What is the speed of light in gravity?

[Zman]

“It is a well proven fact, that the speed of light is reduced in a gravitational field. As a consequence, a light beam, which passes a big object, is bent towards the object.”

I read the above quote on the internet but I am not sure if it is a well proven fact that c is reduced in a gravitational field.

What is the accepted wisdom in physics on this issue?

 

[George Jones]

It depends on what one means by "the speed of light".

All observers who measures the speed of a photon that whizzes by in their local (vacuum) neighbourhoods, near or far from large masses and even inside black holes, get the same result c.

 

[A.T.]

“It is a well proven fact, that the speed of light is reduced in a gravitational field. As a consequence, a light beam, which passes a big object, is bent towards the object.”

I read the above quote on the internet but I am not sure if it is a well proven fact that c is reduced in a gravitational field.

Near a big mass the speed of light is reduced when measured by a distant clock. Measured locally it is still c due to gravitational time dialtion:
http://en.wikipedia.org/wiki/Gravitational_time_dilation

The same happens in accelerated frames of reference;
http://en.wikipedia.org/wiki/Propagation_of_light_in_non-inertial_reference_frames

 

[Zman]

It depends on what one means by "the speed of light".

Is there an interpretation where the "speed of light" in a gravitational field can be said to vary.

All observers measure the speed of light to be c locally but can the speed of light be inferred as having altered at some remote gravitational potential?

 

[A.T.]

Is there an interpretation where the "speed of light" in a gravitational field can be said to vary.

From http://en.wikipedia.org/wiki/Propagation_of_light_in_non-inertial_reference_frames:

In non-inertial frames the local speed of light is also c, but the average speed of light measured over a finite distance may differ from c.

 

[Ich]

Is there an interpretation where the "speed of light" in a gravitational field can be said to vary.

You can work in a weak-field approximation with a flat background, and treat gravitation as a perturbation. You then get g11/g00 (coordinate dx / coordinate dt) different from 1. Interpreting this as a different speed of light, you can calculate e.g. light deflection like you do in an optics problem. That's exactly what Einstein did in his original paper on GR.