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:

f₂/f₁ = √[(1-2GM/(c²r₁))/(1-2GM/(c²r₂))]

If the above are true, then the event horizon for different frequencies of light varies.

The location of the event horizon is independent of the frequency of light.

 

[VantagePoint72]

Another way of looking at the event horizon is looking at how spacetime curves once you go past it. An escape velocity of c, according to GR, denotes such an extreme curvature of spacetime that it literally doubles back on itself. So, it doesn't matter what the light's frequency is, beyond the event horizon nothing can escape the curvature of spacetime.