The Kerr metric is the stationary axisymmetric vacuum metric of a rotating mass. Parameters and determine whether its geometry has the horizons of a Kerr black hole; the metric also admits over-extremal parameters with no horizon.
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The Kerr metric is a solution to the Einstein field equations of general relativity that describes the geometry of spacetime around a rotating, uncharged black hole. It generalizes the earlier Schwarzschild solution, which describes a non-rotating black hole. The Kerr metric accounts for the effects of angular momentum and can describe the rotation of the black hole as well as the gravitational fields that result from it.