jdstokes
Aug18-08, 03:32 AM
Is it possible to obtain the stress-energy for dust/perfect fluid from an action principle? Ie does there exist \mathcal{L} such that
(\rho + p)U^\mu U^\nu + p g^{\mu\nu} = \mathcal{L} g^{\mu\nu} + 2 \frac{\partial \mathcal{L}}{\partial g_{\mu\nu}}}.
How about when p = 0 (dust).
After some playing around, I've not been able to show that such a lagrangian exists.
(\rho + p)U^\mu U^\nu + p g^{\mu\nu} = \mathcal{L} g^{\mu\nu} + 2 \frac{\partial \mathcal{L}}{\partial g_{\mu\nu}}}.
How about when p = 0 (dust).
After some playing around, I've not been able to show that such a lagrangian exists.