We consider the Dirichlet-to-Neumann map
on a
cylinder-like Lorentzian manifold related to the wave equation related to the metric
, the magnetic field
and the potential
. We show that we can
recover the jet of
on
the boundary from
up to a gauge transformation in a stable way. We also show that
recovers the following three invariants in a stable way: the lens relation of
, and the light ray
transforms of
and
.
Moreover,
is an FIO away from the diagonal with a canonical relation given
by the lens relation. We present applications for recovery of
and
in a
logarithmically stable way in the Minkowski case, and uniqueness with partial
data.
Keywords
Lorentz, DN map, inverse problem, light ray transform,
microlocal
