Chapter 6 - The Solution of Some Physical Problems on the Basis of the Nonlocal Relativistic Equations Without Taking Into Account the External Forces

Abstract

In this chapter, we consider three “classical” problems of relativistic kinetic theory. Investigation of these problems does not lead to taking into account the external forces. Namely:1.The propagation of plane harmonic waves in a relativistic environment. This task is in some sense a test for the previously obtained generalized nonlocal relativistic hydrodynamic equations.2.The propagation of shock waves in a gaseous environment is a classical problem in hydrodynamics, which allows checking the validity of different kinetic theories. A generalized nonlocal kinetic equation for relativistic environment was derived in the previous sections. On the basis of the generalized relativistic equation, an appropriate system of nonlocal hydrodynamic equations was obtained. In this section on the basis of the system of nonlocal equations, we consider the propagation of shock waves in a relativistic environment.3.One of the possible methods of the investigation of the nuclear matter properties consists in accelerating ions to relativistic collision velocities. Modern accelerators like RHIC (Relativistic Heavy Ion Collider) can accelerate ions to very high velocities and, correspondingly, energies. In the ultra-relativistic heavy ion collisions at RHIC, the total number of the produced particles exceeds several thousands; therefore one can expect that the produced system behaves as a relativistic hydrodynamic system. Strictly speaking, the hydrodynamic models are well justified during the intermediate stages of the reaction: from the time when local equilibrium is reached until the freeze out when the hydrodynamic description breaks down. This so-called freeze stage (freeze out, FO) the matter becomes so dilute and cold that particles stop interacting and stream towards the detectors freely, their momentum distribution freezes out. Then we have the typical situation known from the local Boltzmann physical kinetics—the problem of “through” description of physical system from the hydrodynamic regime to the collisionless expansion of rarefied gas. This “through” description cannot be realized in the frame of local models in principle. Taking into account the previous positive experience of application of the generalized nonlocal hydrodynamics (including asymptotic for the rarefied gas, here FO stage), it is reasonable to investigate the possibilities of nonlocal kinetic description.