The Case Against Smooth Null Infinity

Penrose's proposal of smooth conformal compactification is not only of geometric elegance, it also has concrete, physical implications, such as the "peeling off" of gravitational radiation near infinity. One natural question to ask is then: Do physically relevant spacetimes admit a smooth conformal compactification? To answer this question, I will present a scattering construction of spacetimes describing the far region of $N$ infalling masses coming from the infinite past and following approximately Keplerian orbits, and prove that such spacetimes violate the "peeling property" both in the past and in the future. This violation is in principle measurable in the form of leading-order deviations from the usual late-time tails of gravitational radiation.