Chronology protection and quantized fields: Nonconformal and massive scalar fields in Misner space.

Abstract

In the absence of an adequate theory of quantum gravity, the search for a mechanism of ``chronology protection'' is currently focused on the vacuum energy divergence of quantized matter fields at chronology horizons and its back reaction on the metric via the semiclassical theory of gravity. The divergence of the vacuum energy at the chronology horizon was first demonstrated by Hiscock and Konkowski for a conformal massless scalar field in the Misner space. In this paper, we extend this earlier work to calculate the vacuum stress-energy tensor of a massive nonconformally coupled scalar field in Misner space. We find that the asymptotic behavior of 〈${\mathit{T}}_{\mathrm{\ensuremath{\mu}}\ensuremath{\nu}}$〉 as it diverges at the chronology horizon is, to leading order, independent of the curvature coupling and mass of the scalar field. Thus the vacuum energy of nonconformal and/or massive scalar fields diverges with the same strength as the massless conformal case. Since one important aspect of gravity is its nonconformal nature, this suggests that quantum gravity may be unable to act as the protector of chronology.