Abstract: One of the most useful tools to study the effects of quantized fields in curved spacetime is the stress-energy tensor for these fields. The stress-energy tensor gives information about the effects the spacetime has on the quantized fields that propagate in it and also provides a source for that geometry via the semiclassical backreaction equations. In static black hole spacetimes it can be computed using the Euclidean Green's function for a given field. The method for doing so will be outlined and the results of calculations of the stress-energy for spin 0 and ½ fields in static black hole spacetimes will be presented. Solutions to the resulting semiclassical backreaction equations will be discussed.
The Euclidean Green's function can also be used to compute the part of the retarded Green's function that contributes to the "tail" term in the expression for the radiation reaction force that a compact object such as a black hole experiences as it spirals into a supermassive black hole. The method for doing this will be discussed along with the results of a calculation of this part of the retarded Green's function for the case of a massless minimally coupled scalar field in Schwarzschild spacetime.