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.
open access link
@article{Bussola:2017wki, author = "Bussola, Francesco and Dappiaggi, Claudio and Ferreira, Hugo R. C. and Khavkine, Igor", title = "{Ground state for a massive scalar field in BTZ spacetime with Robin boundary conditions}", year = "2017", eprint = "1708.00271", archivePrefix = "arXiv", primaryClass = "gr-qc", SLACcitation = "%%CITATION = ARXIV:1708.00271;%%" }

Keywords: 
black holes, Hadamard states, scalar field