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## Homework Statement

Given the energy-momentum tensor for a perfect fluid, what is the conservation laws that I can compute from

[tex]

\nabla_b T^{ab}=0

[/tex]

in a curve space-time.

## Homework Equations

[tex]

T^{ab}=(\rho + p) u^a u^b - p g^{ab}

[/tex]

where p is the pressure and [itex]\rho[/itex] is the density.

## The Attempt at a Solution

I have already compute the geodesic equation, the equivalent to the equation of motion in a flat space-time.

I would like to know if there is any other conservation law to get. I supose that might be another one equivalent to the Navie-Strokes in flat space-time...

Thanks in advance