What would the effects of an artificial gravity well/hole/ledge be? (Thought experiment)

[Zerilia]

What I'm talking about is more sci-fiy than anything it's probably not possible in a real life scenario, but I'm just curious what would be the result.

For example if we could somehow make an artificial gravity well that only works on a person and does not effect anything around them (on the fabric of spacetime it would basically look like a hole where the person is, while the surroundings outside that person are flat and not affected by the hole).

I'm curious of the possibilities of what could happen, with a higher gravity inside the hole, would the person inside be basically in slo mo compared to everything outside? How would it look from their perspective? Would more light enter their eyes from time dilation? Would they see everything in faster speed? With lowered gravity inside the "hole" (would be a ledge now), the speed of the surroundings should would reverse and they would be the fast ones.

If we increase the gravity would the person look red from the redshift? Also if we increased to the point of a singularity would it just look like a black spot in the shape of a human? Could a person survive in that hole since they aren't accelerating towards anything or does the math break so much we can't really figure that out.

Maybe my theories are just plain wrong, but I think its an interesting concept even though it's not really doable in practice, but the effects of it would be real. Overall it's more or less just a thought exercise. Would like to hear your thoughts.

[Genady]

I don't get what is special in this thought experiment. I see just a standard situation with two places where gravity in one is stronger than in the other.

[beecee]

25 minutes ago, Zerilia said:

I'm curious of the possibilities of what could happen, with a higher gravity inside the hole,(1) would the person inside be basically in slo mo compared to everything outside? (2) How would it look from their perspective? (3)Would more light enter their eyes from time dilation? Would they see everything in faster speed? (4)With lowered gravity inside the "hole" (would be a ledge now), the speed of the surroundings should would reverse and they would be the fast ones.

To the (1) highlight, yes. (2) highlight everything would appear as normal in each and every frame of reference, to anyone in that frame of reference.From the (3) highlighted bit, yes, that is how they would observe anything outside their FoR. With the (4) highlight, again everything from any FoR, to anyone in that FoR, would appear as normal...1 second will pass as 1 second, it is only when comparing the elapsed time within, to the elapsed time outside, that discrepencies would surface.

33 minutes ago, Zerilia said:

(5)If we increase the gravity would the person look red from the redshift? (6)Also if we increased to the point of a singularity would it just look like a black spot in the shape of a human? (7)Could a person survive in that hole since they aren't accelerating towards anything or does the math break so much we can't really figure that out.

With the (5) highlight,  Gravitational redshift would be obvious to anyone outside that gravity well. With the (6) highlight, increasing the gravity so that the escape velocity exceeds "c" would create a BH, and nothing can ever get our beyond the EH of that BH. With(7) highlight, any person/thing within the EH of a BH, will always only ever have one direction...towards the central core and the singularity. He would be likley spaghetiffied and torn asunder into his most basic constituents, as the singularity was approached. How long he could survive would depend on the size of the BH...A SMBH could see someone survive for a time, as the tidal gravitational effects between head and feet would not be as severe.

[Zerilia]

Sorry if I confused anyone with my wording, I was kind of thinking in the line of the gravity well being in the 3d shape of a person like this (you could just imagine the hole as that person).

Since that way someone else could be 5 meters away from the person inside it and be unaffected by any effects of it. I guess in the same normal rules of relativity would apply, just on more visible/personal level.

[Janus]

From your image:

Depth of the hole would be the difference in gravitational potential.  The " steepness" at any point is local gravitational strength.

So, from this diagram, local gravity would be zero both inside and outside of the "hole".  The walls (if straight up and down) would represent infinite gravitational strength over zero distance.  (Not a realistic scenario) The edges between the walls and the flat areas would have an infinite tidal force.

Since gravitational time dilation is related to difference in gravitational potential and not a difference in gravitational strength,  Time would run slower at the "floor" of the hole by an amount determined by by the depth of the hole.

[MigL]

In addition to Janus' post, as far as I know, a 'square well' potential is impossible with gravity.
Certainly there can be no solutions to the EFEs as the manifold is not continuously differentiable.