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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 general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find.
A rotating black hole is a solution of Einstein's field equation. There are two known exact solutions, the Kerr metric and the Kerr–Newman metric, which are believed to be representative of all rotating black hole solutions, in the exterior region.
The Kerr–Newman metric describes the spacetime geometry around a mass which is electrically charged and rotating. It is a vacuum solution which generalizes the Kerr metric (which describes an uncharged, rotating mass) by additionally taking into account the energy of an electromagnetic field, making it the most general asymptotically flat and stationary solution of the Einstein–Maxwell ...
To account for charge, the metric must satisfy the Einstein field equations like before, as well as Maxwell's equations in a curved spacetime. A charged, non-rotating mass is described by the Reissner–Nordström metric. Rotating black holes are described by the Kerr metric (uncharged) and the Kerr–Newman metric (charged).
A Schwarzschild black hole or static black hole is a black hole that has neither electric charge nor angular momentum (non-rotating). A Schwarzschild black hole is described by the Schwarzschild metric, and cannot be distinguished from any other Schwarzschild black hole except by its mass.
Non-rotating charged black holes are described by the Reissner–Nordström metric, while the Kerr metric describes a non-charged rotating black hole. The most general stationary black hole solution known is the Kerr–Newman metric, which describes a black hole with both charge and angular momentum. [71]
The horizon r = 2GM and finite v (the black hole horizon) is different from that with r = 2GM and finite u (the white hole horizon) . The metric in Kruskal–Szekeres coordinates covers all of the extended Schwarzschild spacetime in a single coordinate system. Its chief disadvantage is that in those coordinates the metric depends on both the ...
Schwarzschild metric – In Einstein's theory of general relativity, the Schwarzschild solution, named after Karl Schwarzschild, describes the gravitational field outside a spherical, uncharged, non-rotating mass such as a star, planet, or black hole. Rotating black hole – black hole that possesses spin angular momentum.