Questions regarding Hawking radiation

[ShayanJ]

Not good for Hawking radiation being a reliable thing if it depends on this. This would mean that we have to know the future to find out if there is Hawking radiation or not. Because you can easily define a time-like coordinate so that the horizon is formed only in the future. Schwarzschild time would do it.

I don't quite understand what you're trying to say.

As if this would prove anything.

Hm, let's try. Take a charge and move it, up and down, at home once in a second. What will be the wavelength of the EM wave created by this moving charge? What does this tell us about the size of the origin of this wave?

Here we're talking about particles. If there is an electron with de Broglie wavelength of the order of a stadium, it doesn't make sense to say where in the stadium that electron is.

 

[Ilja]

I don't quite understand what you're trying to say.

Hm, let's try again. I think a theory which predicts that I observe / do not observe radiation in dependence of some fact which happens only in the future, with everything which has already happened in the past, and up to now, being equal, would have a big problem with causality.

This holds for every time-like coordinate. If I have a time-like coordinate, and the fact if I observe Hawking radiation or not depends on something which is, according to this time coordinate, in the future, this sounds like a problem for Einstein causality, not?

For every event for an observer at infinity, who observes Hawking radiation, one can easily find a time-like coordinate where the horizon is not yet formed. Outside the collapsing body, standard Schwarzschild time will define one such coordinate. So, your claim
"The presence of the horizon matters. Its not like we need a special place for Hawking radiation, we need the horizon itself."
suggests me that such a position has a serious problem with Einstein causality.

In my opinion, all what can matter for the prediction of Hawking radiation at some far away event is what is part of the past light cone of this event. And this part does not contain any horizon, for all those events horizon formation is yet only future, so that it may be not even certain if a horizon will form or not.

Here we're talking about particles. If there is an electron with de Broglie wavelength of the order of a stadium, it doesn't make sense to say where in the stadium that electron is.

Sorry, no, I'm not talking about particles. I'm talking about radiation. And I know that to attribute a position to a photon is not unproblematic, so I do not talk about such positions. I was talking about the region which has caused the radiation. My example suggest that such a region may be much smaller than what the wavelength suggests.