gravity - Does light accelerate as it nears a black hole?

As light is affected by gravity ( gravitational lending and black holes), it would seem that gravity causes acceleration.

Acceleration has two parts: direction and magnitude. It is clearly evident that gravity affects the former of the two. It would seem that it does not affect the later component because light is currently at the universal 'speed limit' (not counting taychons).

What is going on here? Is the magnitude component affected by gravity?

Answer

Light always travels at the same speed. What happens as photons move through changes in gravitational potential is that they gain and lose energy, which manifests itself as red shift or blue shift.

In the specific case of light moving towards a black hole, where an object with a rest mass would gain kinetic energy as it fell, a photon is blue-shifted, carrying more energy (and momentum) for each photon - in classical terms, the light is shifted to a higher frequency i.e. a shorter wavelength.

For the reverse situation, light coming from deep within a potential well to an observer far away, the light is red shifted to a lower frequency (higher wavelength), with lower energy per photon.