If gravity can accelerate a photon by bending its trajectory why doesn't it slow down a photon? If gravity can accelerate a photon by bending its trajectory why doesn't it slow down a photon? This looks like magnetism effects on particles(changes direction but not magnitude of the velocity) ...
 A: Because it's an experimentally verified fact that the speed of light is constant whether it is bending or not.
In ordinary speech, to accelerate means to increase your speed. In physics, acceleration is the rate of change of velocity. Now velocity is a normed vector and hence has both a magnitude and a direction. So in acceleration, both the magnitude and direction can change.
When light accelerates, its magnitude remains constant but its direction can change.
A: Gravity does change the energy of photons, and it can both increase or decrease that energy depending whether the photon is going in or out of the gravitational well. That's called gravitational red- or blue shift. Of course photons still always travel at the speed of light.
A: In everyday language "accelerate" implies making the photons go faster, but in physics parlance, it suffices to change the direction. In other words, if you change the direction but not the magnitude of a velocity, you still have an acceleration, but the object neither speeds up nor slows down.
That's what gravity does with photons - it can accelerate photons, but not speed it up nor slow it down.
