Relativistic rotating Boltzmann gas using the tetrad formalism

TL;DR

This paper applies the tetrad formalism to analyze a relativistic rotating Boltzmann gas in thermal equilibrium, providing detailed calculations and exploring potential applications to relativistic lattice Boltzmann simulations.

Contribution

It introduces a detailed application of the tetrad formalism to a rotating relativistic gas, including explicit calculations and potential simulation applications.

Findings

Explicit transformation to the comoving frame

Calculation of equilibrium particle flow four-vector

Analysis of equilibrium stress-energy tensor

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.