= Weak energy condition for a perfect fluid
{title2=$\rho\ge0,\quad\rho+p\ge0$}
For a <perfect fluid in general relativity> in <metric signature> $(-,+,+,+)$, the <weak energy condition> is equivalent to $\rho\ge0$ and $\rho+p\ge0$. A normalized observer's <four-velocity> $W$ has <Lorentz factor> $\gamma=-u\cdot W\ge1$ relative to the fluid, and $T_{ab}W^aW^b=\rho+(\rho+p)(\gamma^2-1)$. The case $\gamma=1$ forces the first inequality and arbitrarily large $\gamma$ forces the second; conversely the same expression proves sufficiency.
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