Hyperfinite type II factor

Template:Unreferenced stub 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 $T^{\mu \nu }$:

${\mathrm{\nabla }}_{\mu }{T}^{\mu \nu }=0.$

For a perfect fluid,

$T^{\mu \nu }=(e+p)u^{\mu }{u}^{\nu }+p{\eta }^{\mu \nu }.$

Here $e$ is the relativistic rest energy density of the fluid, $p$ is the fluid pressure, $u^{\mu }$ is the four-velocity of the fluid, and ${\eta }^{\mu \nu }$ is the Minkowski metric tensor with signature Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

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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

${\mathrm{\nabla }}_{\mu }(n{u}^{\mu })=0.$

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; $e=\rho c^2+\rho e^C$ where $e^C$ is the classical internal energy per unit mass).

Under these circumstances, the speed of sound $S$ is given by

$S^2=c^2{\frac{\partial p}{\partial e}|}_{\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{c}}.$

(note that

$e=\rho (c^2+e^C)$

is the relativistic internal energy density). This formula differs from the classical case in that $\rho$ has been replaced by $e/c^2$.

See also

• Relativistic heat conduction
• Equation of state (cosmology)

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