  We determine the $s$-waves contribution of a scalar field to the four
dimensional effective action for arbitrary spherically symmetric external
gravitational fields. The result is applied to $4d$-black holes and it is shown
that the energy momentum tensor derived from the (nonlocal) effective action
contains the Hawking radiation. The luminosity is close to the expected one in
the $s$-channel. The energy momentum tensor may be used as starting point to
study the backreaction problem.
