I Falling through the event horizon of an evaporating black hole

[PeterDonis]

As with all derivations you start with some assumptions and derive some conclusions. When the assumptions are violated the conclusion doesn’t follow.

To expand on my comment in post #50 just now, let's go back to your original post referencing the paper:

In an eternal black hole, all maximally extended geodesics that cross the event horizon reach the center in finite proper time. In an evaporating black hole there are geodesics that reach the center in finite proper time before it evaporates and these are what form the interior of the horizon.

https://arxiv.org/abs/1102.2609

As far as I can tell, Section II.B of the paper, titled "The forbidden region of light cone", is saying that there are no geodesics at all that reach $r = 0$ during the period after the horizon of an evaporating black hole forms but before it evaporates. This appears to me to be the basis for the paper's claim that it is impossible to have an event horizon that forms and evaporates. In other words, the paper is claiming the opposite of what you say in the bolded portion of the quote above.

The paper appears to be basing this on the assumption that the energy conditions are satisfied. But, as I have said, it has been known since the 1970s that black hole evaporation must violate the energy conditions. So the paper is just rediscovering, in a roundabout way, what has been known since the 1970s. (But it's not clear to me that the author of the paper actually recognizes that.)

 

[Dale]

As far as I can tell, Section II.B of the paper, titled "The forbidden region of light cone", is saying that there are no geodesics at all that reach r=0 during the period after the horizon of an evaporating black hole forms but before it evaporates. This appears to me to be the basis for the paper's claim that it is impossible to have an event horizon that forms and evaporates. In other words, the paper is claiming the opposite of what you say in the bolded portion of the quote above.

Yes, I misunderstood that. The paper doesn’t describe the metric I thought it did. It has the same limitations as the Viadya metric.

if the assumptions are ones that have been known to be violated by evaporating black holes for almost four decades at the time a paper using those assumptions but purporting to be about evaporating black holes is written, then the paper would seem pointless

This is an opinion I don’t share. Lots of proofs of impossibility have some assumptions that are known to be violated and yet are not pointless, IMO. The 2nd law of thermo and Earnshaws theorem come to mind. If you want to single this paper out as uniquely pointless or if you want to broadly paint all such proofs as pointless, that is your choice.