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

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

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.