The peeling theorem with arbitrary cosmological constant

TL;DR

This paper introduces a geometric method to analyze the asymptotic behavior of physical fields in spacetimes with any cosmological constant, extending the peeling theorem and explicitly characterizing the Weyl tensor's asymptotics.

Contribution

It provides a new, geometrically meaningful derivation of the peeling properties applicable to arbitrary cosmological constants, including explicit forms for the Weyl tensor's asymptotic terms.

Findings

Derived the asymptotic behavior of physical fields with arbitrary cosmological constant.

Explicit form of the Weyl tensor's asymptotic terms along lightlike geodesics.

Extended the peeling theorem to more general spacetime settings.

Abstract

A method for deriving the asymptotic behaviour of any physical field is presented. This leads to a geometrically meaningful derivation of the peeling properties for arbitrary values of the cosmological constant. Application to the outstanding case of the physical Weyl tensor provides the explicit form of all terms that determine its asymptotic behaviour along arbitrary lightlike geodesics. The results follow under the assumption of a conformal completion \`a la Penrose. The only freedom available is the choice of a null vector at the conformal boundary of the space-time (which determines the lightlike geodesic arriving there).