Related papers: Jet Geometrical Objects Depending on a Relativisti…
The jet formalism for Classical Field theories is extended to the setting of Lie algebroids. We define the analog of the concept of jet of a section of a bundle and we study some of the geometric structures of the jet manifold. When a…
The measurement of the arrival time of a particle, such as a lepton, a photon, or a pion, reaching the detector provides valuable information. A similar measurement for a hadronic final state, however, is much more challenging as one has to…
When a Hamiltonian system is subject to constraints which depend explicitly on time, difficulties can arise in attempting to reduce the system to its physical phase space. Specifically, it is non-trivial to restrict the system in such a way…
Relativistic jets are ubiquitous in astrophysical systems that contain compact objects. They transport large amounts of energy to large distances from the source, and their interaction with the ambient medium has a crucial effect on the…
We extend the results of our previous work on the conformal invariant description of two relativistic point particles. We consider here the most general lagrangian by using a conformal tensor $h_{\mu\nu}$, transforming as a Wilson line, and…
The recent improvement in VLBI arrays is providing information of the emission and magnetic field structure of relativistic jets, both extragalactic and galactic (microquasars), with unprecedented spatial and temporal resolution. These…
The formalism of spacetime dependent lagrangians developed in Ref.1 is applied to the Sine Gordon and massive Thirring models.It is shown that the well-known equivalence of these models (in the context of weak-strong duality) can be…
We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific…
Outstanding questions in the study of relativistic jets in their various astrophysical settings are discussed in the context of a general dynamical model.
A magnetohydrodynamic model is constructed for a cylindrical jet immersed in an external uniform magnetic field. It is shown that, as in the force-free case, the total electric current within the jet can be zero. The particle energetics and…
In this paper, we overlay a continuum of analytical relations which essentially serve to compute the arc-length described by a celestial body in an elliptic orbit within a stipulated time interval. The formalism is based upon a…
Lagrangian Descriptors (LDs) are scalar quantities able to reveal separatrices, manifolds of hyperbolic saddles, and chaotic seas of dynamical systems. A popular version of the LDs consists in computing the arc-length of trajectories over a…
We reinterpret special relativity, or more precisely its de Sitter deformation, in terms of 3d conformal geometry, as opposed to (3+1)d spacetime geometry. An inertial observer, usually described by a geodesic in spacetime, becomes instead…
We consider the space of geodesic laminations on a surface, endowed with the Hausdorff metric d_H and with a variation of this metric called the d_log metric. We compute and/or estimate the Hausdorff dimensions of these two metrics. We also…
We describe the dynamics of a relativistic extended object in terms of the geometry of a configuration of constant time. This involves an adaptation of the ADM formulation of canonical general relativity. We apply the formalism to the…
In this paper, we deal with a generalization of the geometry of parallelizable manifolds, or the absolute parallelism (AP-) geometry, in the context of generalized Lagrange spaces. All geometric objects defined in this geometry are not only…
A dynamical system on the total space of the fibre bundle of second order accelerations, $T^2M$, is defined as a third order vector field $S$ on $T^2M$, called semispray, which is mapped by the second order tangent structure into one of the…
We classify simply-connected homogeneous ($D+1$)-dimensional spacetimes for kinematical and aristotelian Lie groups with $D$-dimensional space isotropy for all $D\geq 0$. Besides well-known spacetimes like Minkowski and (anti) de Sitter we…
A solution for the Weinstein's Problem in the general framework of generalized Lie algebroids is the target of this paper. We present the mechanical systems called by use, mechanical (?; ?)-systems, Lagrange mechanical (?; ?)-systems or…
Evidence has been mounting that many of the transverse jet B fields observed in BL Lac objects on parsec scales represent the dominant vvroidal compoent of the intrinsic jet B fields. Such fields could come about, for example, as a result…