= Particle number conservation in a relativistic fluid
{title2=$\nabla_a(nu^a)=0$}
The number current is $J^a=nu^a$, where $n$ is the rest-frame <number density> and $u^a$ the unit <four-velocity>. Its covariant continuity equation is $\nabla_aJ^a=0$, equivalently $u^a\nabla_an+n\nabla_au^a=0$. Integration over a spacetime volume and the <divergence theorem> equate the particle numbers crossing its boundary. This conservation law is separate from <stress-energy conservation>.
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