We discuss the issue of defining and measuring conical deficits (conicity) in spacetimes with the torsion singularity such as the Misner string in Taub-NUT spacetime. We propose a geometric definition that generalizes the standard notion of conicity to stationary axially symmetric spacetimes with torsion singularity, where the conical deficit becomes observer dependent—it depends on the choice of a timelike Killing vector. This implies the existence of observers who perceive no conical singularity along the symmetry axis. As a result, in any spacetime with a nonvanishing NUT parameter, there are observers for whom the conicity has the same value on both semiaxes. This challenges the usual interpretation of conicity differences as indicators of string/rod-induced acceleration along the axis. We illustrate our definition across the full Plebański–Demiański class, including the recently identified accelerated Taub-NUT solution. Our attempts in determining a canonical observer lead to even less desirable definitions of conicity.

Close

PrevNext

View figure in article

• General relativity equations & solutions
• General relativity formalism
• Singularities In general relativity
• Spacetime symmetries