  We study the Lorentzian metric independent of the time variable in the
cylinder $\mathbb{R}\times\Omega$ where $x_0\in\mathbb{R}$ is the time variable
and $\Omega$ is a bounded smooth domain in $\mathbb{R}^n$. We consider forward
null-geodesics in $\mathbb{R}\times \Omega$ starting on
$\mathbb{R}\times\partial\Omega$ at $t=0$ and leaving $\mathbb{R}\times\Omega$
at some later time. We prove the following rigidity result: If two Lorentzian
metrics are close enough in some norm and if corresponding null-geodesics have
equal lengths then the metrics are equal.
