papers: Type III and N universal spacetimes
We consider four dimensional spaces of neutral signature and give examples of universal spaces of Walker type. These spaces have no analogue in other signatures in four dimensions and provide with a new class of spaces being universal.
We study pure Lovelock vacuum and perfect fluid equations for Kasner-type metrics. These equations correspond to a single $N$th order Lovelock term in the action in $d=2N+1,\,2N+2$ dimensions, and they capture the relevant gravitational…
Spacetimes, which are representations of a bridge-like geometry in gravity theory, are constructed as vacuum solutions to the first order equations of motion. Each such configuration consists of two copies of an asymptotically flat sheet,…
We study the class of vacuum (Ricci flat) six-dimensional spacetimes admitting a non-degenerate multiple Weyl aligned null direction l, thus being of Weyl type II or more special. Subject to an additional assumption on the asymptotic…
We provide a general contractibility criterion for subsets of Riemannian metrics on the disc. For instance, this result applies to the space of metrics that have positive Gauss curvature and make the boundary circle convex (or geodesic).…
The Kundt conjecture states that a Lorentzian manifold of arbitrary dimension which is not characterized by its scalar polynomial curvature invariants (SPIs) allows for a non-twisting, non-shearing and non-expanding (in short, Kundt) null…
Under normal circumstances most members of the general relativity community focus almost exclusively on the local properties of spacetime, such as the locally Euclidean structure of the manifold and the Lorentzian signature of the metric…
As quotient spaces, Minkowski and de Sitter are fundamental, non-gravitational spacetimes for the construction of physical theories. When general relativity is constructed on a de Sitter spacetime, the usual Riemannian structure is replaced…
Non-Euclidean method of the generalized geometry construction is considered. According to this approach any generalized geometry is obtained as a result of deformation of the proper Euclidean geometry. The method may be applied for…
In the present paper we give conclusive arguments pointing at physical equivalence among conformally related metrics. Based on the argument that any consistent effective theory of spacetime must be invariant under the one-parameter group of…
It is generally believed that any quantum theory of gravity should have a generic feature --- a quantum of length. We provide a physical ansatz to obtain an effective non-local metric tensor starting from the standard metric tensor such…
We present a topological classification of vacuum space-time. Assuming the 3-dimensional space allows a global chart, we show that the static vacuum space-time of Einstein's theory can be classified by the knot topology…
Quasi-topological terms in gravity can be viewed as those that give no contribution to the equations of motion for a special subclass of metric ans\"atze. They therefore play no r\^ole in constructing these solutions, but can affect the…
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.…
A quantum Schwarzschild spacetime and a quantum Schwarzschild-de Sitter spacetime with cosmological constant $\Lambda$ are constructed within the framework of a noncommutative Riemannian geometry developed in an earlier publication. The…
Let $\mathcal{M} (X)$ denote the space of complete Riemannian metrics with non-positive sectional curvature and with negatively curved ends, on a manifold $X$. We show that $\mathcal{M} (\mathbb{R} \times S ^{1}) $ and $\mathcal{M}…
The fundamental physical object of the Global Time Theory is a three-dimensional curved space dynamically developing in global time. The equations of its dynamics are derived from the Lagrangian, and the Hamiltonian of ravitation turns out…
In spacetime dimensions $n+1\geq 4$, we show the existence of solutions of the Einstein vacuum equations which describe asymptotically de Sitter spacetimes with prescribed smooth data at the conformal boundary. This provides a short…
The most general form of non-static plane symmetric space-times is considered to study proper curvature collineations by using the rank of the 6X6 Riemann matrix and direct integration techniques. Studying proper curvature collineations in…
We parametrize pp-wave spacetimes with compact codimension 2 hypersurfaces. In the vacuum case, we show that these spacetimes are locally in one-to-one correspondence with smooth curves of Riemannian Ricci-flat metrics modulo smooth curves…