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EDIT: See my answer. Question is malformed as it was based on the assumption that something like Hawking radiation (i.e. mass draining) occurred prior to the formation of the event horizon based merely on the mass of the object.

This is essentially the version of this question that asks Hawking radiation be thrown into the mix. I've attempted to describe the scenario for the most part in terms of observational compatibility and only a few GR terms to minimize the chance my ignorance will render the question incoherent.

Can one construct (or prove existence of) a spacetime compatible both with both Hawking radiation and an infalling observer following a collapsing star's surface down with an event horizon in their future.

The concern being that Hawking radiation might melt away the concentration of matter too quickly for the infalling observer to ever reach the event horizon. I suspect the answer to this question will simply be "Yes, such a solution can be proved to/suspected to exist" but that will finally explain to my why (not if since I do assume physicists know what they are doing) Hawking radiation doesn't let us dispense entirely without trapped surfaces in our GR solutions by melting the almost black-holes before they pass that final threshold.

I'm not interested in QM style answers about particles having to cross the event horizon for Hawking radiation. I just want the answer if you calculate dumbly in classical GR with the equations governing rate of mass loss from Hawking radiation just taken for granted without presuming any particular mechanism or complex/controversial possible GR/QM interaction.

This question is somewhat similar to this question but it differs in that I'm not asking about solution to the information paradox or anything of the kind. I just want to know what kind of solutions one gets by simply stupidly combining Hawking radiation and GR since such a solution would seem to be what is needed to raise the information paradox in the first place. In particular, shouldn't the answer to this question have to be YES to send people out looking for other less stupid ways to confront the information paradox?

As an aside, would the answer change if bodies very very close to generating an event horizon emitted Hawking radiation?

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  • $\begingroup$ How do you "tack on" Hawking radiation? Once the black hole/horizon loses energy by it, it cannot be a pure GR solution anymore since classical GR doesn't have Hawking radiation. Also, your second paragraph (the actual question) seems grammatically ill-formed, maybe proofread that sentence again. $\endgroup$ – ACuriousMind Dec 19 '17 at 12:49
  • $\begingroup$ I mean ignore the process just plug in the equations governing rate of mass loss derived from QM and don't ask questions about why or other complex possible effects. $\endgroup$ – Peter Gerdes Dec 19 '17 at 12:53
  • $\begingroup$ But, again, then your solution is no longer a "GR solution" - you've used an evolution equation for the spacetime (since the mass is a parameter of the spacetime) that's not just the EFE, and indeed likely inconsistent with the EFE. I don't understand how you intend to have this process yield a consistent solution instead of just a contradiction. $\endgroup$ – ACuriousMind Dec 19 '17 at 12:58
  • $\begingroup$ THAT (the intuition that this would be inconsistent without heavy theoretical lifting) is exactly what I wanted to know. $\endgroup$ – Peter Gerdes Dec 31 '17 at 10:19
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This question is malformed as the underlying assumption was that Hawking radiation or something like it would occur as the infalling star approached the point it would form an event horizon. As ACuriousMind points out assuming the mass is just vanishing once it has already formed such an event horizon would be obviously inconsistent with GR. So even if no one else has been enlightened I finally understand why the answer isn't just 'well black holes don't actually form only things coming very very close do'....it's only once the actual event horizon forms that we predict Hawking radiation with our current theories (and at that point any solution requires stepping outside of GR)

However, the question remains if the speculations mentioned in this question about Hawking radiation before the formation of the horizon turn out to be valid. But the impression I got was this was quite speculative.

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