Related papers: On Spacetimes with Constant Scalar Invariants
This article investigates the stability of a generic Kasner spacetime to linear perturbations, both at late and early times. It demonstrates that the perturbation of the Weyl tensor diverges at late time in all cases but in the particular…
General properties of Kerr-Schild spacetimes with (A)dS background in arbitrary dimension are studied. It is shown that the geodetic Kerr-Schild vector k is a multiple WAND of the spacetime. Einstein Kerr-Schild spacetimes with…
The space of time-like geodesics on Minkowski spacetime is constructed as a coset space of the Poincar\'e group in (3+1) dimensions with respect to the stabilizer of a worldline. When this homogeneous space is endowed with a Poisson…
In numerical studies of Gowdy spacetimes evidence has been found for the development of localized features (spikes) involving large gradients near the singularity. The rigorous mathematical results available up to now did not cover this…
In this paper we study sectional curvature of invariant hyper-Hermitian metrics on simply connected 4-dimensional real Lie groups admitting invariant hypercomplex structure. We give the Levi-Civita connections and explicit formulas for…
We provide the full classification, in arbitrary even and odd dimensions, of global conformal invariants, i.e., scalar densities in the spacetime metric and its derivatives that are invariant, possibly up to a total derivative, under local…
I investigate a discrete model of quantum gravity on a causal null-lattice with \SLC structure group. The description is geometric and foliates in a causal and physically transparent manner. The general observables of this model are…
Noncommutative spacetimes are widely believed to model some properties of the quantum structure of spacetime at the Planck regime. In this contribution the construction of (anti-)de Sitter noncommutative spacetimes obtained through quantum…
We discuss a Lorentz covariant space-time uncertainty relation, which agrees with that of Karolyhazy-Ng-van Dam when an observational time period delta t is larger than the Planck time lp. At delta t < lp, this uncertainty relation takes…
We introduce a non-commutative product for curved spacetimes, that can be regarded as a generalization of the Rieffel (or Moyal-Weyl) product. This product employs the exponential map and a Poisson tensor, and the deformed product maintains…
We study the isometry groups of (non-compact) Lorentzian manifolds with well-behaved causal structure, aka causal spacetimes satisfying the ``no observer horizons'' condition. Our main result is that the group of time orientation-preserving…
By applying the lightlike Eisenhart lift to several known examples of low-dimensional integrable systems admitting integrals of motion of higher-order in momenta, we obtain four- and higher-dimensional Lorentzian spacetimes with irreducible…
There is a by now well-established isomorphism between stationary 4-dimensional spacetimes and 3-dimensional purely spatial Randers geometries - these Randers geometries being a particular case of the more general class of 3-dimensional…
Complex and real, vacuum spaces with both self-dual and anti-self-dual parts of the Weyl tensor being of the type [N] are considered. Such spaces are classified according to two criteria. The first one takes into account the properties of…
We develop solution-generating techniques for stationary metrics with one angular momentum and axial symmetry, in the presence of a cosmological constant and in arbitrary spacetime dimension. In parallel we study the related lower…
A multidimensional cosmological model with space-time consisting of n (n>1) Einstein spaces M_i is investigated in the presence of a cosmological constant Lambda and a homogeneous minimally coupled free scalar field. Generalized de Sitter…
We construct Lewis-Riesenfeld invariants from two dimensional point transformations for two oscillators that are coupled to each other in space in a PT-symmetrical and time-dependent fashion. The non-Hermitian Hamiltonian of the model is…
We study the stability under linear perturbations of a class of static solutions of Einstein-Gauss-Bonnet gravity in $D=n+2$ dimensions with spatial slices of the form $\Sigma_{\k}^n \times {\mathbb R}^+$, $\Sigma_{\k}^n$ an $n-$manifold of…
It is shown that in the noncommutative spacetime defined by the generalized Moyal product, consistent noncommutativity can be obtained independent of the coordinate system such as Cartesian or polar one. In addition, based on the fact that…
All classes of spatially homogeneous space-time models in the generalized scalar-tensor theory of gravity are found that allow the integration of the equations of motion of test particles and the eikonal equation by the method of %complete…