Gravitational vacuum polarization. IV. Energy conditions in the Unruh vacuum

Building on a series of earlier papers, I investigate the various pointwise and averaged energy conditions in the Unruh vacuum. I consider the quantum stress-energy tensor corresponding to a conformally coupled massless scalar field, work in the test-field limit, restrict attention to the Schwarzschild geometry, and invoke a mixture of analytical and numerical techniques. I construct a semianalytic model for the stress-energy tensor that globally reproduces all known numerical results to within $0.8\%$, and satisfies all known analytic features of the stress-energy tensor. I show that in the Unruh vacuum (1) all standard pointwise energy conditions are violated throughout the exterior region, all the way from spatial infinity down to the event horizon, and (2) the averaged null energy condition is violated on all outgoing radial null geodesics. In a pair of appendices I indicate a general strategy for constructing semianalytic models for the stress-energy tensor in the Hartle-Hawking and Boulware states, and show that the Page approximation is in a certain sense the minimal Ansatz compatible with general properties of the stress energy in the Hartle-Hawking state.