system
Given the following post, respond as if you're commenting on Reddit:
human
Can photons move slower than the speed of light when near a black hole?

We know photons always move at the speed of light. 

However my theory is that when a black hole is made there is a point where 1 photon is still going away from the black hole and the other one will be sucked in by the black hole. So the last photon was moving away from the black hole but the force of gravity massively increases and the photon will be forced to go in the direction of the black hole. 

What if all forces on that photon pull it the exact same amount which means there is no side besides up or down to which the photon can move. The black hole pulls harder than the rest of the sides of the photon which means the photon can't bend in any direction. The photon will then be forced to slow down to 0 and then ramp up again to the speed of ligh towards the black hole.

I hope you can understand me as this is quite hard to explain for me since i'm not natively english.
gpt
The **local** speed of a massless particle is always c. So if you're observing the motion of a photon from very close by, you'll always see it moving at c.

However if you're watching the photon move from far away in curved spacetime, the rate at which its position changes in *your* coordinate system doesn't have to be c.

The classic example is the speed of a photon moving radially near a Schwarzschild black hole.

It's speed in the Schwarzschild coordinates of an observer at infinity is:

dr/dt = (1 - 2GM/rc^(2))c,

where G is the gravitational constant, M is the mass of the black hole, r is the radial coordinate, t is the Schwarzschild time coordinate, and c is the speed of light.

You can see that as r goes to infinity, dr/dt goes to c. But as r goes to 2GM/c^(2) (the event horizon of the black hole), the speed goes to zero.

So an outside observer will never see an inwardly-traveling photon cross the horizon of the black hole.

A similar calculation can be done for a photon moving in the azimuthal direction rather than the radial direction.

So yes, a photon will move slower near a black hole if you watch it from far away.