  We study the scattering rigidity problem in Lorentzian geometry: recovery of
a Lorentzian metric from the scattering relation known on a lateral timelike
boundary. We show that one can recover the jet of the metric up to a gauge
transformation near a lightlike strictly convex point. Assuming that the metric
is real analytic, we show that one can recover the metric up to a gauge
transformation as well near such a point.
