The book EXACT SPACE-TIMESIN EINSTEIN’SGENERAL RELATIVITY by Podolsky and Griffiths has a section on Taub-Nut space-time metrics and there is defines the singularity made in the Taub metric as quasi-regular singularity $$ \mathrm{d} s^{2}=-f(r)\left(\mathrm{d} t+4 l \sin ^{2} \frac{1}{2} \theta \mathrm{d} \phi\right)^{2}+\frac{\mathrm{d} r^{2}}{f(r)}+\left(r^{2}+l^{2}\right)\left(\mathrm{d} \theta^{2}+\sin ^{2} \theta \mathrm{d} \phi^{2}\right) $$s.

When we set $$ \theta=0 \text { and } \theta=\pi $$

We get a singularity on one of the axises.

What is a quasi-regular singularity as opposed to a curvature singularity?


Quasi-regular singularities are points of incomplete and in-extensible geodesics that spiral infinitely around a topologically closed spatial dimension. These are the weakest form of singularity, in that the Riemann tensor is completely finite in all parallelly propagated orthonormal frames.No observer near a quasi-regular singularity, nor one who falls in to the singularity, feels unbounded tidal forces.

Reference: https://pdfs.semanticscholar.org/3f03/a70f148528e55f9391b6b02d52f86a30f1f9.pdf

Basically, as I understand it, it's a line singularity that has no tidal forces tied to it since it's not produced by curvature. Exactly the same as Dirac strings.(well maybe not exactly the same)


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