Quantum inequalities in two dimensional curved spacetimes
Abstract
We generalize a result of Vollick constraining the possible behaviors of the renormalized expected stress-energy tensor of a free massless scalar field in two dimensional spacetimes that are globally conformal to Minkowski spacetime. Vollick derived a lower bound for the energy density measured by a static observer in a static spacetime, averaged with respect to the observers proper time by integrating against a smearing function. Here we extend the result to arbitrary curves in non-static spacetimes. The proof, like Vollick's proof, is based on conformal transformations and the use of our earlier optimal bound in flat Minkowski spacetime. The existence of such a quantum inequality was previously established by Fewster.
Cite
@article{arxiv.gr-qc/0208066,
title = {Quantum inequalities in two dimensional curved spacetimes},
author = {Eanna E. Flanagan},
journal= {arXiv preprint arXiv:gr-qc/0208066},
year = {2020}
}
Comments
revtex 4, 5 pages, no figures, submitted to Phys. Rev. D. Minor corrections. v4 Correction to Eq. (2.11)