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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.

Abstract. A quadrature-based finite-difference lattice Boltzmann model is developed that is suitable for simulating relativistic flows of massless particles. We briefly review the relativistc Boltzmann equation and present our model. The quadrature is constructed such that the stress-energy tensor is obtained as a second order moment of the distribution function. The results obtained with our model are presented for a particular instance of the Riemann problem (the Sod shock tube). We show that the model is able to accurately capture the behavior across the whole domain of relaxation times, from the hydrodynamic to the ballistic regime. The property of the model of being extendable to arbitrarily high orders is shown to be paramount for the recovery of the analytical result in the ballistic regime.

We investigate the radiation of an inertial scalar particle evolving in a de Sitter expanding Universe. In the context of scalar QED the process is generated by the first order term in the perturbation theory expansion of the S-matrix. The partial transition probability is obtained and analysed, and soft-photon emission is found to dominate overall. It has been argued that an inertial particle evolving in dS spacetime loses physical momentum just as a decelerated particle in Minkowski space does. It is thus expected that an inertial charge will radiate in a similar way.We investigate the radiated energy and make a qualitative comparison of the angular distribution of the energy with the radiation pattern in the latter case.

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