  We consider the relativistic Schr\"odinger (Gordon-Klein) equation with a
time dependent vector and a scalar potential on a bounded cylindrical domain.
Using a standard Geometric Optics Ansatz, we establish a logarithmic stability
estimate for the recovery of the vector potentials. We also study the recovery
of the potentials in the presence of obstacles. It is shown that under some
geometric restrictions, the recovery of the potentials is possible up to a
gauge transform.
