# Diffeomorphisms

by latentcorpse
Tags: diffeomorphisms
 Quote by latentcorpse Also, for the $\nabla_\mu T^{\mu \nu}$ question, can I take $u^\mu=(1,0,0,0)$ as we are assuming a comoving observer. And apparently they have $u^\alpha=\delta^\alpha{}_0$. However, even though our notes say we can do this for a comoving observer, I find that $\nabla_\mu T^{\mu \nu}=0$ $\nabla_\mu ( \rho u^\mu u^\nu ) + \nabla_\mu ( p u^\mu u^\nu) - \nabla_\mu (pg^{\mu \nu})=0$ Taking $\nu=0$ we get $\nabla_0 ( \rho u^0) + \nabla_i ( \rho u^i) + \nabla_0 ( pu^0) + \nabla_i ( p u^i) - \nabla_0p$ $\frac{\partial \rho}{\partial t}=0$ which is clearly incomplete so something isn't right... Thanks.
If you take the calculation another line you should find something like $$\dot{\rho} + (\rho +p){\Gamma^0}_{00}=0$$.
 Quote by fzero If you take the calculation another line you should find something like $$\dot{\rho} + (\rho +p){\Gamma^0}_{00}=0$$.
How did you manage to get any $p$ terms surviving? All of mine cancel.