Related papers: Symplectic evolution of an observed light bundle
We review the role that infinite-dimensional symmetries arising at the boundary of asymptotically flat spacetimes play in the context of the celestial holography program. Once recast into the language of conformal field theory, asymptotic…
We derive angle differences between two null geodesics, propagating from light sources to an observer, on the de Sitter spacetime with multi-lensing objects. Assuming the lensing objects are mass monopoles on the de Sitter background, we…
The purpose of this paper is to study the evolution of moving interacting particles on the mesoscopic scale. We will introduce an uncertainty principle and a new priori bound for the evolution of particles subject to a general mesoscopic…
An analytical solution for time evolution of the gravitational wave damping in the early Universe due to freely streaming neutrinos is found in the late time regime. The solution is represented by a convergent series of spherical Bessel…
Classical constrained Hamiltonian theory assumes complete observability of system states, but in reality only partial state information is often available. This paper establishes a complete geometric theoretical framework for handling such…
We investigate Snyder space-time and its generalizations, including Yang and Snyder-de-Sitter spaces, which constitute manifestly Lorenz invariant noncommutative geometries. This work initiates a systematic study of gauge theory on such…
Studies of the distribution and evolution of galaxies are of fundamental importance to modern cosmology; these studies, however, are hampered by the complexity of the competing effects of spectral and density evolution. Constructing a…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
This paper presents a "historical" formalism for dynamical systems, in its Hamiltonian version (Lagrangian version was presented in a previous paper). It is universal, in the sense that it applies equally well to time dynamics and to field…
We define a relativistic version of the global symmetries responsible for the restricted mobility of fracton quasiparticles. The theories have a symmetry current that is proportional to a vector field that spontaneously breaks Lorentz boost…
Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…
We give an elementary construction of symplectic connections through reduction. This provides an elegant description of a class of symmetric spaces and gives examples of symplectic connections with Ricci type curvature, which are not…
Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary…
Gravitational lensing, a compelling physical phenomenon, offers a unique avenue to investigate the morphology and physical properties of distant and faint celestial objects. This paper seeks to provide a comprehensive overview of the…
We study strong gravitational lensing in a static, spherically symmetric, naked singularity spacetime, without a photon sphere. The nature of the singularity is found to be lightlike. We discuss the characteristic lensing features of this…
A rigorous demonstration that given appropriate data on our past light cone leads to the determination of the metric functions and all their time derivatives on our past light cone is presented, thus showing how to evolve the solution we…
Given a null geodesic $\gamma_0(\lambda)$ with a point $r$ in $(p,q)$ conjugate to $p$ along $\gamma_0(\lambda)$, there will be a variation of $\gamma_0(\lambda)$ which will give a time-like curve from $p$ to $q$. This is a well-known…
Time-space noncommutativity leads to quantisation of time and energy nonconservation when time is conjugate to a compact spatial direction like a circle. In this context energy is conserved only modulo some fixed unit. Such a possibility…
We have recently derived a manifestly covariant evolution law, under the geometrical optics approximation of the vacuum Maxwell's equations, for the electric field along null geodesics in a general spacetime, relative to an arbitrary set of…
Symplectic integrators are widely used for long-term integration of conservative astrophysical problems due to their ability to preserve the constants of motion; however, they cannot in general be applied in the presence of nonconservative…