Can one detect a non-smooth null infinity?

TL;DR

This paper proposes using gyroscope precession measurements to determine whether null infinity in an asymptotically flat spacetime is smooth or non-smooth, based on differences in precession decay rates.

Contribution

It introduces a model showing distinct precession decay behaviors for smooth versus non-smooth null infinity, providing a potential observational criterion.

Findings

Precession effects decay as r^{-2} log r in non-smooth case.

Precession effects decay as r^{-3} in smooth case.

The decay rate difference can distinguish null infinity smoothness.

Abstract

It is shown that the precession of a gyroscope can be used to elucidate the nature of the smoothness of the null infinity of an asymptotically flat spacetime (describing an isolated body). A model for which the effects of precession in the non-smooth null infinity case are of order $r^{-2}\ln r$ is proposed. By contrast, in the smooth version the effects are of order $r^{-3}$. This difference should provide an effective criterion to decide on the nature of the smoothness of null infinity.