Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1996-04-03
Phys.Rev.D54:5116-5122,1996
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
8 pages, ReV_TeX
Scientific paper
10.1103/PhysRevD.54.5116
I show that in the Boulware vacuum (1) all standard (point-wise 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 point-wise energy conditions are violated in a maximal manner: they are violated at all points and for all null/timelike vectors. (The region inside the event horizon is considerably messier, and of dubious physical relevance. Nevertheless the standard point-wise energy conditions also seem to be violated even inside the event horizon.) This is rather different from the case of the Hartle--Hawking vacuum, wherein violations of the energy conditions were confined to the region inside the unstable photon orbit. These calculations are for the quantum stress-energy tensor corresponding to a conformally-coupled massless scalar field in the Boulware vacuum. I work in the test-field limit, restrict attention to the Schwarzschild geometry, and invoke a mixture of analytical and numerical techniques. This *suggests* that general self-consistent 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.
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