Revealing Noncanonical Hamiltonian Structures in Relativistic Fluid Dynamics
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909602835070976 |
|---|---|
| author | Takeda, Keiichiro Sato, Naoki |
| author_facet | Takeda, Keiichiro Sato, Naoki |
| contents | We present the noncanonical Hamiltonian structure of the relativistic Euler equations for a perfect fluid in Minkowski spacetime. By identifying the system's noncanonical Poisson bracket and Hamiltonian, we show that relativistic fluid flows preserve helicity and enstrophy as conserved quantities in three-dimensional and two-dimensional cases, respectively. This holds when the fluid follows a relativistic $γ$-barotropic equation of state, which generalizes the classical barotropic condition. Furthermore, we demonstrate that these conserved quantities are Casimir invariants associated with the noncanonical Poisson structure. These findings open new avenues for applying Hamiltonian theory to the study of astrophysical fluids and relativistic plasmas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22612 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revealing Noncanonical Hamiltonian Structures in Relativistic Fluid Dynamics Takeda, Keiichiro Sato, Naoki Mathematical Physics We present the noncanonical Hamiltonian structure of the relativistic Euler equations for a perfect fluid in Minkowski spacetime. By identifying the system's noncanonical Poisson bracket and Hamiltonian, we show that relativistic fluid flows preserve helicity and enstrophy as conserved quantities in three-dimensional and two-dimensional cases, respectively. This holds when the fluid follows a relativistic $γ$-barotropic equation of state, which generalizes the classical barotropic condition. Furthermore, we demonstrate that these conserved quantities are Casimir invariants associated with the noncanonical Poisson structure. These findings open new avenues for applying Hamiltonian theory to the study of astrophysical fluids and relativistic plasmas. |
| title | Revealing Noncanonical Hamiltonian Structures in Relativistic Fluid Dynamics |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2410.22612 |