Non-relativistic transport from frame-indifferent kinetic theory
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914142951047168 |
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| author | Matus, Paweł Biswas, Rajesh Surówka, Piotr Peña-Benítez, Francisco |
| author_facet | Matus, Paweł Biswas, Rajesh Surówka, Piotr Peña-Benítez, Francisco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08805 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-relativistic transport from frame-indifferent kinetic theory Matus, Paweł Biswas, Rajesh Surówka, Piotr Peña-Benítez, Francisco High Energy Physics - Theory Statistical Mechanics General Relativity and Quantum Cosmology 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. |
| title | Non-relativistic transport from frame-indifferent kinetic theory |
| topic | High Energy Physics - Theory Statistical Mechanics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2407.08805 |