Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-02-09
AnnalesHenriPoincare9:425-455,2008
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
31 pages. Corrections and clarifications added. Final version to appear in Ann. H. Poincare
Scientific paper
10.1007/s00023-008-0361-0
Quantum Energy Inequalities (QEIs) are results which limit the extent to which the smeared renormalised energy density of the quantum field can be negative, when averaged along a timelike curve or over a more general timelike submanifold in spacetime. On globally hyperbolic spacetimes the minimally-coupled massive quantum Klein--Gordon field is known to obey a `difference' QEI that depends on a reference state chosen arbitrarily from the class of Hadamard states. In many spacetimes of interest this bound cannot be evaluated explicitly. In this paper we obtain the first `absolute' QEI for the minimally-coupled massive quantum Klein--Gordon field on four dimensional globally hyperbolic spacetimes; that is, a bound which depends only on the local geometry. The argument is an adaptation of that used to prove the difference QEI and utilises the Sobolev wave-front set to give a complete characterisation of the singularities of the Hadamard series. Moreover, the bound is explicit and can be formulated covariantly under additional (general) conditions. We also generalise our results to incorporate adiabatic states.
Fewster Christopher J.
Smith Calvin J.
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