Vacuum polarization in the Schwarzschild spacetime and dimensional reduction - art. no. 084029

A massless scalar field minimally coupled to gravity and propagating in Sch warzschild spacetime is considered. After dimensional reduction under spher ical symmetry the resulting 2D field theory is canonically quantized and th e renormalized expectation values [T-ab] Of the relevant energy-momentum te nsor operator are investigated. Asymptotic behaviors and analytical approxi mations are given for [T-ab] in the Boulware, Unruh and Hartle-Hawking stat es. Special attention is devoted to the black-hole horizon region where the WKB approximation breaks down.