Related papers: Two-dimensional Einstein numbers and associativity
In this paper we give an attempt to extend some arithmetic properties such as multiplicativity, convolution products to the setting of operators theory. We provide a significant examples which are of interest in number theory. We also give…
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 investigate a class of cosmological solutions of Einstein's field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject…
An intriguingly natural generalization, using complex octonions, of general relativity is pointed out. The starting point is the vierbein-based double dual formulation of the Einstein-Hilbert action. In terms of two natural structures on…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
For states in infinite dimensional Hilbert spaces entanglement quantities like the entanglement of distillation can become infinite. This leads naturally to the question, whether one system in such an infinitely entangled state can serve as…
Using the characterizations in terms of various differential operators including partial, normal, and tangential derivatives, we extend the family of Bergman spaces of $\mathcal H$-harmonic functions on the real hyperbolic ball from…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
We present a systematic approach to embed $n$-dimensional vacuum general relativity in an $(n + 1)$-dimensional pseudo-Riemannian spacetime whose source is either a (non)zero cosmological constant or a scalar field minimally-coupled to…
We introduce a new generalization of Stirling numbers of the second kind and analyze their properties, including generating functions, integral representations, and recurrence relations. These numbers are used to approximate Riemann zeta…
Connection, torsion and curvature are introduced for general (local) Leibniz algebroids. Generalized Bismut connection on $TM \oplus \Lambda^{p} T^{\ast}M$ is an example leading to a scalar curvature of the form $R + H^2$ for a closed…
We show how the Einstein equations with cosmological constant (and/or various types of matter field sources) can be integrated in a very general form following the anholonomic deformation method for constructing exact solutions in four and…
For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…
A multidimensional gravitational model with several scalar fields, fields of forms and cosmological constant is considered. When scalar fields are constant and composite p-brane monopole-like ansatz for the fields of forms is adopted, a…
Well-posedness of the initial (boundary) value problem is an essential property, both of meaningful physical models and of numerical applications. To prove well-posedness of wave-type equations their level of hyperbolicity is an essential…
Modified gravity provides a possible explanation for the currently observed cosmic accelaration. In this paper, we study general classes of modified gravity models. The Einstein-Hilbert action is modified by using general functions of the…
We collect evidence that the notion of path-ordered non-abelian integration admits an extension to two dimensions. We propose the corresponding notion of non-abelian 2-form along the lines of Lie algebroid theory and argue it is an…
We generalize the concept of a field by allowing addition to be a partial operation. We show that elements of such a "partially additive field" share many similarities with physical quantities. In particular, they form subsets of mutually…
The paper proposes a 4-dimensional generalization of the Hamilton equations of motion to the case of the Minkowski space-time. The approach can be applied to quantum as well as to classical, non-relativistic as well as relativistic…
For (2+2)-dimensional nonholonomic distributions, the physical information contained into a spacetime (pseudo) Riemannian metric can be encoded equivalently into new types of geometric structures and linear connections constructed as…