= Null energy condition for a canonical scalar field
{title2=$T_{ab}\ell^a\ell^b=(\ell^a\partial_a\phi)^2\geq0$}
The classical <stress-energy tensor of a canonical scalar field> has a gradient-product term and a metric-proportional term. Contracting with a real <null vector> removes the latter, leaving the displayed square for a real field. This proves the <null energy condition> for a minimally coupled canonical scalar, including the massless case. It is not a statement about arbitrary curvature couplings, wrong-sign kinetic terms or a renormalized quantum <stress-energy tensor>.
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