Perfect-fluid null energy condition
= Perfect-fluid null energy condition
{title2=$\rho+p\geq0$}
For $T_{ab}=(\rho+p)u_au_b+pg_{ab}$ and nonzero null $k$, contraction gives $T_{ab}k^ak^b=(\rho+p)(u\cdot k)^2$. A timelike fluid velocity has nonzero scalar product with every nonzero null vector, so the <null energy condition> is exactly the displayed inequality. Individual nonnegativity of pressure or density is unnecessary for null focusing. A <cosmological constant> term has zero null contraction.