  In this Letter we make a critique of, and comparison between, the anomaly
method and WKB/tunneling method for obtaining radiation from non-trivial
spacetime backgrounds. We focus on Rindler spacetime (the spacetime of an
accelerating observer) and the associated Unruh radiation since this is the
prototype of the phenomena of radiation from a spacetime, and it is the
simplest model for making clear subtle points in the tunneling and anomaly
methods. Our analysis leads to the following conclusions: (i) neither the
consistent and covariant anomaly methods gives the correct Unruh temperature
for Rindler spacetime and in some cases (e.g. de Sitter spacetime) the
consistent and covariant methods disagree with one another; (ii) the tunneling
method can be applied in all cases, but it has a previously unnoticed temporal
contribution which must be accounted for in order to obtain the correct
temperature.
