How gravity time dilation affect radio wave communication? I'm not in any way an expert so sorry if my question is silly.
So i was wondering about a hypothetical situation. I'm orbiting a black hole and I'm trying to contact via radio with someone outside the gravitational effect of that black hole. As far I understand the radio wave similarly to light can be bent but cannot be slowed down by gravity. So is the communication possible? How would time dilation due to black hole gravity affect my attempt to communicate?
Regards
Sebastian
 A: As long as you remain outside the black hole, you can send messages by radio signal to distant receivers.  You will have to contend with some challenges, however, that are purely relativistic.  First, your signal will shift frequency as it moves away from the black hole, so you'll need to compensate for that when you send or your receiving party will have to understand this is happening and have their receiver tuned to the frequency that they will observer (rather than the one that you sent).  Second, it may take a loooong time for your signal to travel with the limit that, if you're just outside at the event horizon, it will take essentially infinitely long, as counted by the receiving party, for your signal to arrive.
A: Simply put, if you are outside the event horizon, transmitting data by radio to someone farther from the black hole, there would be two main obstacles. While the transmission would move at the same speed as light, the frequency would be received more stretched out, redshifted, than what you sent. So the receiver would have to allow for the frequency shift. Also since you would experience different time dilation, the data received would have to be recorded, then sped up for the receivers to experience it in real time for their frame.
A: First of all let's make the situation more concrete. The effect of gravity extends to infinity, although it drops off as a factor of $(\sim \frac{1}{r^2})$ according to Newtonian mechanics(which suffices in terms of building our intuition here). When you are just outside the event horizon of the black hole, all the signals you send can eventually reach any observer who is not him/herself inside a black hole. A radio wave travels at the speed of light in vacuum so in your example it would be the same as sending a beam of light.
Let's think about the signal just outside the event horizon and somewhere far away from there. Because of the gravitational well, the clock of the source of the beam will run slower than the clock at the receiving end of the signal. This creates a shift in the signal as it passes through space. This is what creates a redshift in the signal.
For a Schwarzschild black hole, the frequency difference is given by the formula $$
\frac{\lambda_{\infty}}{\lambda_{e}}=\left(1-\frac{r_S}{R}\right)^{-\frac{1}{2}}
$$
Where $\lambda_{\infty}$ the wavelength far away from the black hole,$\lambda_e$ the wavelength of the emitted wave, $r_S$ the radius of the black hole and $R$ the distance from the centre of the black hole.
