 the kerr metric or kerr vacuum describes the geometry of empty spacetime around a rotating uncharged axially-symmetric black hole with a spherical 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. the kerr metric is a generalization of the schwarzschild metric, which was discovered by karl schwarzschild in 1916 and which describes the geometry of spacetime around an uncharged, spherically-symmetric, and non-rotating body. the corresponding solution for a charged, spherical, non-rotating body, the reissnerânordstrÃ¶m metric, was discovered soon afterwards (1916â1918). however, the exact solution for an uncharged, rotating black-hole, the kerr metric, remained unsolved until 1963, when it was discovered by roy kerr. the natural extension to a charged, rotating black-hole, the kerrânewman metric, was discovered shortly thereafter in 1965. these four related solutions may be summarized by the following table: {| class="wikitable" style="margin:1.0em auto;" | | non-rotating (j = 0) | rotating (j â  0) |- | uncharged (q = 0) | schwarzschild | kerr |- | charged (q â  0) | reissnerânordstrÃ¶m | kerrânewman |} where q represents the body's electric charge and j represents its spin angular momentum. according to the kerr metric, such rotating black-holes should exhibit frame dragging, an unusual prediction of general relativity. measurement of this frame dragging effect was a major goal of the gravity probe b experiment. roughly speaking, this effect predicts that objects coming close to a rotating mass will be entrained to participate in its rotation, not because of any applied force or torque that can be felt, but rather because of the curvature of spacetime associated with rotating bodies. at close enough distances, all objects must rotate with the black-hole; the region where this holds is called the ergosphere. rotating black holes have surfaces where the metric appears to have a singularity; the size and shape of these surfaces depends on the black hole's mass and angular momentum. the outer surface encloses the ergosphere and has a shape similar to a flattened sphere. the inner surface marks the "radius of no return" also called the "event horizon"; objects passing through this radius can never again communicate with the world outside that radius. however, neither surface is a true singularity, since their apparent singularity can be eliminated in a different coordinate system. object
Black_holes Exact_solutions_in_general_relativity Metric_tensors