If no signal can overtake a photon, then disassembling a Schwarzschild black hole does not seem to succeed
Suppose that we send a symmetric photon sphere down a Schwarzschild black hole. Let us then overspin the black hole. It looks like that no change in the metric can overtake the photons. The metric below the forming horizon, and all the matter there remains exactly like in the Schwarzschild black hole. Nothing can ever come out.
Movement by a "translation"
If no change in the gravity field can overtake a photon, and the local speed of light (in Schwarzschild coordinates) is very slow inside a heavy neutron star or a black hole, then it may take very long for anything to change inside the neutron star or black hole.
But we must be able to move the neutron star or a black hole in a binary star. We have suggested that a "translation" implements the movement. The idea is that in the Einstein-Hilbert action we accept paths where a part of the system moves as a whole. Moving as a whole means that all matter and the metric move as is. An observer inside the translated volume does not notice any change.
Let us start to rotate a Schwarzschild black hole. Then the inside of the black hole and a thin layer above the forming horizon would move through a translation.
A translation can be understood as "total" frame dragging.
A translation in the context of electric fields
Suppose that we have a block of an electric insulator. We assume that the speed of light is very slow inside the insulator, but the speed of sound in the material is close to the speed of light in vacuum. The block is electrically charged.
|
| field line
___
/ + \ _____
\____/ ● - Q charge
insulator
The electric field of the charge Q interacts of with the electric field outside the insulator and pulls the block as a whole. It is not necessary that the field of Q meets with the charge inside the insulator at all.
The insulator is very much electrically polarized. The charge Q actually interacts with the induced charge close to the surface of the insulator.
Here we have a model where the center of the insulator remains oblivious of the field of Q, but the center is pulled along as the block starts to move.
The center is pulled by stress forces (pressure) within the insulator. In this model, there are faster than light signals.
Stress forces (sound) propagate much faster than electromagnetic fields inside the insulator.
What if the speed of sound is slow, too?
Then the inside of the block stays static while the surfaces start to move. The charge and the matter inside the block is pressed against one side of the block.
The movement of the block would appear strange to an external observer.
An aside: interpreting the Schwarzschild gravity through polarization
In our example of an electrical insulator, polarization has two effects:
1. it slows down light,
2. it reduces the electric field inside the insulator.
For gravity, we have item 1, of course.
The gravity potential in the Schwarzschild solution is steeper than in newtonian gravity. Hypothetical polarization draws mass-energy in the surrounding empty space closer to the mass. The polarization would then make gravity stronger.
A translation in our own Minkowski & newtonian gravity model
In general relativity, gravitational forces and fictitious acceleration forces, like the centrifugal force, are treated as a whole, in the metric. The Moon orbits Earth in the Schwarzschild metric. There is no separate gravity force and centrifugal force.
Our own gravity model claims that gravity is an ordinary force and does not have a special status. There have to exist separate fictitious acceleration forces.
___
/ \
\____/
compact, massive
object
Hypothesis. In a compact massive object, all parts acquire a large amount of inertia from other parts. It is like a gearbox where turning any cogwheel involves inertia from other cogwheels. Different parts of the object can communicate through the inertia mechanism with the "combined" field of the "whole object". The communication speed is the speed of light in the spatial volume surrounding the object.
If we have a compact object, we can make it to move as a whole by exerting an external force. This is obvious from binary neutron stars and black holes.
The idea in the hypothesis is that the gravity of the object itself cannot slow down communication with the "combined" field of the "whole object".
But if the object is in the gravity field of another object, then the communication is slowed down by the field of the other object. This preserves an equivalence principle.
An object cannot use a "Baron Munchausen" trick of slowing down its reaction to external forces. Such a trick might break conservation laws. But the object can slow down its internal processes through the inertia which it imposes on its parts.
Our hypothesis is vague. We have to find a precise mathematical formulation.
No communication is allowed to happen faster than the speed of light of the surrounding empty space. In this way we avoid time travel paradoxes.
Accelerating a compact object in the Minkowski & newtonian model
Let us then assume that we, by some means, are able to accelerate (linearly) a compact object. A crucial question is if an observer inside the object can feel an acceleration, and how quickly.
___
/ • m\ ---> acceleration
\____/
compact, massive
object
Let us have a test mass m inside the compact object. The test mass m has acquired a lot of inertia from the field of the object. It sounds natural that the acquired inertia tends to move with the compact object.
What about the inertia of the mass m itself? That inertia would probably cause m to lag behind. But since all the surrounding matter behaves in the exact same way, an observer riding on m would not notice anything.
A linear translation in the Minkowski & newtonian model looks very much like the one in general relativity. However, there is slight squeezing and compression because the amount of inertia depends on how far the test mass m is from the center.
If we start to rotate the object, there is an associated fictitious centrifugal force. If the object is strong enough not to come apart, an observer feels a centripetal acceleration. If the object starts to disintegrate, then an observer sees radial distances of particles start to grow.
Conclusions
If we assume that in general relativity no change in the metric can overtake a photon, then it looks like one cannot disassemble a Schwarzschild black hole by overspinning it.
Textbooks on general relativity are vague about if a change of the metric can spread faster than a photon.
In our own Minkowski & newtonian gravity model, it might be possible to disassemble the black hole. This requires that the inertia of the field can communicate at the light speed of the surrounding space. It must be able to communicate faster than the local speed of light.
We have to look further into the Kerr metric of extremal spinning black holes. That may offer us clues if an overspun black hole really comes apart.
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