Related papers: On the algebraic classification of spacetimes

Using the Gitman-Lyakhovich-Tyutin generalization of the Ostrogradsky method for analyzing singular systems, we consider the Hamiltonian formulation of metric and tetrad gravities in two-dimensional Riemannian spacetime treating them as…

Surprisingly, the issue of events localization in spacetime is poorly understood and a fortiori realized even in the context of Einstein's relativity. Accordingly, a comparison between observational data and theoretical expectations might…

We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.

First, we review the basic mathematical structures and results concerning the gauge orbit space stratification. This includes general properties of the gauge group action, fibre bundle structures induced by this action, basic properties of…

The paper reviews the most illustrative cases of the "peculiar/anomalous" experiences of time (and, to a lesser extent, also space) and discusses a simple algebraic geometrical model accounting for the most pronounced of them.

We determine a four-function generalization of the Plebanski spacetime, depending on three arbitrary functions of the radial coordinate, and one function on the angular coordinate. For the generalized Plebanski spacetime, we analyze the…

We provide a classification, up to isomorphism, of four-dimensional ternary Leibniz algebras over an algebraically closed field of characteristic zero. For each non-abelian algebra in the classification, we explicitly determine its centroid…

Certain difficulties of quantum gravity can be avoided if we embed the spacetime $V_4$ into a higher dimensional space $V_N$; then our spacetime is merely a 4-surface in $V_N$.What remains is conceptually not so difficult: just to quantise…

We generalize Rado's extension theorem to complex spaces.

We introduce many new generalizations of Poisson algebras which can be constructed inside the associative algebra of linear transformations over a vector space.

We extend Dirac's approach about the quantization of the electric charge to the case of gravitational configurations. The spacetime curvature is used to define a phase-like object which allows us to extract information about the behavior of…

A general theory of topological classification of defects is introduced. We illustrate the application of tools from algebraic topology, including homotopy and cohomology groups, to classify defects including several explicit calculations…

We prove embeddings of Sobolev and Hardy-Sobolev spaces into Besov spaces built upon certain mixed norms. This gives an improvment of the known embeddings into usual Besov spaces. Applying these results, we obtain Oberlin type estimates of…

The Einstein Equation on 4-dimensional Lorentzian manifolds admitting recurrent null vector fields is discussed. Several examples of a special form are constructed. The holonomy algebras, Petrov types and the Lie algebras of Killing vector…

This is the first in a series of two papers concerned with relative birational geometry of algebraic spaces. In this paper, we study Pr\"ufer spaces and Pr\"ufer pairs of algebraic spaces that generalize spectra of Pr\"ufer rings. As a…

Starting from any unital colored PROP $P$, we define a category $P(P)$ of shapes called $P$-propertopes. Presheaves on $P(P)$ are called $P$-propertopic sets. For $0 \leq n \leq \infty$ we define and study $n$-time categorified $P$-algebras…

I review the holographic theory of space-time and its applications to cosmology. Much of this has appeared before, but the discussion is more unified and concise. I also include some material on work in progress, whose aim is to understand…

We consider the problem of calculating the Gaussian curvature of a conical 2-dimensional space by using concepts and techniques of distribution theory. We apply the results obtained to calculate the Riemannian curvature of the 4-dimensional…

Let $A$ be a simple algebra over a field $F$. Under a mild cardinality assumption on $F$, we determine the greatest possible dimension for an $F$-affine subspace of $A$ that is included in the group of units $A^\times$, and we describe the…

The general line element corresponding to the family of algebraically general, gravito-electric, expanding, rotating dust models with one functionally independent zero-order Riemann invariant is constructed. The isometry group is at most…