gravitational lensing and the speed of light

[Nereid]

'Gravitational lensing' is an effect which is predicted by Einstein's Theory of General Relativity. It has been observed, and so far observations match theory to the limits of the observations.

We often read that 'the speed of light (in a vacuum) is constant'. This comes from Special Relativity.

There's another, less-well known, prediction from GR - the Shapiro time-delay (http://www.astro.ucla.edu/~wright/deflection-delay.html). This has also been observed, and the match between observation and theory is as good as the limits of the experiment.

To what extent can the Shapiro time-delay be considered a change in c (in a gravitational field)?

What does GR itself have to say about c?

[peteshimmon]

Dunno but I can certainly speculate from
classical observations of wave propagation in
dense and less dense media. Dense media
gives higher propagation speeds than less
dense. So if c is shown to be less within
a gravitational field than outside it then
some sort of media is made less dense by the
field. Or is this too logical?

[Fr. Wayne]

Time-space curvature preserves the constant.

[Grey]

To what extent can the Shapiro time-delay be considered a change in c (in a gravitational field)?

What does GR itself have to say about c?I believe that in the early stages of developing general relativity, Einstein considered this to be a change in the speed of light. In the final form, this is instead a result of an increased path length through curved spacetime. So light still travels at the same speed, but it has to travel a longer distance.