Anderson-Witting transport coefficients for flows in general relativity

The transport coefficients induced by the Anderson-Witting approximation of the collision term in the relativistic Boltzmann equation are derived for close to equilibrium flows in general relativity. Using the tetrad formalism, it is shown that the expression for these coefficients is the same as that obtained on flat space-time, in agreement with the generalized equivalence principle.Comment: 6 pages, 1 figure, proceedings of TIM 15-16 conference (26-28 May 2016, Timisoara, Romania

Quantum non-equilibrium effects in rigidly-rotating thermal states

Based on known analytic results, the thermal expectation value of the stress-energy tensor (SET) operator for the massless Dirac field is analyzed from a hydrodynamic perspective. Key to this analysis is the Landau decomposition of the SET, with the aid of which we find terms which are not present in the ideal SET predicted by kinetic theory. Moreover, the quantum corrections become dominant in the vicinity of the speed of light surface (SOL). While rigidly-rotating thermal states cannot be constructed for the Klein-Gordon field, we perform a similar analysis at the level of quantum corrections previously reported in the literature and we show that the Landau frame is well-defined only when the system is enclosed inside a boundary located inside or on the SOL. We discuss the relevance of these results for accretion disks around rapidly-rotating pulsars.Comment: 6 pages, 2 figures, accepted for publication in Physics Letters

Quadrature-based Lattice Boltzmann Model for Relativistic Flows

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.Comment: 6 pages, 2 figures, proceedings of TIM 15-16 conference (26-28 May 2016, Timisoara, Romania

Lattice Boltzmann study of the one-dimensional boost-invariant expansion with anisotropic initial conditions

A numerical algorithm for the implementation of anisotropic distributions in the frame of the relativistic Boltzmann equation is presented. The implementation relies on the expansion of the Romatschke-Strickland distribution with respect to orthogonal polynomials, which is evolved using the lattice Boltzmann algorithm. The validation of our proposed scheme is performed in the context of the one-dimensional boost invariant expansion (Bjorken flow) at various values of the ratio $\eta / s$ of the shear viscosity to the entropy density. This study is limited to the case of massless particles obeying Maxwell-J\"uttner statistics.Comment: 6 pages, 2 figures, submitted to the proceedings of the TIM-18 Physics Conference, 24-26 May 2017, Timisoara, Romania. Matches the accepted versio