# Taub–NUT space

(Redirected from Taub-NUT vacuum)

The Taub–NUT space ([1] or ) 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.

## References

1. ^ McGraw-Hill Science & Technology Dictionary: "Taub NUT space"