Was I wrong about this? No one called me out on it.
Quantum Wave, I also was wondering why Przxk and AlphaNumeric did not answer this question of yours; both just skipped it. It is a very good question, and is one of the main tenants of General Relativity.
I do believe like you, that Farsight, got this reversed, and was hoping that he would have corrected this. I happen to like Farsight, because he does have a passion for science, and he does propose different ideas and concepts for others to contemplate, discuss, and debate. This is really good for science and physics in general. I hope that Farsight is not discouraged by AlphaNumeric's "put downs" and keeps up the good work!
Here is my humble attempt to answer your question:
The main difference between Special Relativity (SR) and General Relativity (GR) is that there is a gravitational field associated with (GR) that is not included in (SR).
In Special Relativity Light Speed ($$c_{Light}$$) is Constant relative to all observers; whether the observer is at rest or in uniform motion will measure light speed to be the same to everybody.
The real problem with (SR) is that the conditions of this situation is completely hypothetical, because in the real world, gravity fields are everywhere throughout the universe.
In General Relativity the question now becomes is the speed of light ($$c_{Light}$$) constant in a gravity field just like SR?
Einstein considering this question in his early years (1911) postulated that light speed would vary in a gravitational field. However, four or five years later when Einstein completed his theory of General Relativity(1915 - 1916), this concept was brought into question by very many, because they were converted by Einstein in (1911) to accept light speed as being constant. This concept that light varies, threw many physicist for a loop.
See link:
Speed of Light Varies
Shortly after 1916 and around 1917, physicist came to the conclusion that light is indeed affected by the gravitational field. However, light speed in a gravitational field does not change but what does change for the light is the: Frequency ($$f_{frequency}$$), Wavelength ($$\lambda_{Wavelength}$$), Proper Time ($$\Delta t_{0}$$), and Space ($$r$$).
Ok, so what happens to light in a gravitational field:
1) In a strong gravitational field near the event horizon black hole:
a) The Frequency increases or blue shifts
b) The Wavelength decreases or gets smaller
c) The Proper Time Clock ticks at a slower rate. Meaning that if the normal clock is not in a Gravity field it takes an event ten (10) seconds, then drop that same clock in the strong gravity field that same event could take fifteen (15) seconds.
1) In a weak gravitational field far away from the event horizon black hole:
a) The Frequency decreases or red shifts
b) The Wavelength increases or gets longer
c) The Proper Time Clock ticks at either a faster or normal rate. Meaning that if the normal clock is not in a Gravity field it takes an event ten (10) seconds, then drop that same clock in the weak gravity field that same event could take eleven (11) seconds or event ten (10) seconds as if there were no gravity field present.
Gravitational Redshift
General Red Shift
Let's look at the math:
Where, the Space-time Expansion ratio term is given by:
$$\frac{dS}{dr} = \frac{1}{sqrt{1 - (\frac{r_{S}}{r})}} = \(1 + z_{shift} \) = \frac{\lambda_{observed}}{\lambda_{emitted}} = \frac{f_{emitted}}{f_{observed}}$$ $$ -> unitless $$.
The Red/Blue Shift Parameter:
$$z_{shift} = \frac{\lambda_{observed} - \lambda_{emitted}}{\lambda_{emitted}} = \frac{f_{emitted} - f_{observed}}{f_{observed}}$$ $$ -> unitless $$.
The above Red/Blue Shift Parameter is maximum near the Black Hole Event Horizon and is minimum far far away from the Event Horizon.
Where, the Frequency in a Gravitational Field is given by:
$${f_{emitted}} = \frac{f_{observed}}{sqrt{1 - (\frac{r_{S}}{r})}} = f_{observed} (1 + z_{shift}) $$ $$ -> 1/s $$.
Where, the Wavelength in a Gravitational Field is given by:
$${\lambda_{emitted}} = {\lambda_{observed}}{sqrt{1 - (\frac{r_{S}}{r})}} = \frac{\lambda_{observed}}{\(1 + z_{shift}\)} $$ $$ -> m $$.
The Schwarzschild Radius of the source of the Gravitational Field:
$$r_{S} = \frac{2m_{Net}G}{c^2_{Light}} = \frac{m_{Net}}{\mu_{S}}$$$$ -> m$$
Now let's look at the Clock Time
Let the proper time and distance be given by
$$dr = {c_{Light}}dt_{0}$$ $$ -> m $$.
Let's also return to our original equation and substitute
$${dS} = \frac{dr}{sqrt{1 - (\frac{r_{S}}{r})}}$$ $$ -> m $$.
$${dS} = \frac{c_{Light}dt_{0}}{sqrt{1 - (\frac{r_{S}}{r})}}$$ $$ -> m $$.
Next dividing both sides by the speed of light $$c_{Light}$$
$$dt = \frac{dS}{c_{Light}} = \frac{dt_{0}}{sqrt{1 - (\frac{r_{S}}{r})}}$$ $$ -> s $$.
If you integrate both sides of the above term you can also write.
$$\Delta t = \frac{S}{c_{Light}} = \frac{\Delta t_{0}}{sqrt{1 - (\frac{r_{S}}{r})}}$$ $$ -> s $$.
Where the above equation allows you to predict how a clock behaves in a gravitational field.
This completes the derivation and explanation of light behavior in a gravitational field.