  We study the wave equation for a massive scalar in three-dimensional
AdS-black hole spacetimes to understand the unitarity issues in a semiclassical
way. Here we introduce four interesting spacetimes: the non-rotating BTZ black
hole (NBTZ), pure AdS spacetime (PADS), massless BTZ black hole (MBTZ), and
extremal BTZ black hole (EBTZ). Our method is based on the potential analysis
and solving the wave equation to find the condition for the frequency $\omega$
exactly. In the NBTZ case, one finds the quasinormal (complex and discrete)
modes which signals for a non-unitary evolution. Real and discrete modes are
found for the PADS case, which means that it is unitary obviously. On the other
hand, we find real and continuous modes for the two extremal black holes of
MBTZ and EBTZ. It suggests that these could be candidates for the unitary
system.

High Energy Physics - Theory