Remarks about Static Back-Reaction on Black Hole Spacetimes

Recently, it has been claimed that the back reaction of vacuum polarization on a black hole spacetime naturally regularizes infinities in the black hole entropy. We examine the back reaction calculation and find no such short-distance cut-off,in contradiction with these recent claims. Moreover, the intuitive expectation that the perturbative calculation breaks down near the event horizon is confirmed. The new surface gravity diverges and the metric is degenerate at the stretched horizon.