In the perfect fluid solution for general relativity, you get
$$T_{ab} = u_a u_b (\mu + p) - g_{ab} \, p$$
I've seen varying descriptions of what $\mu$ is, and some places describe it as the local energy density. But I also thought that $T_{00}$ was the energy density.
So, what is the physical interpretation and difference between these two quantities? Because they are clearly not equal.