Related papers: Goedel-type Universes and the Landau Problem
We show that the Goedel solution of five-dimensional gauged supergravity contains either closed time-like curves through every space-time point or none at all, dependent on the rotational parameter. In addition, we present a deformation of…
We study a rotating and expanding, Godel type metric, originally considered by Korotkii and Obukhov, showing that, in the limit of large times and nearby distances, it reduces to the open metric of Friedmann. In the epochs when radiation or…
In this paper we established the global well-posedness theorem for a special type of wave-Klein-Gordon system that have the strong coupling terms in divergence form on the right hand side of its wave equation. We cope with the problem by…
Relativistic Coulomb systems are studied in velocity space, prompted by the fact that the study of Newtonian Kepler/Coulomb systems in velocity space provides a method much simpler (and more elegant) than the familiar analytic solutions in…
We present a solution for the geodesic motion in G\"odel's universe that provides a particular proof of Hawking's chronology protection conjecture in three-dimensional gravity theory. The solution is based upon the fact that the group of…
We examine the dynamical behavior of matter coupled to gravity in the context of a linear Klein-Gordon equation coupled to a Friedman-Robertson-Walker metric. The resulting ordinary differential equations can be decoupled, the effect of…
We consider Randall-Sundrum model with localized gravity, replacing the extra compact space-like dimension by a time-like one. In this way the solution to the hierarchy problem can be reconciled with a correct cosmological expansion of the…
Defining gravitational subsystems has long been challenging due to the lack of the conventional notion of locality in gravity. In this work, we define gravitational subsystems from the observable spacetime subregions of a set of…
Let $\rho_1$ and $\rho_2$ be a pair of residual, odd, absolutely irreducible two-dimensional Galois representations of a totally real number field $F$. In this article we propose a conjecture asserting existence of "safe" chains of…
The paper presents a generalization and further development of our recent publications where solutions of the Klein-Fock-Gordon equation defined on a few particular $D=(2+1)$-dim static space-time manifolds were considered. The latter…
This is the continuation of an earlier work where Godel-type metrics were defined and used for producing new solutions in various dimensions. Here a simplifying technical assumption is relaxed which, among other things, basically amounts to…
A ladder algebraic structure for $L^2(\mathbb{R}^+)$ which closes the Lie algebra $h(1)\oplus h(1)$, where $h(1)$ is the Heisenberg-Weyl algebra, is presented in terms of a basis of associated Laguerre polynomials. Using the Schwinger…
In this article we will prove the global existence of a type of wave-Klein-Gordon system in $2+1$ spacetime dimension. Some technical tools such as conformal energy estimate on hyperboloid, normal form transform on Klein-Gordon equations…
In this paper we study the global existence and completeness of classical solutions of gravity coupled a scalar field system called Einstein-Klein-Gordon system in higher dimensions. We introduce a new ansatz function to reduce the problem…
The spatial Kepler problem with a perturbation satisfying the rotational symmetry w.r.t. the $z$-axis and the reflection symmetry w.r.t. the $(x, y)$-plane, can be reduced to an Hamiltonian system with 2 degrees of freedom after fixing the…
We consider a Weyl-Lorentz-$U(1)$-invariant gravity model written in terms of a scalar field, electromagnetic field and nonmetricity without torsion and curvature, the so-called symmetric teleparallel geometry, in three dimensions. Firstly,…
We consider the general scalar field Horndeski Lagrangian coupled to matter. Within this class of models, we present two results that are independent of the particular form of the model. First, we show that in a Friedmann-Robertson-Walker…
One parameter family of exact solutions in General Relativity with a scalar field has been found using the Liouville metric. The scalar field potential has exponential form. This model is interesting, because, in particular, the solution…
We consider an Abelian Gauge Theory in R4 equipped with the Minkowski metric. This theory leads to a system of equations, the Klein-Gordon- Maxwell equations, which provide models for the interaction between the electromagnetic field and…
It is well known that the incompressible Euler equations can be formulated in a very geometric language. The geometric structures provide very valuable insights into the properties of the solutions. Analogies with the finite-dimensional…