Massless scalar fields with dominant logarithmic terms at null infinity obey an antipodal matching condition with a minus sign, opposite to the standard no-log matching.
Can one detect a non-smooth null infinity?
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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.
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Logarithmic matching between past infinity and future infinity: The massless scalar field
Massless scalar fields with dominant logarithmic terms at null infinity obey an antipodal matching condition with a minus sign, opposite to the standard no-log matching.