We claimed that an observer falling into a Schwarzschild black hole is frozen close to the horizon and never reaches the horizon. The speed of light is zero at the horizon. We claimed that the observer cannot move faster than the speed of light.
However, we we not sure what happens inside the horizon. Can matter still move there?
In traditional newtonian gravity (in the style of the year 1687), a collapse of a dust ball does end up in a singularity. Can this happen in our Minkowski & newtonian model?
Our considerations of a collapsing sphere of dust in the blog posts October 16 and 18, 2021 suggest that collective movements of matter can still happen inside the horizon. In our example of the two neutron stars approaching each other, the speed of light inside the star and near it can be close to zero relative to the moving mass, but the neutron stars still move at a great speed.
Syrup and pancakes. Photo https://www.publicdomainpictures.net/en/view-image.php?image=242756
It is like syrup: an observer finds it impossible to move quickly relative to the syrup, but the syrup can still flow fast.
The mass-energy of a collapsing star is huge. Even if an individual test mass inside the horizon would appear to have negative energy, the collective material holds firmly positive energy. Thus, the problem of a negative mass-energy does not really appear in a collapsing star.
Hypothesis. A collapse to a black hole is essentially a traditional newtonian (1687) collapse, where the collapsing matter and the space near it is "syrup": an observer finds it impossible to escape from the collapse. He is stuck in the syrup.
Our Minkowski & newtonian model starts to resemble general relativity more and more.
Question. How does the syrup behave? Can it flow all the way to a singularity? Or does pressure from some other force win gravity?
If we dethrone gravity from position as the geometry of spacetime, and demote it to an ordinary force, then the Einstein-Hilbert action may allow very large pressure from some other force to stop the contraction of a star.
We showed in our October 16, 2021 blog post that a sudden increase of pressure breaks the Friedmann equations. In an Oppenheimer-Snyder collapse, the internal metric of a collapsing uniform ball of dust is the FLRW metric, that is, a solution of the Friedmann equations. But pressure breaks those equations. The road to singularity is not so simple then.
If we again look at the newtonian gravity (1687) analogue, there strong pressure does stop the contraction, though a dust ball would collapse to a singularity.
Question. What happens to a small test mass which we drop to the horizon of an old black hole? Does it "go with the flow", or freeze just above the horizon?
Close to the horizon, a clock ticks extremely slowly because its mechanical parts have huge inertia, and non-gravity forces are extremely weak. However, the inertia probably cannot exceed the mass of the black hole, and the progress of the test mass downward is not dependent on non-gravity forces. The test mass might slip through the horizon in a finite time.
The waterfall and sound analogy of a black hole and a neutron star
The syrup model reminds us of the waterfall analogy of a black hole. Close to the waterfall, the water flows faster than the speed of sound in water. The event horizon is at the point where the speed of water is equal to the speed of sound. A sound wave behind the horizon cannot escape.
The corresponding analogy for a neutron star is a waterfall where the speed of water does not exceed the speed of sound. A sound wave can escape, but it moves slowly against the flow of water.
In these analogies, the flow of water is created by the mass itself. A single sound wave cannot escape from behind the horizon, but through a collective effort, the mass itself might be able to escape.
A white hole is a waterfall with time reversed. We may imagine that it is the movement of the great mass upward which forces the water to flow up in the waterfall.
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