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

TL;DR

This paper uses path integral methods to analyze black-hole radiation in massive gravity, revealing how extra degrees of freedom deform propagator poles and influence particle creation and detection.

Contribution

It introduces a novel path integral approach to study black-hole radiance within the de-Rham-Gabadadze-Tolley massive gravity framework, highlighting effects of extra degrees of freedom.

Findings

Deformation of propagator pole periodicity due to extra degrees of freedom.

Shift in pole positions affecting particle detection times.

Existence of finite or infinite branch points depending on parameters.

Abstract

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.