Asymptotic Behaviour of Zero Mass spin 2 Fields propagating in the external region of Kerr spacetime

TL;DR

This paper analyzes the asymptotic decay behavior of zero mass spin 2 fields in the external region of Kerr spacetime, providing decay conditions and detailed estimates for linearized solutions related to gravitational perturbations.

Contribution

It introduces new detailed estimates for the decay of linearized gravitational perturbations in Kerr spacetime, extending the Christodoulou-Klainerman approach.

Findings

Derived decay rates for linearized solutions

Established conditions on source terms for peeling decay

Provided new estimates useful for gravitational perturbation analysis

Abstract

After describing the inhomogeneous equation suitable to describe W{\nu}{\mu}{\rho}{\sigma}, a solution of the linearized version of the full quasilinear equation for the conformal part of the Riemann tensor connected to the perturbations of the Kerr spacetime far from the origin, we find the right decays we have to impose to the source term to obtain the peeling decays for this linearized solution. We basically follow the ideas of the Christodoulou Klainerman approach, [Ch-Kl] and [Kl-Ni1]. This result requires some new detailed estimates which could be considered a useful result by themselves.