Ground state for a massive scalar field in BTZ spacetime with Robin boundary conditions
Abstract
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.
Keywords
Cite
@article{arxiv.1708.00271,
title = {Ground state for a massive scalar field in BTZ spacetime with Robin boundary conditions},
author = {Francesco Bussola and Claudio Dappiaggi and Hugo R. C. Ferreira and Igor Khavkine},
journal= {arXiv preprint arXiv:1708.00271},
year = {2017}
}
Comments
17 pages, 3 figures