# I Radio communication between two points at different gravity

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1. Jul 5, 2016

### Hongo

A source that is orbiting close to a singularity of a black hole is transmitting a radio frequency signal that lasts 60 seconds and is repeated infinitely. The signal is being transmitted using the amplitude modulation method (AM Radio). Let suppose that each minute passing in the transmitting source location is equivalent to 100 minutes for the receiver, and that the distance between the transmitter and receiver is time invariant. For this situation to be consistent, it must mean that the electromagnetic wave is stretched. Therefore, if the original signal was modulated on a 1000 kHz electromagnetic wave, the wave received must be of 10 kHz. That would be a similar effect as a doppler effect but the shift of the frequency is produced by gravity instead of the velocity. Is this statement true? Would this mean also that the frequency of a source of light will different depending on the curvature of space-time in the location of the source and the observer? My field is Chemistry so I am sorry in advance for my lack of expertise in General Relativity.

2. Jul 5, 2016

3. Jul 5, 2016

### Jorrie

I guess you meant to write "orbiting close to the event horizon of a black hole"?
Yes, but it is not good to view it as "stretched waves", because it tends to conjure up images of 'expanding space' between the source and receiver, which can be very confusing. It is simply gravitational (and velocity) time dilation due to speed and gravitational potential differences between the source and receiver.
If you ignore any relative orbital speeds between source and receiver, the frequency ratio is
$$\frac{f_r}{f_s}= \frac{\sqrt{1-2GM/r_s c^2}}{\sqrt{1-2GM/r_r c^2}}$$
where the subscripts indicate source and receiver and r are the orbital radii.

4. Jul 5, 2016

### pervect

Staff Emeritus
Essentially, yes. Though I'd change "orbiting" to "hovering" - unless you have a rapidly spinning black hole like the one Kip Thorne imagined in "Interstellar", you won't get a stable orbit with that sort of time dilation, and keeping the distance / propagation delay to the receiver time invariant is easier, too.