Dust stress-energy tensor ($T^{\mu \nu }=m{n}_0{u}^{\mu }{u}^{\nu }$)

A pressureless fluid with proper number density $n_0$, rest mass $m$ and four-velocity $u$ has tensor $m{n}_0{u}^{\mu }{u}^{\nu }$. 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.