NUT 4‐momenta are forever

TLDR: In this paper, the asymptotic structure of the gravitational field at null infinity is re-examined by allowing certain potentials to develop "wire singularities" keeping the physical fields smooth.

Abstract: The asymptotic structure of the gravitational field at null infinity is re‐examined by allowing certain potentials to develop ‘‘wire singularities’’, keeping the physical fields smooth. This relaxation of the regularity conditions leads to the introduction of the Newman–Unti–Tamburino (NUT) 4‐momentum which is the ‘‘magnetic’’ or the ‘‘dual’’ counterpart of the Bondi–Sachs 4‐momentum. It is shown that, unlike the Bondi–Sachs 4‐momentum, the NUT 4‐vector is absolutely conserved even in the presence of gravitational radiation. Thus, while the gravitational field resembles the nonabelian Yang–Mills fields in its ‘‘electric’’ properties, it is analogous to the abelian Maxwell field in its ‘‘magnetic’’ properties. It is pointed out that gravitational fields with nonvanishing NUT 4‐momenta may have a substantial role in quantum gravity even though they are not physically significant in classical general relativity.