Relativistic Rotating Boltzmann Gas Using the Tetrad Formalism

Abstract

We consider an application of the tetrad formalism introduced by Cardall et al. [Phys. Rev. D 88 (2013) 023011] to the problem of a rigidly rotating relativistic gas in thermal equilibrium and discuss the possible applications of this formalism to relativistic lattice Boltzmann simulations. We present in detail the transformation to the comoving frame, the choice of tetrad, as well as the explicit calculation and analysis of the components of the equilibrium particle flow four-vector and of the equilibrium stress-energy tensor.

Thermal expectation values of fermions on anti-de Sitter space-time

“…The kinetic theory formulation gives the macroscopic SET Tαρ as the second order moment of the distribution function f : 5) where the integration measure d 3 p/p0 is Lorentz-invariant. The SET corresponding to the distribution (7.2) can be found by first performing a series expansion of the equilibrium distribution function (7.2) in powers of ǫ [18,19,20]:…”

“…The energy density and pressure arising from the Maxwell-Jüttner distribution function (7.7) can be found in closed form [18,19,29]:…”

“…Using Maxwell-Jüttner statistics (the results can be extended to Bose-Einstein and Fermi-Dirac statistics following [19,20]), it is found that the energy density and pressure depend only on the local temperature of the gas. For a massless, conformally coupled scalar field, this property is not shared by the quantum t.e.v.s [8].…”

Analysis of scalar and fermion quantum field theory on anti-de Sitter spacetime

“…For comparison with our later work on adS, it is instructive to compare the above QFT results on Minkowski space-time with the classical energy density and pressure for a thermal gas of particles, computed in the framework of RKT. For particles with mass m, momentum pα, at inverse temperature β, the Bose-Einstein and Fermi-Dirac thermal distribution functions are, respectively [12][13][14]…”

“…Remarkably, on Minkowski space-time, for both scalars and fermions the classical thermal SET is identical to the quantum t.e.v. (2.8) [12,13,15]:…”