Ground state for a massive scalar field in BTZ spacetime with Robin boundary conditions

Understand

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.