Work

Nonrelativistic transport from frame-indifferent kinetic theory

Year: 2025

Type: article

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.

Source: Physical review. D/Physical review. D.

DOI: 10.1103/fk7x-bkd9

Authors: Paweł Matus, Rajesh Biswas, Piotr Surówka, Francisco Peña-Benítez

Institutions: Max Planck Institute for the Physics of Complex Systems, Wrocław University of Science and Technology

Language: English

Topic: Relativity and Gravitational Theory

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid