  Hawking radiation is generally derived using a non-interacting field theory.
Some time ago, Leahy and Unruh showed that, in two dimensions with a
Schwarzschild geometry, a scalar field theory with a quartic interaction gets
the coupling switched off near the horizon of the black hole. This would imply
that interaction has no effect on Hawking radiation and free theory for
particles can be used. Recently, a set of exact classical solutions for the
quartic scalar field theory has been obtained. These solutions display a
massive dispersion relation even if the starting theory is massless. When one
considers the corresponding quantum field theory, this mass gap becomes a tower
of massive excitations and, at the leading order, the theory is trivial. We
apply these results to Hawking radiation for a Kerr geometry and prove that the
Leahy-Unruh effect is at work. Approaching the horizon the scalar field theory
has the mass gap going to zero. We devise a technique to study the interacting
scalar theory very near the horizon increasing the coupling. As these solutions
are represented by a Fourier series of plane waves, Hawking radiation can be
immediately obtained with well-known techniques. These results open a question
about the behavior of the Standard Model of particles very near the horizon of
a black hole where the interactions turn out to be switched off and the
electroweak symmetry could be restored.
