Let an infinitesimal test mass m approach the black hole. Where is the event horizon in the new system?
• test mass m
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Oppenheimer-
Snyder collapse M
If the test mass would carry an electric charge, we know how the electric field would settle:
The diagram is from the paper by Hanni and Ruffini (1973):
Some lines of force would go extremely close to the horizon. From far away, it would look like that there is a negative induced charge at the locations where the lines of force approach the horizon, and a positive induced charge at the locations where the lines of force leave the horizon.
Perturbation of the event horizon
Suppose that an infinitesimal test mass dm approaches the horizon of a Schwarzschild black hole. What is the perturbation of the gravity field like?
It might be that the perturbation caused by dm is somewhat similar to the field lines of the electric test charge. Let us assume that dm falls on one side of the black hole. Let us study what happens to the field on the other side.
We assume that "causal" changes into a gravity field can propagate only at the local speed of light.
Suppose that dm would make the horizon to move dr farther. If dm is very small, it takes a very long time (in the global Schwarzschild time coordinate) for the metric close to the horizon to "know" that the horizon should be moved dr farther.
Is it so that in the Schwarzschild time coordinate, it takes an infinite time for the horizon to become "complete", in the sense that the metric of time at the horizon is zero?
Let us assume that the metric is "updated" to a new version in the order of a descending r coordinate. This is a natural assumption because it takes a very long time for light to reach points whose r coordinate is close to the old horizon.
A faraway observer sends down light signals which propagate a little behind the updating process. Let us assume that the metric is updated to a new Schwarzschild metric whose Schwarzschild radius is dr larger. It takes a long Schwarzschild time interval T for the light signal to come very close to the new Schwarzschild radius. If we assume that an observer sitting close to the new radius immediately sends the signal back, it takes another T for the faraway observer to receive the reply.
In this sense, we could say that the new Schwarzschild metric is never completed, from the point of view of a faraway observer.
Conclusion
In this blog we believe that the metric of spacetime near a mass is simulated by the gravity force through adding inertia to particles. Clocks tick slower when inertia is larger. The "true" underlying metric is the Minkowski metric - that never changes.
A question is if the inertia can become infinite. Then clocks would stop entirely. This does not sound right. Our hypothesis is that clocks can slow down arbitrarily much, but never stop entirely.
At the Schwarzschild event horizon, the metric of time would be zero. We try to show that such horizon can never form.
Since the speed of light (in the global Schwarzschild coordinates) is extremely slow inside a forming event horizon, does all movement essentially stop there? Is the frozen star model right? In a merger of two black holes, how do both objects get inside a common, spherical horizon, if nothing can move inside the horizon? We will look at this in the next blog post.
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