Electromagnetic Waves frequency

Question

Does Gravity affect the frequency of an electromagnetic wave? If so, does it increases or decreases it? Please explain me. Thank you!

Answer 1

If we describe a plane-wave (or a single photon) by its wave vector:

$$ k^{\mu} = (\omega/c, \vec k) $$

what pops out is that the frequency is the time-like part of a 4-vector. We can look at energy and momentum:

$$ p^{\mu} = \hbar k^{\mu} = (E/c, \vec p) $$

to try to find a natural rest frame:

$$ p^{\mu}p_{\mu} = \frac 1 {c^2}[(E)^2-||p||^2c^2] = \frac {\hbar^2} {c^2}[\omega^2 - (ck)^2] = 0 $$

so that there is no rest frame.

Energy is a property of the observer's frame, not the wave. The wave just goes at $c$, locally.