Why? Couldn’t one build a dyson sphere around a blackhole? Wouldn’t the blackhole have properties of a Bose–Einstein condensate given the matter at the center

Why? Couldn’t one build a dyson sphere around a blackhole? Wouldn’t the blackhole have properties of a Bose–Einstein condensate given the matter at the center cannot vibrate? It would be the coldest temperature possible. Heat moves downhill, you deposit heat into a singularity and have a shell around it. That aside, at even a scale of a single dyson sphere, something tells me when a civilization has the power to bend spacetime, the rules of possibilities begin to change. I think it is unwise to operate with so much certainty in the face of possibilities.