Abstract
We consider a real, massive scalar field in Bañados-Teitelboim-Zanelli spacetime, a -dimensional black hole solution of 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. Second, 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.
- Received 2 August 2017
DOI:https://doi.org/10.1103/PhysRevD.96.105016
© 2017 American Physical Society