Light from a person falling into a black hole getting dimmer I have read that to an observer at rest outside a black hole, they will see the light from the free faller get redshifted and dimmer.  What is the mathematical explanation for the light actually getting dimmer?
 A: Suppose I am a long way from a black hole watching you are hovering near the event horizon, then your time is dilated with respect to mine. I won't go into the details since lots of questions hereabouts involve this calculation. I'll just mention the result:
$$ \frac{d\tau}{dt} = \sqrt{1 - \frac{2GM}{c^2r}} \tag{1} $$
In this equation $d\tau$ is the number of seconds you measure while $dt$ is the number of seconds I measure, and $r$ is your distance from the black hole.
Suppose you are emitting EM radiation with a frequency on one hertz i.e. one cycle per second. One of you seconds corresponds to more than one second of my time. Using equation (1) we find the time I measure corresponding to your one second is:
$$ \Delta t = \frac{1}{\sqrt{1 - \frac{2GM}{c^2r}}} $$
For me the one cycle of EM radiation you emit every second lasts for $\Delta t$ seconds, so the period has increased and therefore the original 1 Hertz frequency has decreased to:
$$ \nu = \sqrt{1 - \frac{2GM}{c^2r}} $$
which is less than one so the radiation I receive has been red shifted. I used the example of 1Hz radiation to make the calculating simple. More generally, if you emit radiation with a frquency $\nu_0$ the frequency I observe is:
$$ \nu = \nu_0 \sqrt{1 - \frac{2GM}{c^2r}} $$
A: It is not dimmer in the sense that one photon is dimmer after climbing out of the gravitational well of the black hole. It is dimmer in the sense that fewer photons arrive per second.
A: A black hole's gravity has so much force that light doesn't have enough speed to escape the gravitational pull being emitted by the black hole. 
A: Assuming you are stationary with respect to the black hole, the light source appears dimmer due to the fact that the distance between you and it is increasing. This is described by the the equation for luminous intensity.
see https://en.wikipedia.org/wiki/Intensity_(physics)
