Kinetic theory for a relativistic charged gas: mathematical foundations of the hydrodynamic limit and first-order results within the projection method
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915900426289152 |
|---|---|
| author | Gabarrete, Carlos García-Perciante, Ana Laura Sarbach, Olivier |
| author_facet | Gabarrete, Carlos García-Perciante, Ana Laura Sarbach, Olivier |
| contents | In this work, the first-order constitutive equations for a relativistic charged gas are obtained based on the Chapman-Enskog expansion of near-equilibrium solutions to the Boltzmann equation by implementing the projection method. To this purpose we consider an arbitrary fixed background spacetime and electromagnetic field, and present a novel procedure within the Chapman-Enskog approximation which is the relativistic generalization of the projection method developed in the Newtonian case. Motivated by a rigorous study of the linearized collision operator, we argue that the most natural frame to derive a relativistic dissipative fluid theory from kinetic theory is the trace-fixed particle frame. This frame determines the state variables by requiring compatibility of the first few moments of the one-particle distribution function with those of the Jüttner distribution. The resulting constitutive relations are derived, and it is shown that the corresponding transport coefficients are, in fact, frame-independent if suitably defined. We point out that, in frame, there exists an additional freedom which we refer to as a choice of representation. Moreover, we discuss how both of these choices can be implemented at the microscopic level within the projection method. This allows for a systematic derivation of general first-order constitutive equations starting from the ones obtained in the trace-fixed particle frame. We obtain a fluid theory which, in the trace-fixed particle frame and for a suitable choice of the parameters associated with the representation freedom, is strongly hyperbolic, causal, and for which global equilibrium states are stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14251 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kinetic theory for a relativistic charged gas: mathematical foundations of the hydrodynamic limit and first-order results within the projection method Gabarrete, Carlos García-Perciante, Ana Laura Sarbach, Olivier General Relativity and Quantum Cosmology Statistical Mechanics High Energy Physics - Theory In this work, the first-order constitutive equations for a relativistic charged gas are obtained based on the Chapman-Enskog expansion of near-equilibrium solutions to the Boltzmann equation by implementing the projection method. To this purpose we consider an arbitrary fixed background spacetime and electromagnetic field, and present a novel procedure within the Chapman-Enskog approximation which is the relativistic generalization of the projection method developed in the Newtonian case. Motivated by a rigorous study of the linearized collision operator, we argue that the most natural frame to derive a relativistic dissipative fluid theory from kinetic theory is the trace-fixed particle frame. This frame determines the state variables by requiring compatibility of the first few moments of the one-particle distribution function with those of the Jüttner distribution. The resulting constitutive relations are derived, and it is shown that the corresponding transport coefficients are, in fact, frame-independent if suitably defined. We point out that, in frame, there exists an additional freedom which we refer to as a choice of representation. Moreover, we discuss how both of these choices can be implemented at the microscopic level within the projection method. This allows for a systematic derivation of general first-order constitutive equations starting from the ones obtained in the trace-fixed particle frame. We obtain a fluid theory which, in the trace-fixed particle frame and for a suitable choice of the parameters associated with the representation freedom, is strongly hyperbolic, causal, and for which global equilibrium states are stable. |
| title | Kinetic theory for a relativistic charged gas: mathematical foundations of the hydrodynamic limit and first-order results within the projection method |
| topic | General Relativity and Quantum Cosmology Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2508.14251 |