Dissipative properties of relativistic two-dimensional gases

Abstract

The constitutive equations for the heat flux and the Navier tensor are established for a high temperature dilute gas in two spatial dimensions. The Chapman-Enskog procedure to first order in the gradients is applied in order to obtain the dissipative energy and momentum fluxes from the relativistic Boltzmann equation. The solution for such equation is written in terms of three sets of orthogonal polynomials which are explicitly obtained for this calculation. As in the three dimensional scenario, the heat flux is shown to be driven by the density, or pressure, gradient additionally to the usual temperature gradient given by Fourier's law. For the stress (Navier) tensor one finds, also in accordance with the three dimensional case, a non-vanishing bulk viscosity for the ideal monoatomic relativistic two-dimensional gas. All transport coefficients are calculated analytically for the case of a hard disk gas and the non-relativistic limit for the constitutive equations is verified.

Bulk viscosity in 2D relativistic uids: the effects of temperature and modifications to the Rayleigh-Brillouin spectrum

“…In this section, a formal proof of the non-relativistic and ultrarelativistic limits of the expression for µ obtained in Ref. [3] and quoted in the previous section is detailed. As mentioned above, inspection of Fig.…”

“…The complete calculation will be published elsewhere (a preprint can be found in Ref. [3]) together with the calculation of the rest of the relevant coefficients, to which the reader is refered to for further details. The starting point is the relativistic Boltzmann equation [2] in a flat spacetime with a (+ − −) metric which reads…”

“…The details of the calculation that follows can be found in Ref. [3]. However the authors consider it worthwhile to point out here the particular step to which the occurrence of a finite bulk viscosity in the relativistic regime, opposed to the zero value obtained for non-relativistic gases, can be traced down to.…”

“…Indeed, in a separate publication (see Ref. [3]) the constitutive equations are established and the transport coefficients expressed in terms of collision integrals which, for a hard disks model, can be numerically evaluated. In particular, the bulk viscosity is expressed in terms of the integral…”

“…In sections 2 and 3 we briefly outline the procedure carried out in Ref. [3] in order to establish the analytical expression for the bulk viscosity in the specific case of a hard disks model. Section 4 is devoted to the analysis of the integral defined in Eq.…”