The characteristic features of [T-mu nu] in the Boulware, Unruh and Hartle-
Hawking states for a conformal massless scalar field propagating in the Sch
warzschild space-time are obtained by means of effective actions deduced by
the trace anomaly. The actions are made local by the introduction of auxil
iary fields and boundary conditions are carefully imposed on them in order
to select the different quantum states. (C) 1999 Elsevier Science B.V. All
rights reserved.