We know enough physics to rule out any ftl travel. Assuming that is correct which seems very likely they can't get here, even radio signals is question able - even if radio signals can get here either they have already passed and their civialization (sun) is dead or ours will be dead by the time they arrive.

Cherenkov radiation is a proof, that FTL is possible. We just cannot accelerate enough. However, «burps» from blackholes are proof that blackholes can do that. To achieve singularity, outer layer of blackhole core must spin at a FTL speed anyway.