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So lets say we have a neutron star that is just few inches away from the phantom horizon and only needs 500 kg before collapsing. So lets say hypothetically that a ship that is designed to survive the heat and gravity places a 500 kg object on the neutron star and the phantom event horizon covers the neutron star.

Does that mean the black hole instantly forms once the object is placed and would you see a dark region now? Or is there a delay, and you could still take the 500 kg object out and prevent the neutron star from collapsing?

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  • $\begingroup$ PSE has a 5-tag limit and its current repertory of tags does not include one for Einstein-Cartan Theory (AKA ECSK Theory after modifications by Sciama & Kibble), which reduces to GR in vacuum and was accepted by Einstein in a 1929 telephone conversation with the mathematician Cartan, as the singularity would be avoided by its application instead of GR's: ECSK (which allows a tiny spatial extent to fermions) reduces to GR in vacuum and forms the basis for Nikodem Poplawski's model (described in preprints visible under his name in Arxiv), which has some support in recent JWST observations. $\endgroup$
    – Edouard
    Commented May 28, 2023 at 18:10

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The collapse of a real star is fearsomely complicated. We have no analytic solution of the Einstein equation for it so we have to simulate it numerically on a very large computer. However there is an idealised solution called the Oppenheimer-Snyder metric that captures the main features.

Your neutron star is supported by the neutron degeneracy pressure i.e. the Pauli exchange repulsion between neutrons. When you add the last (500kg) straw to the camel's back the compression becomes too great for the Pauli repulsion to resist. The star starts to collapse, and the event horizon forms first at the centre and then grows outwards towards the surface of the star. The horizon passes through the surface when the surface of the star has collapsed inwards to a distance equal to the Schwarzschild radius:

$$ r_s = \frac{2GM}{c^2} $$

The rate at which the horizon moves outwards depends on how fast the star collapses, and in real stars is likely to be a goodly fraction of the speed of light.

So if you place your 500kg object on the star to start the collapse you would have a few microseconds to pull it away again before the event horizon reaches the surface of the star. Note that pulling the object away will not stop the star collapsing. Once you have triggered the collapse it will continue until the star is consumed whether you pull the object away or not.

What you and the object would see is surprisingly complicated. For any observer outside the horizon it takes an infinite time for the horizon to form. That is, for an external observer the horizon never forms. However you would see an apparent horizon form in a few microseconds and this would be so similar to a real horizon that you could not tell the difference.

If you remain on the surface of the star as it falls inwards, so you fall inwards with it, you would see the horizon remaining just below you. As you fall in the horizon appears to retreat before you. You would only reach the horizon when you hit the singularity at the centre of the black hole.

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  • $\begingroup$ What if you pull the 500 kg object instantly before, then does that prevent the event horizon from forming in the core? What if the 500 kg is inside the phantom event horizon but not in contact with the surface? $\endgroup$ Commented May 28, 2023 at 16:32
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    $\begingroup$ What is the difference between the apparent horizon and the actual event horizon? $\endgroup$ Commented May 28, 2023 at 16:36
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    $\begingroup$ It's not supported by Fermi repulsion between neutrons. It might be supported by strong force repulsion between neutrons (if neutrons still exist at those densities). $\endgroup$
    – ProfRob
    Commented May 28, 2023 at 16:38
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    $\begingroup$ "The rate [...] is likely to be a goodly fraction of the speed of light." - it can't be less than $c$, or else you could escape the interior by outrunning it. It also can't be greater than $c$ except on a set of points of measure zero, or else there would be unescapable points in the exterior. Faster-than-$c$ expansion (on a set of measure 0) does happen in black hole mergers and would probably happen in this anisotropic collapse. $\endgroup$
    – benrg
    Commented May 28, 2023 at 18:35
  • $\begingroup$ @JohnRennie "However there is an idealized solution called the Oppenheimer-Snyder metric that captures the main features." I am afraid that solution is inappropriate to capture the main features of the collapse because matter follows the so-called Quasi-geodesics and not the geodesics like pressureless dust. What is your opinion about that? $\endgroup$
    – JanG
    Commented May 29, 2023 at 15:20

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