Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory

Fuente: arXiv
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Main Author: Gavassino, Lorenzo
Format: Preprint
Published: 2024
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author Gavassino, Lorenzo
author_facet Gavassino, Lorenzo
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2408_14316
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory
Gavassino, Lorenzo
Nuclear Theory
High Energy Astrophysical Phenomena
High Energy Physics - Theory
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.
title Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory
topic Nuclear Theory
High Energy Astrophysical Phenomena
High Energy Physics - Theory
url https://arxiv.org/abs/2408.14316