Could a massive gravitational field influence the speed of light?

[Edriven]

Could the speed of light be accelerated by a huge gravitational field? For example, we know light doesn't escape a black hole and is strong enough to cause lensing, therefore could it accelerate light if it complimented the light's path?

 

[Janus]

Could the speed of light be accelerated by a huge gravitational field? For example, we know light doesn't escape a black hole and is strong enough to cause lensing, therefore could it accelerate light if it complimented the light's path?

No. As light "falls" in a gravity field it gains energy just like anything thing else like a rock, but unlike the rock which gains that energy in the form of kinetic energy and thus speed, light gains the energy by increasing its frequency and maintaining a constant speed. Light falling into a gravity field blue-shifts and light climbing out red-shifts.

 

[jbriggs444]

No. As light "falls" in a gravity field it gains energy just like anything thing else like a rock, but unlike the rock which gains that energy in the form of kinetic energy and thus speed, light gains the energy by increasing its frequency and maintaining a constant speed. Light falling into a gravity field blue-shifts and light climbing out red-shifts.

Agree. Locally, light always moves at c. But since Edriven speaks of gravitational lensing, he may have in mind a global perspective. From that perspective, light always moves at c, but the length of a path from source to receiver can be shorter going around a gravitational potential well than through the well. In an intuitive (but not properly stated) sense, one might say that high gravitational fields slow light down rather than speeding it up.

 

[Nugatory]

Could the speed of light be accelerated by a huge gravitational field? For example, we know light doesn't escape a black hole and is strong enough to cause lensing, therefore could it accelerate light if it complemented the light's path?

No. There's no acceleration here. The reason light doesn't escape from a black hole is that light always travels in a straight line (actually, a particular kind of straight line called a "light-like geodesic", but we can skip that complexity for now). Inside a black hole all such straight-line paths lead into the central singularity, and none lead outside of the black hole.

Gravitational lensing happens because outside the black hole, there are multiple such straight-line paths from the light source to the observer's eyes. If the paths are of approximately equal length, the light from multiple paths gets to our eyes at the approximately the same time and we see multiple images.

In some situations these paths will not all have the same length, and then the light will take different amounts of time to traverse the different paths. That can lead one to think that because the light took a different amount of time to get from here there, its speed must have been affected by gravity - but that is an illusion. Consider point A on the Earth's equator, and point B 1000 kilometers to the east. My airplane takes two hours to get from A to B, so we conclude that it flies at 500 km/hr. However, if I were to fly west from point A, the journey would take about 80 hours; but we wouldn't conclude from this that the airplane moves at only 12.5 kilometers/hr when it's flying west, we'd conclude that the statement "the straight-line distance between A and B is 1000 kilometers" requires some qualification. Note that we only have this problem because we're dealing with straight lines on a curved surface - in flat space there is only one straight-line path between any two points, so no ambiguity when we speak about the distance between the points.

(Be warned that in the discussion above I am being sloppy casual about the difference between three-dimensional space and four-dimensional space-time. Sometimes there' no substitute for knowing the math).