I Light From Black Holes: GR vs QM

[kent davidge]

How should we deal with the fact that GR predicts light not scaping from a BH while QM states BHs radiate?

 

[phyzguy]

By realizing that GR cannot be a completely correct theory without some sort of quantum correction. I think this has been well known for a long time.

 

[Orodruin]

Also, the radiation is not just light. It consists of all sorts of particles and its origin is related to the Unruh effect.

 

[pervect]

How should we deal with the fact that GR predicts light not scaping from a BH while QM states BHs radiate?

I would think that the problem would best be dealt with by a theory of quantum gravity, which AFAIK we don't have. But possibly some insight can be gained by looking at the theory of quantum mechanics in curved space-time, in particular Unruh radiation, a theory that we do have.

I'm afraid while I've read some on the topic (mostly from Wald, IIRC), I'm not really confident in my understanding. I believe it is correct to say that if we consider a quantum mechanical model of a particle detector, if such a detector is in a vacuum and not accelerated it will not detect particles. Furthermore, there will be no Killing horizon. However, if the detector does accelerate in the same vacuum, it will detect the presence of particles and the space-time will have a Killing horizion, the Rindler horizon.

 

[PeterDonis]

I believe it is correct to say that if we consider a quantum mechanical model of a particle detector, if such a detector is in a vacuum and not accelerated it will not detect particles. Furthermore, there will be no Killing horizon. However, if the detector does accelerate in the same vacuum, it will detect the presence of particles and the space-time will have a Killing horizion, the Rindler horizon.

Yes, this is correct. More precisely, if we are in Minkowski spacetime and the quantum field is in the appropriate vacuum state--basically the state which looks like vacuum (zero amplitude to detect particles) to inertial observers--then an accelerated particle detector will have a nonzero amplitude to detect a particle. The detection process, as viewed by an observer moving with the detector, will look like the detector absorbing energy from the quantum field and transitioning from its ground state to an excited state (this is just another way of saying it detects a particle). To an inertial observer, however, this process will look like the detector emitting a particle and transitioning from an excited state to its ground state. Also, of course, the quantum field's state changes--to the accelerated observer it looks like a particle is being removed (because it was absorbed by the detector), but to an inertial observer it looks like a particle is being added.