On a quick read before I've entirely finished my morning coffee, Hawking radiation will still exist.
The argument seems to go like this:
1) the event horizon in GR is infinitely sharp
2) gravity's rainbow implies nothing can be infinitely sharp (because that requires space and time to exist on scales below the Planck scale)
3) therefore gravity's rainbow implies the event horizon does not exist at those scales
Above those scales, something that looks very much like the event horizon still exists. The time taken to fall into a black hole will still be very long, just not infinite. Presumably the details of the theory show how this happens, which is the interesting bit. It's one thing to say "Hey, maybe the horizon is smooth or doesn't exist at small scales!" but to be useful the theory has to show how reality will actually behave if that is the case.
With regard to using black holes as power sources: if we have the technology to do that we'd be unlikely to need black holes as power sources.
I didn't see what about your explanation says why hawking radiation would still exist? It's caused by particle-anti particle pairs being created with one on each side of the event horizon, no?
When I first posted that response I was thinking that the scale that mattered was the compton wavelength of the particles being emitted, but having actually finished my coffee now I'm no longer so sure. My point was that so long as the horizon is sufficiently fine on the scale of the particle's compton wavelength then hawking radiation can still be emitted, even granted the horizon is not infinitely fine. This may be correct, or not.
The argument seems to go like this:
1) the event horizon in GR is infinitely sharp 2) gravity's rainbow implies nothing can be infinitely sharp (because that requires space and time to exist on scales below the Planck scale) 3) therefore gravity's rainbow implies the event horizon does not exist at those scales
Above those scales, something that looks very much like the event horizon still exists. The time taken to fall into a black hole will still be very long, just not infinite. Presumably the details of the theory show how this happens, which is the interesting bit. It's one thing to say "Hey, maybe the horizon is smooth or doesn't exist at small scales!" but to be useful the theory has to show how reality will actually behave if that is the case.
With regard to using black holes as power sources: if we have the technology to do that we'd be unlikely to need black holes as power sources.