Related papers: G_2 cosmological models separable in non-comoving …
Axisymmetric spacetimes with a conformal symmetry are studied and it is shown that, if there is no further conformal symmetry, the axial Killing vector and the conformal Killing vector must commute. As a direct consequence, in conformally…
A known general class of superintegrable systems on 2D spaces of constant curvature can be defined by potentials separating in (geodesic) polar coordinates. The radial parts of these potentials correspond either to an isotropic harmonic…
We study a quantum model with non-isotropic two-dimensional oscillator potential but with additional quadratic interaction $x_1x_2$ with imaginary coupling constant. It is shown, that for a specific connection between coupling constant and…
We study dynamics of scalar fields on a large class of geometries described by integrable sigma models. Although equations of motion are not separable due to absence of isometries and Killing tensors, we completely determine the spectra…
In this paper, conformal motions are studied in plane symmetric static spacetimes. The general solution of conformal Killing equations and the general form of the conformal Killing vector for these spacetimes are presented. All…
A criterion given by Castejon-Amenedo and MacCallum (1990) for the existence of (locally) hypersurface-orthogonal generators of an orthogonally-transitive two-parameter Abelian group of motions (a $G_2I$) in spacetime is re-expressed as a…
The collapsing dynamics of relativistic fluid are explored in $f(R)$ gravity in a detailed systematic manner for the non-static spherically symmetric spacetime satisfying the equation of the conformal Killing vector. With quasi-homologous…
In this note, we study the integrability of geodesic flow in the background of a very general class of spacetimes with NUT-charge(s) in higher dimensions. This broad set encompasses multiply NUT-charged solutions, electrically and…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
We consider anisotropic cosmological models with an universe of dimension 4 or more, factorized into n>1 Ricci-flat spaces, containing an m-component perfect fluid of m non-interacting homogeneous minimally coupled scalar fields under…
The perfect fluid solutions admitting a group G$_3$ of isometries acting on orbits S$_2$ whose curvature has a gradient which is tangent to the fluid flow (T-models) are studied from a thermodynamic approach. All the admissible…
In the present paper we have discussed the mechanics of incompressible test bodies moving in Riemannian spaces with non-trivial curvature tensors. For Hamilton's equations of motion the solutions have been obtained in the parametrical form…
We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine complete sets of integrals, polynomial in the momenta, for…
In this article we find the general, exact solution for the gravitational field equations for diagonal, vacuum, separable metrics. These are metrics each of whose terms can be separated into functions of each space-time variable separately.…
A system of relativistic Snyder particles with mutual two-body interaction that lives in a Non-Commutative Snyder geometry is studied. The underlying novel symplectic structure is a coupled and extended version of (single particle) Snyder…
We consider a (pseudo)Riemannian manifold of arbitrary dimension. The Hamilton-Jacobi equation for geodesic Hamiltonian admits complete separation of variables for some (separable) metrics in some (separable) coordinate systems. Separable…
The Poisson brackets for non-linear sigma models on G/H are set up on the light-like plane. A quantity which transforms irreducibly by the Killing vectors, called Killing scalar, is constructed in an arbitrary representation of G. It is…
In this article we study the relation between flat solvmanifolds and $G_2$-geometry. First, we give a classification of 7-dimensional flat splittable solvmanifolds using the classification of finite subgroups of $\mathsf{GL}(n,\mathbb{Z})$…
We study some symmetry and integrability properties of four-dimensional Einstein-Maxwell gravity with nonvanishing cosmological constant in the presence of Killing vectors. First of all, we consider stationary spacetimes, which lead, after…
We discuss a new class of coordinate systems for a plane, which provide an analytical representation of arbitrary straightline, and then define the form of potential on the plane, under which the equations of motion of a mass point are…