  Semiclassical gravity is investigated in a large class of asymptotically
flat, static, spherically symmetric spacetimes including those containing
static stars, black holes, and wormholes. Specifically the stress-energy
tensors of massless free spin 0 and spin 1/2 fields are computed to leading
order in the asymptotic regions of these spacetimes. This is done for spin 0
fields in Schwarzschild spacetime using a WKB approximation. It is done
numerically for the spin 1/2 field in Schwarzschild, extreme
Reissner-Nordstrom, and various wormhole spacetimes. And it is done by finding
analytic solutions to the leading order mode equations in a large class of
asymptotically flat static spherically symmetric spacetimes. Agreement is shown
between these various computational methods. It is found that for all of the
spacetimes considered, the energy density and pressure in the asymptotic region
are proportional to 1/r^5 to leading order. Furthermore, for the spin 1/2 field
and the conformally coupled scalar field, the stress-energy tensor depends only
on the leading order geometry in the far field limit. This is also true for the
minimally coupled scalar field for spacetimes containing either a static star
or a black hole, but not for spacetimes containing a wormhole.
