Exact Hawking radiation of scalars, fermions, and bosons using the tunneling method without back-reaction

Hawking radiation is studied for arbitrary scalars, fermions and spin-1 bosons, using a tunneling approach, to every order in ℏ but ignoring back-reaction effects. It is shown that the additional quantum terms yield no new contribution to the Hawking temperature. Indeed, it is found that the limit of small ℏ in the standard quantum WKB approximation is replaced by the near-horizon limit in the gravitational WKB approach.