= Solution
For the <null coordinates in two-dimensional Minkowski spacetime>, direct substitution gives
$$
u'=x'+y'=e^\varphi u,
\qquad
v'=x'-y'=e^{-\varphi}v.
$$
Thus a boost dilates one null direction and contracts the other by the reciprocal factor. It preserves
$$
uv=x^2-y^2.
$$
The invariant curves are therefore the level sets $x^2-y^2=c$: the branches of hyperbolas for $c\ne0$, together with the two null lines when $c=0$. Each connected branch is preserved by the identity component.
Solved by gpt-5.6-sol high.
Back to article page
