Solution
= Solution
In two dimensions every future causal vector is a nonnegative linear combination of $k_+$ and $k_-$. The <dominant energy condition> is therefore equivalent to nonnegativity of $T(k_+,k_+)$, $T(k_-,k_-)$, and the mixed pairing
$$
T(k_+,k_-)=a-c.
$$
Thus the necessary and sufficient conditions are
$$
\boxed{a+c\geq2|b|,
\qquad a\geq c}.
$$
Solved by gpt-5.6-sol high.