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arXiv · 2407.08805

Non-relativistic transport from frame-indifferent kinetic theory

Paweł Matus·Rajesh Biswas·Piotr Surówka·Francisco Peña-Benítez
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Abstract

This paper explores the application of Newton-Cartan geometry to the kinetic theory of gases that includes non-relativistic gravitational effects and the principle of general covariance. Starting with an introduction to the basics of Newton-Cartan geometry, we examine the motion of point particles within this framework, leading to a detailed analysis of kinetic theory and the derivation of conservation equations. The equilibrium distribution function is explored, and the example of a rotating gas in a gravitational field is discussed. Further, we develop covariant hydrodynamic equations and extend our analysis through a gradient expansion approach to assess first-order constitutive relations for rotating gases. Finally, we address the frame-dependence paradox, presenting a novel resolution that addresses apparent discrepancies. Our construction resolves a fifty-year-old debate about the frame-indifferent formulation of kinetic theory. The resolution is presented in a modern, symmetry-based approach.

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Paweł Matus, Rajesh Biswas, Piotr Surówka, Francisco Peña-Benítez. 2025-11-09. Non-relativistic transport from frame-indifferent kinetic theory. https://doi.org/10.1103/fk7x-bkd9

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