On 4D-Hawing Radiation from Effective Action
  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. 
V. Mukhanov, A. Wipf and A. Zelnikov