The recent talk about alien constructs and so Dyson spheres got me wondering.

Assuming their existence, why do we expect to see Dyson spheres in other star systems? A new Dyson sphere (that is, the star + Dyson sphere system) would not emit much anything and so would be invisible. Of course, the energy has to go somewhere and even superadvanced aliens -- assuming they haven't developed all new superadvanced physics -- will have a lot of waste heat. That heat, we expect, would be dumped into surrounding space as some sort of radiation and so we would see it.

That leads me to two stupid questions (note that we are talking at the star-system scale):

• Can you dump waste heat directionally? If you built a Dyson sphere and became invisible at interstellar distances, can you radiate your heat signature as a beam and continue to avoid being seen?

• If you have a handy black hole around, can you dump the waste heat into a black hole? What that would look like?

P.S. If the Dyson sphere functions only as an energy source it would be invisible, seems to me. Imagine a scenario where aliens come to a star system, build a Dyson sphere around the star, and then arrange for all that energy to be narrow-beamed to neighbouring star systems where it will be collected and used. The point is that the energy is used elsewhere, so the Dysoned star emits very little and unless you're in the beam you don't see it. Would that work?