  Motivated by the universality of Hawking radiation and that of the anomaly
cancellation technique as well as that of the effective action method, we
investigate the Hawking radiation of a Schwarzschild black hole in the
isotropic coordinates via the cancellation of gravitational anomaly. After
performing a dimensional reduction from the four-dimensional isotropic
Schwarzschild metric, we show that this reduction procedure will, in general,
result in two classes of two-dimensional effective metrics: the conformal
equivalent and the inequivalent ones. For the physically equivalent class, the
two-dimensional effective metric displays such a distinct feature that the
determinant is not equal to the unity ($\sqrt{-g} \neq 1$), but also vanishes
at the horizon, the latter of which possibly invalidates the anomaly analysis
there. ...
  This is an updated version to replace our e-print arXiv:0709.0044 [hep-th].
Abstract is too long to exceed the limit of 24 lines by arXiv.
