Cosmological Redshift in Simulated Universe

[Ibix]

Which observers (besides the one stationary to the hole) can tell that as the shuttle moves faster away from the hole, a greater percent of the light from each flash is being gravitationally redshifted on account of a greater percentage of light moving away from hole (more percentage of light bent towards direction of travel close to light speed relative to hole)?

There is no "can tell" here. No perspective is right or wrong here.

From the point of view of observers at rest with respect to the hole, the light pulses are increasingly beamed away from the hole.

From the perspective of the ship the hole is accelerating away and simply becomes a smaller target so less light hits the hole, but the same amount is launched within 90° of the line to the hole.

From other perspectives the beaming may be towards the hole and reducing, or the beaming may be at an angle to the hole.

In all interpretations actually measurable quantities (like the mass increase of the hole) are the same, but for different reasons and at different rates.

 

[Devin-M]

An observer could be in free fall and reach apogee after initially moving away from the hole, thus be momentarily hovering but also in free fall. If a flashbulb went off on board at apogee, could photodetectors also on board see some light moving towards the hole blueshifted and the some light moving away from hole redshifted?

 

[Ibix]

It does not matter how many times you ask that question. The answer will not change from the one given in #2, #4, #7, #11, and probably others.

 

[Devin-M]

Ok, so we’re invoking the equivalence principle to answer my original question, but on the wikipedia page for equivalence principle it says:

“Here local means that experimental setup must be small compared to variations in the gravitational field, called tidal forces. The test experiment must be small enough so that its gravitational potential does not alter the result.”

Source: https://en.m.wikipedia.org/wiki/Equivalence_principle

Can the equivalence principle really be used in the situation I described, where in the frame of the “cloud” a photon is traveling 46 Gly from edge to center, but in the frame of the “hole” the photon is traveling much farther because the cloud moves very close to the speed of light relative to hole. Is that really small and local enough and absent of tidal forces over the time of flight of the photons in question to use the equivalence principle?

 

[Devin-M]

very large, accreting black hole

I also should have been more specific about what I meant by the “accreting” black hole. I meant the “cloud” moves away from the center of the black hole very close to the speed of light, but the black hole is growing rapidly enough that the event horizon is approaching the cloud, even though the cloud moves away from the center of the hole. In other words the black hole’s event horizon is expanding faster than the cloud recedes from the center of the hole. So even though the cloud is moving away from the center of the hole, the event horizon is actually moving towards the cloud.

 

[PeterDonis]

Can the equivalence principle really be used in the situation I described

Yes, because, as @Ibix has already pointed out, the size of the cloud is small enough compared to the size of the hole that tidal gravity due to the hole can be ignored in the region occupied by the cloud.

 

[Ibix]

in the frame of the “cloud” a photon is traveling 46 Gly from edge to center, but in the frame of the “hole” the photon is traveling much farther because the cloud moves very close to the speed of light

As already answered, yes. If you want to think about changing gravitational time dilation you also need to think of the changing speed of the cloud and the effects this has on clock rates and time taken to absorb a cycle of a light wave. You seem to be consistently ignoring this in your thinking.

Again as already stated, sufficiently precise experiments could detect the failure of spacetime to be flat, which would yield anisotropies, but no global redshift. However, tidal effects are weaker the larger the black hole, so these are very small for this scenario.

 

[Devin-M]

Is a growing event horizon constrained to the speed of light relative to an observer hovering at fixed altitude above the center of the hole?

If the hole wasn’t growing, the clocks in the cloud would be ticking faster as they coasted away from the hole. But if the event horizon was growing fast enough to move towards them, would the “cloud clocks” be slowing down and would this have any effect on their observations of flashes of light in the cloud? The flashes of light are losing gravitational potential energy as they coast upwards, but the observers clocks would be slowing down rather than speeding up as the event horizon approaches them.

 

[Ibix]

Is a growing event horizon constrained to the speed of light relative to an observer hovering at fixed altitude above the center of the hole?

An event horizon is a null surface. To the extent it has a speed, it is always $c$ whether it is growing, shrinking, or static.

But if the event horizon was growing fast enough to move towards them, would the “cloud clocks” be slowing down and would this have any effect on their observations of flashes of light in the cloud?

The equivalence principle is a foundational principle of general relativity. You cannot get round it by adding bells and whistles to a scenario. You can just make your scenario so complicated that you don't understand how to connect your thinking to that foundation. This is especially true with your maths-free approach.

So I refer you to my previous answer.

 

[PeterDonis]

I refer you to my previous answer.

And with that, the OP question has been more than sufficiently answered, and this thread is closed.