Except right at the boundary of the event horizon which is the Hawking radiation. Photons that somehow get started near this boundary, but outside of it, will get Red Shifted, but the red shift is small except very close to the event horizon.

Using General Relativity, a theory that has no gravitational field, only geometric distortion of space, the event horizon is where space is being swallowed up by the black hole at the speed of light. Outside the event horizon, the red shift is due to the inward velocity of space. From observations of galaxies and the motion of their stars, the inward component of space velocity is only significant very close to the event horizon, and does not extend out to infinity.