Trace anomalies and the Hawking effect

The general spherically symmetric, static solution of _T_^ = 0 in the exterior Schwarzschild metric is expressed in terms of two integration constants and two arbitrary functions, one of which is the trace of T_. One constant is the magnitude of Tₓₑ at infinity, and the other is determined if the physically normalized components of T_ are finite on the future horizon. The trace of the stress tensor of a conformally invariant quantum field theory may be nonzero (anomalous), but must be proportional (here) to the Weyl scalar, 48M^2r^-6; we fix the coefficient for the scalar field by indirect arguments to be (2880{^2) }^-1. In the two-dimensional analog, the magnitude of the Hawking blackbody effect at infinity is directly proportional to the magnitude of the anomalous trace (a multiple of the curvature scalar) ; a knowledge of either number completely determines the stress tensor outside a body in the final state of collapse. In four dimensions, one obtains instead a relation constraining the remaining undetermined function, which we choose as T_^-T_{^}4. This, plus additional physical and mathematical considerations, leads us to a fairly definite, physically convincing qualitative picture of 〈T_〉. Groundwork is laid for explicit calculations of 〈T_〉.