Undergrad Sending Signal from Planet Near Gargantua: A Thought Experiment

[kccrossen]

TL;DR

A discussion on the scenes of Interstellar, If a radio signal were to be sent from the planet near Gargantua to the space craft where Romilly was working on his theory what would happen.

The other day my friend asked me a really interesting question regarding the scene from interstellar where they go down to Miller's planet, where every hour on this planet is 7 years of Earth time. He asked me if they were to send a signal to the spaceship where Romilly was, what would happen.

My thought process was that any information travels at the speed of light, we know this, but would the signal be delayed, as spacetime is stretching apart? The speed of light itself doesn't change but the light is taking longer to get to him as space is being stretched between them. Is this a correct thought or am I just making up things?

Also wouldn't it depend on how close Romilly was to the planet? and how close the planet was to the black hole? If he were to get the signal, would the astronauts just talk extremely slowly, almost too slow to tell what they are saying since the time dilation is so large? I haven't taken general relativity, only special so I am just asking out of curiosity. Its a cool thought experiment. Let me know your thoughts.

 

[A.T.]

but would the signal be delayed, as spacetime is stretching apart?

https://en.wikipedia.org/wiki/Shapiro_time_delay

 

[PeterDonis]

spacetime is stretching apart?

No, it isn't. First, spacetime doesn't change, it just is; it's a 4-dimensional geometry that already contains within it all the information about how things "change" with "time". It doesn't have to change at all.

Second, Kerr spacetime, which is the spacetime around a rotating black hole, is stationary, so even pop science descriptions that apply to, say, models of the expanding universe and talk about "space expanding" do not apply to Kerr spacetime. "Stationary" means that, from the standpoint of observers orbiting in the spacetime around Gargantua, nothing about the black hole itself or the space around it "changes" with "time".

The speed of light itself doesn't change but the light is taking longer to get to him as space is being stretched between them.

Why do you think "space is being stretched" in this scenario?

 

[lomidrevo]

Summary:: A discussion on the scenes of Interstellar, If a radio signal were to be sent from the planet near Gargantua to the spacecraft where Romilly was working on his theory what would happen.

Any such signal would be also redshifted:
https://en.m.wikipedia.org/wiki/Gravitational_redshift