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I have a question about the conformal diagram of an ‘astrophysical’ black hole which forms in finite time (but with no evaporation).

Usually I see the conformal diagram presented as something similar to

enter image description here

I understand that the $r=2GM$ surface is null so it must occur at a 45 degree angle on the diagram. Yet drawing this line straight backwards from where the exterior of the objects reaches $2GM$ seems to impose conditions on how the interior of the object will collapse in time. Is this the case? Is there an example of constructing such a diagram for an object with specified matter density? I am especially curious what would occur if the object evolved in such a way that the critical threshold was crossed at the same coordinate time for all radii within the object.

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  • $\begingroup$ My thinking is that this transition needs to be smooth, and the only way for the horizon to appear smoothly is as a single 45 degree line which all the interior radii will intersect. My guess is then that the time coordinates on the conformal diagram will warp to accommodate how the physical object actually collapses, but the boundaries of the conformal diagram will look the same. $\endgroup$
    – Liam Bonds
    Commented Apr 20, 2023 at 22:51
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    $\begingroup$ Have a look at my answer here and at papers referenced in it. $\endgroup$
    – A.V.S.
    Commented Apr 23, 2023 at 4:21

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