Taub–NUT space

G_{\mu \nu }+\Lambda g_{\mu \nu }={8\pi G \over c^{4}}T_{\mu \nu }

Fundamental concepts

Phenomena

Spacetime
Kepler problem Gravitational field Gravitational collapse Gravitational lensing Gravitational waves Gravitational redshift Gravitational time delay Gravitational time dilation Frame-dragging Geodetic effect Gravity well Event horizon Singularity Naked singularity Black hole White hole
Space Time Spacetime diagrams Minkowski spacetime Closed timelike curve (CTC) Wormhole Ellis wormhole

Equations
Formalisms

Equations
Linearized gravity Einstein field equations Friedmann Geodesics Mathisson–Papapetrou–Dixon Hamilton–Jacobi–Einstein
Formalisms
ADM BSSN Post-Newtonian
Advanced theory
Kaluza–Klein theory Quantum gravity

Solutions

Scientists

The Taub–NUT metric (/tɔːb nʌt/^[1] or /tɔːb 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

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 $U=0,t=m+(m^{2}+l^{2})^{1/2}$ , and Newman, Tamburino and Unti showed how to extend the metric across these surfaces.

Notes

↑ McGraw-Hill Science & Technology Dictionary: "Taub NUT space"

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, ISSN 0022-2488, MR 0152345, doi:10.1063/1.1704018
Taub, A. H. (1951), "Empty space-times admitting a three parameter group of motions", Annals of Mathematics. Second Series, 53: 472–490, ISSN 0003-486X, JSTOR 1969567, MR 0041565, doi:10.2307/1969567

Relativity

Special
relativity

Background	Principle of relativity Special relativity
Foundations	Frame of reference Speed of light Hyperbolic orthogonality Rapidity Maxwell's equations
Formulation	Galilean relativity Galilean transformation Lorentz transformation
Consequences	Time dilation Relativistic mass Mass–energy equivalence Length contraction Relativity of simultaneity Relativistic Doppler effect Thomas precession Relativistic disks
Spacetime	Light cone World line Spacetime diagram Biquaternions Minkowski space

General
relativity

Background	Introduction Mathematical formulation
Fundamental concepts	Special relativity Equivalence principle World line Riemannian geometry Minkowski diagram Penrose diagram
Phenomena	Black hole Event horizon Frame-dragging Geodetic effect Lenses Singularity Waves Ladder paradox Twin paradox Two-body problem
Equations	ADM formalism BSSN formalism Einstein field equations Geodesic equation Friedmann equations Linearized gravity Post-Newtonian formalism Raychaudhuri equation Hamilton–Jacobi–Einstein equation Ernst equation
Advanced theories	Brans–Dicke theory Kaluza–Klein Mach's principle Quantum gravity
Solutions	Schwarzschild (interior) Reissner–Nordström Gödel Kerr Kerr–Newman Kasner Taub–NUT Milne Robertson–Walker pp-wave van Stockum dust Weyl−Lewis−Papapetrou

Scientists

Einstein field equations:

G_{\mu \nu }+\Lambda g_{\mu \nu }={8\pi G \over c^{4}}T_{\mu \nu }

and their analytical solution by Ernst equation:

\displaystyle \Re (u)(u_{rr}+u_{r}/r+u_{zz})=(u_{r})^{2}+(u_{z})^{2}.

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