Velocity of light in accelerating spaceship and local inertial frames in GR

[Ratzinger]

1.What happens to the velocity of light measured by a spaceship that is in accelerating motion away from the light source ( light source and spaceship on the x-line)?

2. Inertial frames are only defined locally in GR. That means the falling elevator has to be small. But I think local also means just for short amount time. Why is that? Why local in time?

thanks

 

[Perturbation]

An event is by definition a point in Minkowski space-time. The elevator at some height above the ground whilst accelerating is an event that occurs at a point in time. Something that lasts a period of time consists of a set of events. Events have to be local in time and space. That and space-time in GR is a pesudo-Riemannian manifold, where the curvature is not limited to merely space but time also, and so the time measured in some extended non-local region will differ to that in a local frame of reference.

 

[yogi]

Question 1: The accelerating spaceship is no different than a local G field. SR presupposes that at any instant photons will always be measured to pass the ship at a measured velocity c - but there will be a frequency shift just as there would be if the spaceship were standing still in a comparable G field.

Guestion 2 - In a G field the acceleration increases as the object moves closer, so any measurements must be made in a short amount of time because the G potential is continually changing

 

[Hurkyl]

1.What happens to the velocity of light measured by a spaceship that is in accelerating motion away from the light source ( light source and spaceship on the x-line)?

It will always be c.

Incidentally, if the spaceship is unformly accelerating for all eternity, it will observe the frequency of the light constantly decreasing towards zero. It will only receive a finite amount of the light transmitted by the source.

(Analysis done in SR)

2. Inertial frames are only defined locally in GR. That means the falling elevator has to be small. But I think local also means just for short amount time. Why is that? Why local in time?

For the same reason local in space: "negligible" effects accumulate and become non-negligible over an extended period of time.

 

[Ratzinger]

thanks!

but...

In a G field the acceleration increases as the object moves closer, so any measurements must be made in a short amount of time because the G potential is continually changing

The field is getting stronger the closer the elevator gets to the planet surface. So that alone makes the field inhomogeneous and spacetime curved ( very slightly) and necessitates a very small elevators also to exist only for short times in order to be inertial?

A gravity field had not to vary with direction (as for spherical mass objects) and not to fall off with distance to allow 'more' global inertial frames free falling in it. Or not?

 

[Ratzinger]

Hello?!

I'm still not fully clear why also time needs to be local if already space is local. Why the elevator is required to be small and to exist only for short times.

Any input is apreciated.

thanks