Related papers: Symplectic evolution of an observed light bundle
A symplectic fibration is a fibre bundle in the symplectic category. We find the relation between deformation quantization of the base and the fibre, and the total space. We use the weak coupling form of Guillemin, Lerman, Sternberg and…
We study the bending of light for static spherically symmetric (SSS) space-times which include a dark energy contribution. Geometric dark energy models generically predict a correction to the Einstein angle written in terms of the distance…
In gamma-ray binaries neutron star is orbiting a companion that produces a strong stellar wind. We demonstrate that observed properties of "stellar wind"-"pulsar wind" interaction depend both on the overall wind thrust ratio, as well as…
We investigate the behavior of null geodesics near future null infinity in asymptotically flat spacetimes. In particular, we focus on the asymptotic behavior of null geodesics that correspond to worldlines of photons initially emitted in…
In these notes we discuss Lorentz-Finsler metrics, a notion originated in relativity theory, on certain groups of symplectic and contact transformations. Some basic geometric questions arising in this context concerning distance, geodesics…
In this paper, we introduce a new kind of Siegel upper half space and consider the symplectic geometry on it explicitly under the action of the group of all holomorphic transformations of it. The results and methods will form a basis for…
We present results from a numerical code implementing a new method to solve the master equations describing the evolution of linear perturbations in a spherically symmetric but inhomogeneous background. This method can be used to simulate…
We show that the space of anti-symplectic involutions of a monotone $S^2\times S^2$ whose fixed points set is a Lagrangian sphere is connected. This follows from a stronger result, namely that any two anti-symplectic involutions in that…
We construct a symplectic realisation of the twisted Poisson structure on the phase space of an electric charge in the background of an arbitrary smooth magnetic monopole density in three dimensions. We use the extended phase space…
In symplectic topology one uses elliptic methods to prove rigidity results about symplectic manifolds and solutions of Hamiltonian equations on them, where the most basic example is given by geodesics on Riemannian manifolds. Harmonic maps…
A strictly empirical review is given of presently available data on the evolution of galaxy morphology. From HST observations of distant galaxies and ground-based observations of nearby ones observed at the same rest-frame wavelength it is…
In this paper, we consider a time dependent module field on spacetime extension without modifying commutative relation on noncommutative quantum plane. The significant idea is that $Lorentz$ symmetry is conserved in module and unmodule…
In the contact-geometric approach to general relativity, the sky of an event - namely, the set of all incoming light rays - forms a Legendrian submanifold of the spherical cotangent bundle of a Cauchy hypersurface. When the hypersurface is…
We consider circle bundles over compact three-manifolds with symplectic total spaces. We show that the base of such a space must be irreducible or the product of the two-sphere with the circle. We then deduce that such a bundle admits a…
Advances in our understanding of the origin, evolution and structure of the universe have long been driven by cosmological perturbation theory, model building and effective field theory. In this review, we introduce numerical relativity as…
Combination of topology and general relativity can lead to some profound and farsighted predictions. It is well known that symmetry breaking of the Higgs vacuum field in the early universe possibly induced topological defects in spacetime,…
In this paper we construct a discrete simulation of an expanding homogeneous and isotropic space-time that expands via expansion of its basic elements to figure out properties and characteristics of such a space-time and derive conclusions.…
Given the extreme accuracy reached by future global space astrometry, one needs a global relativistic modeling of observations. A relativistic definition of astrometric observables is then essential to find uniquely coordinates, parallax…
The established way of looking at special relativity is based on Einstein postulates: the principle of relativity and the constancy of the velocity of light. In the most general geometric approach to the theory of special relativity, the…
We use the dynamics of a galaxy, set up initially at a constant proper distance from an observer, to derive and illustrate two counter-intuitive general relativistic results. Although the galaxy does gradually join the expansion of the…