It has long been known that a maximally spinning black hole cannot be overspun by tossing in a test body. Here we show that if instead the black hole starts out with below maximal spin, then indeed overspinning can be achieved. We find that requirements on the size and internal structure of the test body can be met if the body carries in orbital but not spin angular momentum. Our analysis neglects radiative and self-force effects, which may prevent the overspinning.
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