Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory

Lorenzo Gavassino

doi:10.1103/physrevd.110.094012

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arXiv · 2408.14316

Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory

Lorenzo Gavassino

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Abstract

We rigorously prove that, in any relativistic kinetic theory whose non-hydrodynamic sector has a finite gap, the Taylor series of all hydrodynamic dispersion relations has a finite radius of convergence. Furthermore, we prove that, for shear waves, such radius of convergence cannot be smaller than $1/2$ times the gap size. Finally, we prove that the non-hydrodynamic sector is gapped whenever the total scattering cross-section (expressed as a function of the energy) is bounded below by a positive non-zero constant. These results, combined with well-established covariant stability criteria, allow us to derive a rigorous upper bound on the shear viscosity of relativistic dilute gases.

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Lorenzo Gavassino. 2024-08-26. Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory. https://doi.org/10.1103/physrevd.110.094012

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