Dust stress-energy tensor
= Dust stress-energy tensor
{title2=$T^{\mu\nu}=mn_0u^\mu u^\nu$}
A pressureless fluid with proper number density $n_0$, rest mass $m$ and <four-velocity> $u$ has tensor $mn_0u^\mu u^\nu$. In its local rest frame there is energy density but no spatial stress. Particle-number conservation and the Lorentz force make its divergence the electromagnetic force density.