# Does Hawking radiation lead to black hole evaporation / reduction of black hole mass?

As I understand, Hawking radiation leads to black hole evaporation, resp. a black hole would lose mass due to that effect.

Now Hawking radiation is very similar to Unruh radiation, i.e. some (apparent) horizon leads to a thermal bath:

1. An inertial observer in Minkowski space does not see radiation.
2. A Rindler observer sees Unruh radiation.

1. A free falling observer does not observe Hawking radiation from a black hole.
2. An observer hovering somewhere over the event horizon of a black hole does see Hawking radiation.

Hence in either case, the inertial observer (1.) sees no radiation whilst the accelerated observer (2.) sees thermal radiation.

Of course, the case U.2 is stationary, i.e. for a Rindler observer the spacetime does not change and the Rindler horizon does not disappear, evaporate or change its distance due to Unruh radiation.

Doesn't this also apply to H.2, i.e. there is just some thermal bath due to acceleration (or due to some horizon), and the black hole does not change in mass?

Moreover, if the black hole did evaporate due to Hawking radiation, wouldn't that lead to conflicting observations from a free falling observer (black hole does not evaporate because no loss of energy / mass because no radiation is emitted) vs. hovering observer (black hole does evaporate because it loses mass / energy due to Hawking radiation)?

Hawking's derivation predicts named radiation, but does that derivation also show that the black hole's mass is changing?

• If you're familiar with the derivation of the hawking effect, you'd find in some books that they compute the mean value of the energy momentum tensor. What you see in this computation is that there is a negative energy flux going into the black hole, this means it is losing "mass" with mass meaning gravitational charge Feb 21, 2020 at 14:06
• What happens to that energy flux to an in-falling observer? Why does it vanish for her? No, I am not familiar with the derivation, just with a paraphrased version of it (all that I can grasp) like "some areas of spacetime are not accessible due to horizon, which results in radiation". As this derivation is very similar to Unruh radiation (of which I only have a popularized understanding, too) these effects appear to very similar. In particular because inertial observers see nothing special in either case. Feb 21, 2020 at 14:14
• If you are really interested to know why there is no contradiction , you should do some serious study so as to understand the mathematics of general relativity. The popularized versions are just that, for the people, and the true explanation is in the mathematics..see these answers , that a free falling observer does not define an inertial frame except locally Feb 21, 2020 at 14:52
• Are you saying that a free falling observer does see Hawking radiation becausr it is only inertial locally? Feb 21, 2020 at 15:15