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Suppose in a binary stars system there is a dying star and a companion black hole as they orbit around each other. My question is what will possibly happen to the black hole if the partner goes supernova? I understand that the kinetic energy from the supernova cannot destroy the black hole.

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The likely result would either be a black hole-black hole binary system; a neutron star-black hole binary system, or the black hole and the compact remnant from the second supernova explosion would go their separate ways at reasonably high speeds.

You cannot disrupt a black hole in this way. In fact all that will happen to the original black hole is that it will likely get a bit more massive from accreting some of the supernova ejecta.

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    $\begingroup$ No hyper velocity black hole? $\endgroup$ – user6760 Apr 28 '15 at 10:09
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    $\begingroup$ @user6760 If the result is that the black hole and compact remnant "go their separate ways", then a hypervelocity object is possible, yes. $\endgroup$ – Rob Jeffries Apr 28 '15 at 13:24

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