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

Francesco Bussola, Claudio Dappiaggi, Hugo R. C. Ferreira, Igor Khavkine
August 01, 2017
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.

black holes, Hadamard states, scalar field