
We establish a quantitative angular-rate locking theorem for geodesics in Kerr spacetime.For every noncritical trajectory approaching the outer Killing horizon, the coordinate angularvelocity dϕ/dt converges to the horizon angular velocity ΩH . The classification is governed bythe invariant KH = E −ΩH L, which defines a codimension-one critical subset. We derive explicitnear-horizon estimates showing that the deviation from ΩH is bounded linearly by |r − r+| inthe non-extremal case and quadratically in extremal Kerr. Surface gravity determines the linearscaling coefficient.
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