On the construction of the Taub-NUT congruence

It is described how the null congruence tangent to the multiple Debever-Penrose direction of the Taub-NUT solution of Einstein's vacuum field equations may be constructed emanating into the future from a timelike world tube having normal cross sections. The curious shapes of the cross sections of the world tube are plotted, using a computer, for critical ranges of the parameter b/R0 where b is the Taub-NUT parameter and R0 is the 'radius' of the world tube. It is found that these cross sections can be maintained spatially compact only for some values of b/R0. (author)