Kerr solution

The Kerr metric or Kerr geometry 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 1915 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 Reissner–Nordström metric, was discovered soon afterwards (1916–1918). 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 Kerr–Newman metric, was discovered shortly thereafter in 1965. These four related solutions may be summarized by the following table:

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 (also known as the Lense–Thirring effect), 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 – even light itself – must rotate with the black-hole; the region where this holds is called the ergosphere.

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