The Kerr–Newman metric is a solution of the Einstein–Maxwell equations in general relativity that describes the spacetime geometry in the region surrounding a charged, rotating mass.
This solution has not been especially useful for describing astrophysical phenomena, because observed astronomical objects do not possess an appreciable net electric charge. The solution has instead been of primarily theoretical and mathematical interest. (It is assumed that the cosmological constant equals zero which is near enough to the truth.)
Scholarpedia has an outstanding, in depth article about Kerr-Newman metric: http://www.scholarpedia.org/article/Kerr-Newman_metric
Top image: Conceptual photograph of a rotating (angular momentum per unit mass a = 0.8) black hole that is not electrically charged. This is a realistic black hole, such as is surely present in some X-ray binaries and in many galactic nuclei. The curvature, K, of the black hole is shown as a function of distance from the singularity ("radius") and polar angle ("theta"). The most remarkable new feature is the presence of negative curvature.
Bottom image: Conceptual photograph of a general black hole. This particular plot is for a value of a = 0.8 (angular momentum per unit mass) and for electric charge Q = 0.8. Real black holes in the universe are unlikely to be electrically charged.
_M R S S Shourie
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