Taub–NUT space

The Taub–NUT space (/tɑːb nʌt/ or /tɑːb ɛnjuːˈtiː/) is an exact solution to Einstein's equations, a model universe formulated in the framework of general relativity.

The Taub–NUT metric was found by Abraham Haskel Taub (1951), and extended to a larger manifold by E. Newman, L. Tamburino, and T. Unti (1963), whose initials form the "NUT" of "Taub–NUT".

Taub's solution is an empty space solution of Einstein's equations with topology R×S³ and metric

$ds^{2}=-dt^{2}/U(t)+4l^{2}U(t)(d\psi +\cos \theta d\phi )^{2}+(t^{2}+l^{2})(d\theta ^{2}+(\sin \theta )^{2}d\phi ^{2})$

where

$U(t)={\frac {2mt+l^{2}-t^{2}}{t^{2}+l^{2}}}$

and m and l are positive constants.

Taub's metric has coordinate singularities at U=0, t=m+(m²+l²)^1/2, and Newman, Tamburino and Unti showed how to extend the metric across these surfaces.

References

• Newman, E.; Tamburino, L.; Unti, T. (1963), "Empty-space generalization of the Schwarzschild metric", Journal of Mathematical Physics, 4: 915–923, Bibcode:1963JMP.....4..915N, doi:10.1063/1.1704018, ISSN 0022-2488, MR 0152345
• Taub, A. H. (1951), "Empty space-times admitting a three parameter group of motions", Annals of Mathematics. Second Series, 53: 472–490, doi:10.2307/1969567, ISSN 0003-486X, JSTOR 1969567, MR 0041565