Perfect fluid in general relativity
= Perfect fluid in general relativity
{title2=$T_{ab}=(\rho+p)u_au_b+pg_{ab}$}
A relativistic perfect fluid has energy density $\rho$, isotropic pressure $p$ and unit timelike four-velocity $u$. Projecting $\nabla_aT^{ab}=0$ along and orthogonally to $u$ gives its energy and Euler equations.
For a <perfect fluid>, the relativistic stress tensor is $T_{ab}=(\rho+p)u_au_b+pg_{ab}$ in signature $(-,+,+,+)$ with $u^au_a=-1$.