We consider the implications of the presence of ~1 stellar-mass black hole (BH) at the center of a dense globular cluster. We show that BH X-ray binaries formed through exchange interactions are likely to have extremely low duty cycles (<0.001), consistent with the absence of BH X-ray transients in Galactic globular clusters. In contrast, we find that BH X-ray binaries formed through tidal capture would be persistent, bright X-ray sources. Given the absence of any such source and the very high

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... nteraction rates, we conclude that tidal capture of a main-sequence star by a BH most likely leads to the complete disruption of the star.