Peeling theorem for a generic field We know that in asymptotically simple space-times, if the generators of conformal boundary $\mathscr{I}^{\pm}$ satisfies the asymptotic Einstein's condition, then any purely outgoing (incoming) field can be written as polynomial in $1/r$ (Refer to section 9.7 of "Spinors and space-time. Volume-2" by R.Penrose and W.Rindler. A brief derivation for Peeling effect in asymptotically flat space-times can be found in an earlier post)
Is there a peeling theorem for a generic propagating field (which contains both outgoing and incoming field contributions)? How should one modify the line of reasoning presented in the above reference to account for this generic scenario?
 A: 
Is there a peeling theorem for a generic propagating field <…>?

“Peeling” implies that spacetime is smooth near null infinity (in the sense that it possesses conformal compactification with smooth boundary), but suitably generic spacetimes are not, they develop logarithmic singularities around null infinities. So literature calls such phenomena “obstructions to peeling”, “failure of peeling” etc.
For such generic spacetimes the expansions of NP scalars around null infinities are polyhomogeneous, that is, written in powers of both $1/r$ and $\log r$ (with generic term being $r^{-i}\log^{j}r$). Overall, the detailed and rigorous treatments of failure of peeling along null infinities and its connection with behavior of solutions along spacelike and timelike infinities are still missing, but the research area is quite active.
Relatively recent review of the peeling problem could be found here:

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*Friedrich, H. (2018). Peeling or not peeling — is that the question? Classical and Quantum Gravity, 35(8), 083001, doi:10.1088/1361-6382/aaafdb, arXiv:1709.07709.

A monograph about modern state of the art for conformal methods (that also discusses peeling and its failures):

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*Kroon, Juan A. Valiente. Conformal methods in general relativity. Cambridge university press, 2017, Open Access pdf.

