Accelerating Body Creates Space-Time Curvature?

[DarkMattrHole]

TL;DR Summary

Does an accelerating body cause a local curvature of space-time or gradient and wave-front?

If you are floating in space in your spaceship and you kick in the engines and accelerate at a comfortable 1G and you end up standing on the bottom of your ship, a slight curvature of space-time is formed, throughout the ship, perhaps immeasurable, such that without windows on the ship, you might think you were still on the ground, and with a God's eye view of the curvature throughout the ship (or real good equipment) you would measure it to be the same as found on the surface of earth, is that correct? Either way the answer is always interesting, often surprising. thanks.

 

[Dale]

Summary:: Does an accelerating body cause a local curvature of space-time or gradient and wave-front?

is that correct?

No. Curvature is related to tidal gravity and there is no tidal gravity in that scenario.

 

[Nugatory]

The

and with a God's eye view of the curvature throughout the ship (or real good equipment) you would measure it to be the same as found on the surface of earth, is that correct?

Not correct. The gravity-equivalent effect produced by acceleration has nothing to do with spacetime curvature - the spacetime is still flat - and if your measuring instruments are sufficiently accurate they will detect differences from what you’d find on the surface of the earth, where the curvature really is non-zero.

The difference is the lack of tidal effects on the accelerating ship. On the accelerating ship, two objects dropped from the same height at the same time will be exactly as far apart when they hit the floor as when they were dropped, while on the Earth they will have moved a bit closer together. On the accelerating spaceship two objects released from different heights at the same time will maintain the same separation, while on the Earth they will move a bit farther apart. Both of these are tidal effects, present in the curved spacetime around the Earth but not present in the flat spacetime of the accelerating spaceship.

 

[DarkMattrHole]

Thanks guys. I think i can see the tidal difference you would measure.
Is the tidal effect the way all vectors point to the center of mass of an attracting body? If so, being close to the center of a small planet, one would measure trajectories or vectors converge more sharply, but strength of field may be less than large planet with more distant center of mass.

 

[Dale]

Yes, that is correct.