Lightwave moving towards/upwards curvature

[Domenicaccio]

I don't know why this question puzzles me...

I believe I can understand the general idea that a lightwave moving in the vicinity of a source of gravity would be deflected by it, as in the "rubber sheet" model, and would curve slightly towards the mass.

But is this also valid when the light is traveling along a direction that directly passes through the mass?

It would seem impossible for a lightwave going straight into a large mass to be accelerated from it, since it cannot accelerate further beyond c (e.g. a ray of light from sun to earth).

And at the same time it would seem impossible that the lightwave would be "slowed down" when moving straight away from the mass (e.g. an EM wave generated on Earth and sent to space).

So does the curvature have an effect only to the lightwave's trasversal movement?

But OTOH gravity/curvature does indeed have an effect on anything non-relativistic (a "slow" mass) in a radial direction.

How do you link all these things together?

 

[Domenicaccio]

Any guess?

 

[granpa]

gravitational time dilation.

 

[Domenicaccio]

gravitational time dilation.

Could you please put it down in formulas?

If the lightwave goes towards a huge mass, what would an observer on the lightwave register (in terms of time dilatation) and what would instead another observer looking at the lightwave from afar see happen to the wave?

 

[granpa]

i don't have any formulas. if a light wave moves through a gravitational field then it should be slowed by gravitational time dilation. that should have the same effect as moving through a material with lower refractive index. the light wave should be bent.

 

[Domenicaccio]

i don't have any formulas. if a light wave moves through a gravitational field then it should be slowed by gravitational time dilation. that should have the same effect as moving through a material with lower refractive index. the light wave should be bent.

Ok but what if the light wave travels TOWARDS the mass?

 

[granpa]

it would be slowed but nobody there would notice since they would also be slowed. locally, its speed would still be c.

also i think space itself is stretched so there is more space for the light wave to cover.

 

[yuiop]

Ok but what if the light wave travels TOWARDS the mass?

Over a large scale a light wave slows down as it travels towards a gravitational mass. That is called the coordinate speed of light. On a small scale gravitational time dilation and length contraction ensure an observer anywhere in the gravitational field measures the speed of light as c in their immediate vicinity. The equivalence principle also makes it clear that a free falling observer will also see the speed of light as constant in his immediate vicinty. The constant local speed of light according to any observer accelerating or not is an important concept in general relativity.

However...

If a mirror is placed on the surface of a gravitational body a signal sent from an observer 10 light seconds above the surface will take more than 20 seconds to travel down and reflect off the mirror and return to the observer. Some people like to think the light has taken a detour through an additional invisible dimension to account fo the extra time taken. This is akin to the deformed rubber sheet analogy. The trouble with the additional dimension explanation is that it has difficulties explaining why the two way trip takes less than 10 seconds according to an observer on the surface of the body. The same logic implies that the photon has somehow taken a shortcut through the addititional dimension. A possibly better analogy is that the gravitaional body is surrounding by an imaginary medium that increases in density towards the surface of the body. It is easy to imagine that the light slows down as the density (or the refractive index) of the imaginary medium increases. Of course all the above implies that the photon accelerates as it moves away from a gravitational body (on a large scale) which is probably exactly the opposite of what you would assume it would do.