Taub–NUT space - Alchetron, The Free Social Encyclopedia

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

The Taub–NUT space 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

d s 2 = − d t 2 / U ( t ) + 4 l 2 U ( t ) ( d ψ + cos ⁡ θ d ϕ ) 2 + ( t 2 + l 2 ) ( d θ 2 + ( sin ⁡ θ ) 2 d ϕ 2 )

where

U ( t ) = 2 m t + 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 + ( m 2 + l 2 ) 1 / 2 , and Newman, Tamburino and Unti showed how to extend the metric across these surfaces.

References

Taub–NUT space Wikipedia

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