  The electron dynamics in the classically forbidden region during relativistic
tunnel-ionization is investigated. The classical forbidden region in the
relativistic regime is identified by defining a gauge invariant total energy
operator. Introducing position dependent energy levels inside the tunneling
barrier, we demonstrate that the relativistic tunnel-ionization can be well
described by a one-dimensional intuitive picture. This picture predicts that,
in contrast to the well-known nonrelativistic regime, the ionized electron wave
packet arises with a momentum shift along the laser's propagation direction.
This is compatible with results from a strong field approximation calculation
where the binding potential is assumed to be zero-ranged. Further, the
tunneling time delay, stemming from Wigner's definition, is investigated for
model configurations of tunneling and compared with results obtained from the
exact propagator. By adapting Wigner's time delay definition to the ionization
process, the tunneling time is investigated in the deep-tunneling and in the
near-threshold-tunneling regimes. It is shown that while in the deep-tunneling
regime signatures of the tunneling time delay are not measurable at remote
distance, it is detectable, however, in the latter regime.
