How to Measure Velocity in Curved Space?

It's hard to measure or compare velocities in curved space, because i thinks it cannot get kind of wankey because space time is beeng curved. And so this is all really important because it means that you can't define the difference between those two velocity vectors across curved space. So a photon moving around a black hole could appear to have a velocity not the speed of light as it tries to climb out of that gravity. That means that the rules of special relativity no longer reply.