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Relativistic Euler equationsIn fluid mechanics and astrophysics, the relativistic Euler equations are a generalization of the Euler equations that account for the effects of special relativity. Additional recommended knowledgeThe equations of motion are contained in the continuity equation of the stressenergy tensor T^{μν}: where the right hand side is the zero tensor. For a perfect fluid,
Here e is the relativistic rest energy of the fluid, p is the fluid pressure, u is the fourvelocity of the fluid, and η_{μν} is the Minkowski metric tensor. 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 These equations reduce to the classical Euler equations if . 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 = ρc^{2} + ρe^{C} where e^{C} is the classical internal energy per unit mass). Under these circumstances, the speed of sound S is given by (note that
is the relativistic internal energy density). This formula differs from the classical case in that ρ has been replaced by e / c^{2}.

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Relativistic_Euler_equations". A list of authors is available in Wikipedia. 