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

We consider a real, massive scalar field in Bañados-Teitelboim-Zanelli spacetime, a 2+1-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...

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Bibliographic Details
Published in:Physical review. D 2017-11, Vol.96 (10), Article 105016
Main Authors: Bussola, Francesco, Dappiaggi, Claudio, Ferreira, Hugo R. C., Khavkine, Igor
Format: Article
Language:English
Subjects:
Black holes
Boundary conditions
Cosmological constant
Ground state
Spacetime
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Summary:We consider a real, massive scalar field in Bañados-Teitelboim-Zanelli spacetime, a 2+1-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.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.96.105016