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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Relativistic Euler equations ： ウィキペディア英語版 Relativistic Euler equations In fluid mechanics and astrophysics, the relativistic Euler equations are a generalization of the Euler equations that account for the effects of special relativity. The equations of motion are contained in the continuity equation of the stress–energy tensor $T^$: :$\backslash nabla\_\backslash mu\; T^=0.$ For a perfect fluid, :$T^\; \backslash ,\; =\; (e+p)u^\backslash mu\; u^\backslash nu+p\; \backslash eta^.$ Here $e$ is the relativistic rest energy density of the fluid, $p$ is the fluid pressure, $u^\backslash mu$ is the four-velocity of the fluid, and $\backslash eta^$ is the Minkowski metric tensor with signature . To the above equations, a statement of conservation is usually added, usually conservation of baryon number. If $n$ is the number density of baryons this may be stated :$$ \nabla_\mu (nu^\mu)=0. These equations reduce to the classical Euler equations if the fluid three-velocity is much less than the speed of light, the pressure is much less than the energy density, and the latter is dominated by the rest mass density. The relativistic Euler equations may be applied to calculate the speed of sound in a fluid with a relativistic equation of state (that is, one in which the pressure is comparable with the internal energy density $e$, including the rest energy; $e=\backslash rho\; c^2+\backslash rho\; e^C$ where $e^C$ is the classical internal energy per unit mass). Under these circumstances, the speed of sound $S$ is given by :$$ S^2=c^2 \left. \frac \right|_. (note that :$e=\backslash rho\; (c^2+e^C)$ is the relativistic internal energy density). This formula differs from the classical case in that $\backslash rho$ has been replaced by $e/c^2$. ==See also== * Relativistic heat conduction * Equation of state (cosmology) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Relativistic Euler equations」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.