# Red shift frequency from a black hole

Tyro
Can someone tell me if these statements are right/wrong, and if wrong, why they are wrong?

Lets say you have a light (or more generally, EM) source a distance r from a black hole's core, with r > event horizon radius.

As you move closer towards the black hole, since the energy of a photon = hf, with h = constant, and the gravitational PE varies as 1/r...therefore the frequency fall due to red shifting falls as 1/r as well.

I get this equation relating the frequencies at 2 points and the radius from the black hole: (f1 - f2)/(f1 + f2) = GM(1/r1 - 1/r2)

If the above are true, then the event horizon for different frequencies of light varies. High frequency EM radiation will have a larger event horizon than low frequency EM radiation.

AFAIK, the event horizon is a fixed distance for light...

Am I looking at the problem too "classically"?

Ambitwistor
This is more a general relativity question than an astronomy question ...

Originally posted by Tyro
As you move closer towards the black hole, since the energy of a photon = hf, with h = constant, and the gravitational PE varies as 1/r...therefore the frequency fall due to red shifting falls as 1/r as well.

There isn't really "gravitational potential energy" in general relativity.

I get this equation relating the frequencies at 2 points and the radius from the black hole: (f1 - f2)/(f1 + f2) = GM(1/r1 - 1/r2)

You're using Newtonian gravity to do these calculations. The correct relativistic equation is: