Gravitational vacuum polarization. II. Energy conditions in the Boulware vacuum
Abstract
Building on techniques developed in the preceding paper, I investigate the various pointwise and averaged energy conditions for the quantum stressenergy tensor corresponding to a conformally coupled massless scalar field in the Boulware vacuum. I work in the testfield limit, restrict attention to the Schwarzschild geometry, and invoke a mixture of analytical and numerical techniques. In contradistinction to the case of the HartleHawking vacuum, wherein violations of the energy conditions were confined to the region between the event horizon and the unstable photon orbit, I show that in the Boulware vacuum (1) all standard (pointwise and averaged) energy conditions are violated throughout the exterior region, all the way from spatial infinity down to the event horizon, and (2) outside the event horizon the standard pointwise energy conditions are violated in a maximal manner: They are violated at all points and for all null or timelike vectors. (The region inside the event horizon is considerably messier and of dubious physical relevance. Nevertheless, the standard pointwise energy conditions seem to be violated even inside the event horizon.) I argue that this is highly suggestive evidence, pointing to the fact that general selfconsistent solutions of semiclassical quantum gravity might not satisfy the energy conditions and may in fact for certain quantum fields and certain quantum states violate all the energy conditions.
 Publication:

Physical Review D
 Pub Date:
 October 1996
 DOI:
 10.1103/PhysRevD.54.5116
 arXiv:
 arXiv:grqc/9604008
 Bibcode:
 1996PhRvD..54.5116V
 Keywords:

 04.70.Dy;
 04.20.Gz;
 04.62.+v;
 Quantum aspects of black holes evaporation thermodynamics;
 Spacetime topology causal structure spinor structure;
 Quantum field theory in curved spacetime;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 8 pages, ReV_TeX