SR vs GR Simultaneity: Comparing Moving & Static Observers

[smoothoperator]

In SR, we may choose any inertial observer and his reference frame at which he is at rest, and other observers are movin wrt to him. All the moving observers 'slice' spacetime in a different way than the observer at rest, at different angles relative to his simultaneity surfaces. This is all flat space time nature.

My question is, how does this translate to GR and curved space time? How do different observers slice curved space time and what does it look like compared to SR. I know that we have hovering observers and relative to them clocks far away form gravity run faster etc. What about moving observers (free falling observers) and the simultaneity slicing while gravitational time dilation is present? And please don't say that any coordinate system is acceptable, I know that, and my question is basically the comparision in simultaneity differences between moving and static observers in SR and GR.

Thanks in advance.

 

[Orodruin]

This depends completely on how you wish to define simultaneity in GR. In SR there is a natural choice, but this is no longer true in GR. You might think of creating the spacelike hypersurface created by taking the union of all geodesics orthogonal to an observer's world line, or simply take a spacelike coordinate surface. However, my preeference is to simply acknowledge that simultaneity is a convention in SR that does not necessarily have a unambiguous counterpart in a general spacetime. This is why your question will normally be met with the "any coordinate system goes" reply.

 

[seaocean1234]

When you say GR, what do you mean, 1916 or 1917? Also, when you say SR what do you mean, 1905 or 1917? Be specific, please. Also, when you say time space, what structure are you using, Maxwell's equations (cannot use timespace [a coordinate system] without a structure, can you)? But is not Maxwell's equations derived using Faraday's induction law that is not optical, and isn't Hertz's spark gap emitting electrons? Is an induction current the same as an ionization current?

 

[PeterDonis]

When you say GR, what do you mean, 1916 or 1917? Also, when you say SR what do you mean, 1905 or 1917?

He means SR and GR, the current scientific theories. If there were different versions of those theories in prior years (I'm not sure why you are picking the particular years you are picking), that's a matter of history, not physics.

when you say time space, what structure are you using

In SR, Minkowski spacetime. In GR, whatever solution of the Einstein Field Equation is being discussed.

Maxwell's equations

Are not a "time space structure".

is not Maxwell's equations derived using Faraday's induction law that is not optical, and isn't Hertz's spark gap emitting electrons? Is an induction current the same as an ionization current?

This is irrelevant to the topic of this thread. Please start a separate thread in the appropriate forum if you have questions about Maxwell's Equations or electrodynamics.

 

[bcrowell]

Basically Orodruin's #2 is the answer to the question. However, there are certain specific cases in GR where one notion of simultaneity is more natural than another. For example, in a cosmological spacetime we have a preferred time coordinate, which is the time on a clock that is at rest with respect to the Hubble flow. In an asymptotically flat spacetime, you can essentially use SR's notion of simultaneity for distant regions.