Vacuum polarization in Schwarzschild space-time by anomaly induced effective actions

The characteristic features of in the Boulware, Unruh and Hartle-Hawking states for a conformal massless scalar field propagating in the Schwarzschild space-time are obtained by means of effective actions deduced by the trace anomaly. The actions are made local by the introduction of auxiliary fields and boundary conditions are carefully imposed on them in order to select the different quantum states