There is no mention of the problem with building such a sphere around a black hole and starving the star of anymore gas and dust. A solid sphere with the maximum energy collectors would stop any infalling gas and dust from heating up enough to generate the energy mention. And, if you build a relatively small sphere around a black hole, there is no room to encircle the spiraling dust and gas that provides the energy. You, obviously could leave openings for dust and gas to pass through the sphere's surface, but I bet that infalling gas and dust would prove very corrosive to the remaining sphere and energy collectors at its high speeds. Lot's of details not mentioned in this article.