New Insights into Hydrodynamic Gradient Expansion in Relativistic Kinetic Theory

A recent paper titled "Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory" by Lorenzo Gavassino presents significant findings in the field of relativistic kinetic theory. The paper establishes that in any relativistic kinetic theory where the non-hydrodynamic sector has a finite gap, the Taylor series of all hydrodynamic dispersion relations possesses a finite radius of convergence. This is a critical insight as it suggests that the behavior of hydrodynamic systems can be predicted within certain limits, which is essential for understanding complex physical phenomena.

Furthermore, the study reveals that for shear waves, the radius of convergence cannot be smaller than half the size of the gap. This finding has implications for the stability and predictability of fluid dynamics in relativistic contexts. Additionally, the research demonstrates that the non-hydrodynamic sector is gapped when the total scattering cross-section is bounded below by a positive constant. This establishes a connection between scattering processes and the stability of hydrodynamic theories.

The results also allow for the derivation of a rigorous upper bound on the shear viscosity of relativistic dilute gases, which is crucial for applications in high-energy physics and astrophysics. The implications of these findings extend to various fields, including nuclear theory and high-energy astrophysical phenomena, where understanding the behavior of matter under extreme conditions is vital.

This paper can be cited as: Gavassino, L. (2024). Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory. arXiv:2408.14316.