Photons in general relativity actually do have gravitational fields--the stress-energy tensor, which determines spacetime curvature, is a function in part of the local four-momentum which photons do possess. Assuming four-momentum is conserved in the radiator's frame, the photons emitted by the radiator are absorbed (or rather, accumulate on the event horizon surface) by the black hole and contribute to its mass. I think the net mass balance is positive, but someone who actually understands black holes may want to correct me on that.

Edit: I suppose you could always throw in the maintenance engineers when you're done with them. :)

I think 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years would be a pretty usable amount of up time.