  We consider a real, massive scalar field in BTZ spacetime, a 2+1-dimensional
black hole solution of the Einstein's field equations with a negative
cosmological constant. First, we analyze the space of classical solutions in a
mode decomposition and we characterize the collection of all admissible
boundary conditions of Robin type which can be imposed at infinity. Secondly,
we investigate whether, for a given boundary condition, there exists a ground
state by constructing explicitly its two-point function. We demonstrate that
for a subclass of the boundary conditions it is possible to construct a ground
state that locally satisfies the Hadamard property. In all other cases, we show
that bound state mode solutions exist and, therefore, such construction is not
possible.
