ON 4D HAWKING RADIATION FROM THE EFFECTIVE ACTION

We determine the s-waves contribution of a scalar field to the four-di mensional (4D) effective action for arbitrary spherically symmetric ex ternal gravitational fields. The result is applied to 4D black holes a nd it is shown that the energy-momentum tensor derived from the (nonlo cal) effective action contains the Hawking radiation. The luminosity i s close to the expected one in the s-channel. The energy-momentum tens or may be used as starting point to study the backreaction problem.