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

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