The conformal anomaly and one-loop effective action in a midisuperspace model

Abstract

The theory of a scalar field conformally coupled to four dimensional Einsten gravity is dimensionally reduced to yield a conformally invariant two dimensional sigma model. The conformal anomaly, one-loop renormalized effective action and renormalized vacuum expectation value of the two dimensional stress-energy tensor are computed in a semi-classical treatment which includes the contribution from one graviton mode. With additional assumptions, this enables the computation of the flux of Hawking radiation from a static black hole yielding the usual result.