= Cosmological constant preserves null convergence
{title2=$R_{ab}\ell^a\ell^b=8\pi G T_{ab}\ell^a\ell^b$}
Contract the <Einstein field equations> with a <null vector>. Both the trace term and the <cosmological constant> term multiply $g_{ab}\ell^a\ell^b=0$ and disappear. The <null energy condition> therefore still implies the <null convergence condition>, independently of the sign of the <cosmological constant>. A <black-hole area theorem> still needs the appropriate global horizon assumptions as well as this local focusing condition.
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