Do Different Observers Agree on Entropy in the Unruh Effect?

[naima]

As i was looking for what happens with a non eternally accelarated thermometer, i found this paper http://arxiv.org/abs/1307.4360
It is not surprising that if the thermometer's acceleration jumps from 0 to a at time 0 it will not "see" immediatly a thermal bath at temperature T.
This is not my problem. I read in this paper:
Unruh's classic paper offers an illustrative analog for the Hawking effect in black holes, often explained in terms of the geometric notion of an event horizon. However, there is no horizon for detectors undergoing non-uniform or finite-time acceleration.
I have problem with this sentence.
Does he say that at a given moment a Black Hole has no horizon for non eternal observers?

 

[Demystifier]

Does he say that at a given moment a Black Hole has no horizon for non eternal observers?

No, he does not say that. He does not talk about black holes, but about acceleration in Minkowski spacetime.

Concerning radiation from a black hole, the relevant horizon is the apparent horizon, not the event horizon. The event horizon is a property in the infinite future, while the apparent horizon is a property "now". For more details see also
http://lanl.arxiv.org/abs/hep-th/0106111

 

[naima]

Thank you very much Demystifier:
I did not know that there is a difference between these different horizons.
The "apparent horizon" in wiki is not obvious.
In his book Penrose writes that once a BH exists there is an horizon of points. behind it emitted light always moves inward. He calls that an event horizon or absolute horizon. Isnt it what other authors call "apparent horizon"?
Have you a link with clear definitions?Edit:
I found this link about http://www.fysik.su.se/~ingemar/relteori/Emmaslic.pdf
An apparent horizon is the boundary of trapped points. A point is trapped if it belongs to a trapped surface

 

[craigi]

http://arxiv.org/abs/hep-th/0403142

Abstract:The geometric entropy in quantum field theory is not a Lorentz scalar and has no invariant meaning, while the black hole entropy is invariant. Renormalization of entropy and energy for reduced density matrices may lead to the negative free energy even if no boundary conditions are imposed. Presence of particles outside the horizon of a uniformly accelerated observer prevents the description in terms of a single Unruh temperature.