  If we apply the path integral formulation in order to analyze the particle
creation process of black-holes inside the non-linear formulation of massive
gravity, it is possible to demonstrate that the effect of the extra-degrees of
freedom is to deform the periodicity of the poles of the propagator in the
complex $t$-plane. This might create the effect of extra-particle creation
process at scales where the extra-degrees of freedom become relevant. For
stationary solutions, depending on the values taken by the free parameters of
the theory, the periodicity structure of the propagator reveal two effects. The
first one is a shift on the positions of the pole of the propagator with
respect to the GR case, affecting then the instant at which the particles are
detected. The second one is the existence of branch points, affecting then the
perception of particles. The branch point can be finite (including the zero
order case) or infinite depending on the free-parameters of the theory.
