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Nonrelativistic transport from frame-indifferent kinetic theory

Paweł Matus1, Rajesh Biswas2, Piotr Surówka2, and Francisco Peña-Benítez2

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Phys. Rev. D 112, 105007 – Published 7 November, 2025

DOI: https://doi.org/10.1103/fk7x-bkd9

Abstract

This paper explores the application of Newton-Cartan geometry to the kinetic theory of gases that includes nonrelativistic 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 50-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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Phys. Rev. D 112, 105007– Published 7 November, 2025
  • Received 27 November 2024
  • Accepted 15 October 2025
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