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

2017; American Physical Society; Volume: 96; Issue: 10 Linguagem: Inglês

10.1103/physrevd.96.105016

2470-0037

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

Advanced Mathematical Physics Problems

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.