Related papers: Jet Geometrical Objects Depending on a Relativisti…
We prove a number of results on the interrelation between the $L^p$-metric on the group of Hamiltonian diffeomorphisms of surfaces and the subset of all autonomous Hamiltonian diffeomorphisms. More precisely, we show that there are…
Relativistic jets of active galactic nuclei have been known to exist for 100 years. Blazars with their jet pointing close to our line of sight are some of the most variable and extreme objects in the universe, showing emission from radio to…
We consider plane symmetric gravitational fields within the framework of General Relativity in (D+1)-dimensional spacetime. Two classes of vacuum solutions correspond to higher-dimensional generalizations of the Rindler and Taub spacetimes.…
A reference frame consists of: a reference space, a time scale and a spatial metric. The geometric structure induced by these objects in spacetime is developed. The existence of a class of spatial metrics that are rigid, have free mobility…
We propose analogues of horizontal and vertical projections for model filiform jet space Carnot groups. Every pair consisting of the jet of a smooth function on $\mathbb{R}$ and a vertical hyperplane with first coordinate fixed provides a…
The Hamiltonian formulation for the mechanical systems with reparametrization-invariant Lagrangians, depending on the worldline external curvatures is given, which is based on the use of moving frame. A complete sets of constraints are…
High velocity highly collimated beams of plasma -- the jets -- are known as a general phenomenon among astrophysical sources of different energy and spatial scale. The common MHD scenario of astrophysical jet formation allows to describe…
In this paper we present a unified Lagrangian--Hamiltonian geometric formalism to describe time-dependent contact mechanical systems, based on the one first introduced by K. Kamimura and later formalized by R. Skinner and R. Rusk. This…
We investigate matter collineations of plane symmetric spacetimes when the energy-momentum tensor is degenerate. There exists three interesting cases where the group of matter collineations is finite-dimensional. The matter collineations in…
Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a…
Let $\mathbf{g}$ be a pseudo--Riemanian metric of arbitrary signature on a manifold $\mathbf{V}$ with conventional $n+n$ dimensional splitting, $\ n\geq 2,$ determined by a nonholonomic (non--integrable) distribution $\mathcal{N}$ defining…
In the jet bundle description of Field Theories (multisymplectic models, in particular), there are several choices for the multimomentum bundle where the covariant Hamiltonian formalism takes place. As a consequence, several proposals for…
We study the evolution of one-dimensional relativistic jets, using the exact solution of the Riemann problem for relativistic flows. For this purpose, we solve equations for the ideal special relativistic fluid composed of dissimilar…
In this study we investigate jet interaction at a microscopic level in a cosmological environment, which responds to a key open question in the study of relativistic jets. Using small simulation systems during prior research, we initially…
The generalization of Cohen and Glashow's Very Special Relativity to curved space-times is considered. Gauging the SIM(2) symmetry does not, in general, provide the coupling to the gravitational background. However, locally SIM(2) invariant…
We classify invariant Lagrangians of the form $L(g_{ij},g_{ij,k},g_{ij,kl},D_I,D_{I,j})$ depending at most quadratically on the variables $g_{ij,k},g_{ij,kl}$ and $D_I,D_{I,j}$, where $g$ is a Lorentz metric and $D$ is a tensor field of…
Context. Relativistic jets are ubiquitous in astrophysics. High Mass Microquasars (HMMQs) are useful labs to study such jets, as they are relatively close and evolve over observable time scales. The ambient medium into which the jet…
The structure of a relativistically hot, strongly magnetized jet is investigated at large distances from the source. Asymptotic equations are derived describing collimation and acceleration of the externally confined jet. Conditions are…
Relativistic elasticity on an arbitrary spacetime is formulated as a Lagrangian field theory which is covariant under spacetime diffeomorphisms. This theory is the relativistic version of classical elasticity in the hyperelastic, materially…
We describe fully relativistic three dimensional calculations of the slowing down and spreading of a relativistic jet by an external medium like the ISM. We calculate the synchrotron spectra and light curves using the conditions determined…