A black hole shrouded in dark matter is like a whirlpool in invisible water. This substance reveals itself only through gravity. Physicists added a special electromagnetic field to the model, but the main effect comes from dark matter: it warps spacetime, shifting stable orbits and the photon sphere (the ring of trapped light).
It can be thought of as a heat engine: the efficiency of converting heat into work depends on the density of the surrounding dark matter. This builds on the ideas of Hawking and Bekenstein about black hole thermodynamics and their entropy (a measure of disorder).
If our Galaxy's central black hole found itself inside a dense dark matter cloud, the orbits of stars would be noticeably warped, and astronomers could glimpse this invisible hand.