- Kerr-Newman metric
The Kerr-Newman metric is a solution of Einstein's
general relativityfield equation that describes the spacetime geometry in the region surrounding a charged, rotating mass. Like the Kerr metric, the interior solution exists mathematically and satisfies Einstein's field equations, but is probably not representative of the actual metric of a physical black hole due to stability issues.
The Kerr-Newman metriccite journal | last = Kerr | first = RP | authorlink = Roy Kerr | year = 1963 | title = [http://prola.aps.org/abstract/PRL/v11/i5/p237_1 Gravitational field of a spinning mass as an example of algebraically special metrics] | journal = Physical Review Letters | volume = 11 | pages = 237–238 | doi = 10.1103/PhysRevLett.11.237] [cite book | last = Landau | first = LD | authorlink = Lev Landau | coauthors = Lifshitz, EM | year = 1975 | title = The Classical Theory of Fields (Course of Theoretical Physics, Vol. 2) | edition = revised 4th English ed. | publisher = Pergamon Press | location = New York | isbn = 978-0-08-018176-9 |pages = pp. 321–330] describes the geometry of
spacetimein the vicinity of a mass "M" rotating with angular momentum"J" and charge "Q"
where "r""s" is the Schwarzschild radius
and the length-scale "r""Q" corresponds to the
where 1/4π"ε"0 is Coulomb's force constant. The length-scales α, ρ and Λ have been introduced for brevity
Alternative mathematical form
The Kerr-Newman metric can also be written in
where: "M" is the mass of the black hole: "J" is the angular momentum of the black hole: "Q" is the charge of the black hole
The Kerr-Newman metric becomes the ...
Kerr metricif the charge "Q" (or, equivalently, "r""Q") is zero.
Reissner-Nordström metricif the angular momentum "J" (or, equivalently, "α") is zero.
Schwarzschild metricif the charge "Q" and the angular momentum "J" are zero.
* orthogonal metric for the
oblate spheroidal coordinatesin the non-relativistic limit where "M" (or, equivalently, "r""s") goes to zero.
::which are equivalent to the
Boyer-Lindquist coordinates[cite journal | last = Boyer | first = RH | coauthors = Lindquist RW | year = 1967 | title = Maximal Analytic Extension of the Kerr Metric | journal = J. Math. Phys. | volume = 8 | pages = 265–281 | doi = 10.1063/1.1705193] ::::::
Minkowski spacebut in a usual spherical coordinate system if .
As for the Kerr metric, the Kerr-Newman metric defines a black hole only when :
Newman's result represents the most general stationary, axisymmetric asymptotically flat solution of
Einstein's equationsin the presence of an electromagnetic fieldin four dimensions. Since the matter content of the solution reduces to an electromagnetic field, it is referred as an electrovacsolution of Einstein's equations. Although it represents a generalization of the Kerr metric, it is not considered as very important for astrophysical purposes since one does not expect that realistic black holes have an important electric charge.
The Kerr-Newman solution is named after
Roy Kerr, discoverer of the uncharged rotating solution named after him (see Kerr metric) and Ezra T. Newman, co-discoverer of the charged solution in 1965.
In 1965, Ezra Newman found the axi-symmetric solution for Einstein's field equation for a black hole which is both rotating and electrically charged. This solution is called the
Kerr-Newman metric. It is a generalisation of the Kerr metric.
Rotating black hole
Exact solutions in general relativity
* [http://scienceworld.wolfram.com/physics/Kerr-NewmanBlackHole.html Kerr-Newman Black Hole]
* [http://www.geocities.com/zcphysicsms/chap11.htm SR Made Easy, chapter 11: Charged and Rotating Black Holes and Their Thermodynamics]
* [http://rvgs.k12.va.us/electives/TRAP/students/ckafura/paper.html Black Holes: Where God Divided by Zero]
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