Spin-0 fields and the NP-constants close to spatial infinity in Minkowski spacetime

Understand

The NP constants of massless spin-0 fields propagating in Minkowski spacetime are computed close to spatial and null infinity by means of Friedrich's \emph{$i^0$-cylinder}.

• Assuming certain regularity condition on the initial data ensuring that the field extends analytically to the critical sets, it is shown that the NP constants at future $\mathscr{I}^{+}$ and past null infinity $\mathscr{I}^{-}$ are independent of each other.
• In other words, the classical NP constants at $\mathscr{I}^{\pm}$ stem from different parts of the initial data given on a Cauchy hypersurface.
• In contrast, it is shown that, using a slight generalisation of the classical NP constants, the associated quantities ($i^0$-cylinder NP constants) do not require the regularity condition being satisfied and give rise to conserved quantities at $\mathscr{I}^{\pm}$ that are determined by the same piece of initial data which, in turn, correspond to the terms controlling the regularity of the field.