The Taub–NUT metric (,
McGraw-Hill
McGraw Hill is an American education science company that provides educational content, software, and services for students and educators across various levels—from K-12 to higher education and professional settings. They produce textbooks, ...
''Science & Technology Dictionary'': "Taub NUT space" ) is an
exact solution to
Einstein's equations. It may be considered a first attempt in finding the metric of a spinning black hole. It is sometimes also used in
homogeneous
Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image. A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, i ...
but
anisotropic
Anisotropy () is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit ver ...
cosmological model
Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of fu ...
s formulated in the framework of
general relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
.
The underlying Taub space was found by , and extended to a larger manifold by , whose initials form the "NUT" of "Taub–NUT".
Description
Taub's solution is an empty space solution of Einstein's equations with topology R×S
3 and metric (or equivalently
line element
In geometry, the line element or length element can be informally thought of as a line segment associated with an infinitesimal displacement vector in a metric space. The length of the line element, which may be thought of as a differential arc ...
)
:
where
:
and ''m'' and ''l'' are positive constants.
Taub's metric has coordinate singularities at
, and Newman, Tamburino and Unti showed how to extend the metric across these surfaces.
Related work
Kerr metric
When
Roy Kerr developed the
Kerr metric
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of gen ...
for spinning black holes in 1963, he ended up with a four-parameter solution, one of which was the mass and another the angular momentum of the central body. One of the two other parameters was the NUT-parameter, which he threw out of his solution because he found it to be nonphysical since it caused the metric to be not asymptotically flat,
[Roy Kerr: ]
Spinning Black Holes
' (Lecture at the University of Canterbury, 25. May 2016). Timecode
21m36s
/ref>[Roy Kerr: ]
Kerr Conference
' (Lecture at the New Zealand Residence in Berlin, 4. July 2013). Timecode
19m56s
/ref> while other sources interpret it either as a gravomagnetic monopole parameter of the central mass,[Mohammad Nouri-Zonoz, Donald Lynden-Bell: ]
Gravomagnetic Lensing by NUT Space
' arXiv:gr-qc/9812094 or a twisting property of the surrounding spacetime.[A. Al-Badawi, Mustafa Halilsoy: ]
On the physical meaning of the NUT parameter
', from ResearchGate
ResearchGate is a European commercial social networking site for scientists and researchers to share papers, ask and answer questions, and find collaborators. According to a 2014 study by ''Nature'' and a 2016 article in ''Times Higher Education' ...
Misner spacetime
A simplified 1+1-dimensional version of the Taub–NUT spacetime is the Misner spacetime.
References
Notes
*
*
Exact solutions in general relativity
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