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Relativistic Euler equations
Additional recommended knowledge
The equations of motion are contained in the continuity equation of the stress-energy tensor Tμν:
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 four-velocity of the fluid, and ημν 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 = ρc2 + ρeC where eC is the classical internal energy per unit mass).
Under these circumstances, the speed of sound S is given by
is the relativistic internal energy density). This formula differs from the classical case in that ρ has been replaced by e / c2.
|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.|