Asymptotic behavior of zero mass spin 2 fields propagating in Kerr spacetime

We introduce D-(0)(nu) W-nu mu rho sigma = h(mu rho sigma), the inhomogeneous equation suitable to describe the solution of the linearized version of the conformal part of the Riemann tensor connected to the perturbations of the Kerr spacetime far from the origin. Then we find the right decays we have to impose to the source term h(mu rho sigma) to obtain the peeling decays for this linearized solution. We explain how these decays are compatible with the ones we need to attack the full nonlinear problem following the Christodoulou-Klainerman approach, see [7, 11]. This result is expressed explicitly in Theorem 1.1 and requires some new detailed estimates for the connection coefficients related to the null cone foliation in Kerr, see [10], which could be considered as a useful result by itself.