Thinking about gravitational RedShift

There are at least two ways of calculating and three ways of thinking about
gravitational redshift.

Consider a massive body, say a planet sized non-rotating spherical body. We
have a space observer that can measure a beam of light emitted from the
massive body.

The beam of light emitted from the surface of the planet will have a lower
measured frequency and a correspondingly longer wavelength as measured by
the space observer.

We can think of this as:
1) a clock on the surface of the massive object runs slower than a clock the
space observer may have. Any measure of frequency is done against a clock
(directly or indirectly) and so the frequency of the wave will be lower. We
assume that neither the space observer or planet observer notice anything
unusual about their respective clocks (local time does not seem to be
running faster/slower) so the lower frequency of the light beam will appear
red shifted if in the visible range.

2) As spacetime around the planet is curved, the light beam is
correspondingly stretched as it passes over the expanded spacetime. Thus
the wavelength of the light will be longer as measured by the space
observer.

3) As gravity exerts a force on all objects moving away from the gravitating
body, objects require a force to move (ie to accelerate away from the
gravitating body). Photons lose energy as they move away from a gravitating
body. A loss of energy of a photon corresponds to a lower frequency and
longer wavelength of a light beam.

When discussing light attempting to escape from a black hole, we hear
explanations corresponding to (2) and (3) but not (1). Why?

Let us consider a simple test of the three mentioned above.

Clocks on the surface of the sphere and in space are partially synchronised
in the following way: A signal is sent from the planet based clock at 12:00
exactly (to the highest available precision). The space based clock is
zeroed to 12:00 exactly when the light beam reaches it. The planet clock
sends a second signal after 100 hours exactly. The space based clock stops
upon receipt of the signal.

If the only cause of redshift is the loss of energy of photons or the
stretching of wavelength, as in (2) and (3), then the space based clock will
stop exactly 100 hours after it starts. If the planet based clock is
actually running slower then more than 100 hours will be measured by the
space based clock.

It is my understanding that clocks near massive bodies do in fact run slower
in a measurable way and that atomic clocks at higher altitude on Earth
require periodic adjustment due to their faster pace as compared to sea
level clocks.

If this is correct then (2) and (3) are only valid for instantaneous
measurements, ie snapshots of space-time. As there are three ways of
looking at redshift, any theory of redshift and its causative agent should
also account for (1) eg the non-emission of light from black holes (clocks
on the surface of the Black Hole must be actually and physically frozen
relative to a space observer) and the redshift of the objects at great
distances (if the stretching of space time is offered in the form of (2) ie
light stretched as it passes over expanding space-time).


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Kind Regards
Robert Karl Stonjek