A relativistic particle is a particle moving with a speed close to the speed of light, such that effects of special relativity are important for the description of its behavior.

Massless particles (e.g., photons) are always moving at the speed of light, therefore they are always relativistic.

Massive particles are relativistic when their kinetic energy is comparable or greater than the energy $mc^2$ corresponding to their rest mass. (This condition implies that their speed is close to the speed of light.) Such relativistic particles are generated in particle accelerators, and are naturally occurring in cosmic radiation. In astrophysics, jets of relativistic plasma are produced by the centers of active galaxies and quasars.

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JMP: General Relativity and Gravitation

An extension theorem for conformal gauge singularities
Christian Lubbe and Paul Tod We analyze conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theor ... [J. Math. Phys. 50, 112501 (2009)] published Tue Nov 3, 2009.
A conformal extension theorem based on null conformal geodesics
Christian Lubbe In this article we describe the formulation of null geodesics as null conformal geodesics and their description in the tractor formalism. A conformal extension theorem through an isotropic singularity is proven by requiring the boundedness of the tractor curvature and its derivatives to sufficient o ... [J. Math. Phys. 50, 112502 (2009)] published Tue Nov 3, 2009.
Determination of elementary first integrals of a generalized Raychaudhuri equation by the Darboux integrability method
A. Ghose Choudhury, Partha Guha, and Barun Khanra The Darboux integrability method is particularly useful to determine first integrals of nonplanar autonomous systems of ordinary differential equations, whose associated vector fields are polynomials. In particular, we obtain first integrals for a variant of the generalized Raychaudhuri equation, wh ... [J. Math. Phys. 50, 102502 (2009)] published Fri Oct 23, 2009.
Weyl's Lagrangian in teleparallel form
James Burnett and Dmitri Vassiliev The Weyl Lagrangian is the massless Dirac Lagrangian. The dynamical variable in the Weyl Lagrangian is a spinor field. We provide a mathematically equivalent representation in terms of a different dynamical variable the coframe (an orthonormal tetrad of covector fields). We show that when written i ... [J. Math. Phys. 50, 102501 (2009)] published Tue Oct 20, 2009.
Geometry of universal magnification invariants
M. C. Werner Recent work in gravitational lensing and catastrophe theory has shown that the sum of the signed magnifications of images near folds, cusps, and also higher catastrophes is zero. Here, it is discussed how Lefschetz fixed point theory can be used to interpret this result geometrically for a subfamily ... [J. Math. Phys. 50, 082504 (2009)] published Wed Aug 26, 2009.
A complete cosmological solution to the averaged Einstein field equations as found in macroscopic gravity
R. J. van den Hoogen A formalism for analyzing the complete set of field equations describing macroscopic gravity is presented. Using this formalism, a cosmological solution to the macroscopic gravity equations is determined. It is found that if a particular segment of the connection correlation tensor is zero and if th ... [J. Math. Phys. 50, 082503 (2009)] published Tue Aug 25, 2009.

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