Path-integral derivation of black-hole radiance inside the de-Rham-Gabadadze-Tolley formulation of massive gravity

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.