  We consider the entanglement dynamics between two-level atoms in a rotating
black hole background. In our model the two-atom system is envisaged as an open
system coupled with a massless scalar field prepared in one of the physical
vacuum states of interest. We employ the quantum master equation in the
Born-Markov approximation in order to describe the time evolution of the atomic
subsystem. We investigate two different states of motion for the atoms, namely
static atoms and also stationary atoms with zero angular momentum. The purpose
of this work is to expound the impact on the creation of entanglement coming
from the combined action of the different physical processes underlying the
Hawking effect and the Unruh-Starobinskii effect. We demonstrate that, in the
scenario of rotating black holes, the degree of quantum entanglement is
significantly modified due to the phenomenon of superradiance in comparison
with the analogous cases in a Schwarzschild spacetime. In the perspective of a
zero angular momentum observer (ZAMO), one is allowed to probe entanglement
dynamics inside the ergosphere, since static observers cannot exist within such
a region. On the other hand, the presence of superradiant modes could be a
source for violation of complete positivity. This is verified when the quantum
field is prepared in the Frolov-Thorne vacuum state. In this exceptional
situation, we raise the possibility that the loss of complete positivity is due
to the breakdown of the Markovian approximation, which means that any arbitrary
physically admissible initial state of the two atoms would not be capable to
hold, with time evolution, its interpretation as a physical state inasmuch as
negative probabilities are generated by the dynamical map.
