Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912110476263424 |
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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 |
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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 |